An Overview of Hesitant Fuzzy Linguistic Term Set Applications in Supply Chain Management: The State of the Art and Future Directions

2. HFLTSs and HFLTS Extensions

Ever since it was proposed by Professor Lofti Zadeh [23], Fuzzy Set Theory has been applied successfully to various problems which involve imprecise, vague, and imperfect information [14,24]. This theory is also the foundation of new approaches to deal with decision-making problems under conditions of uncertainty. These approaches are based on various forms of representing information which are used by DMs to express their preferences [16,25].

Based on Fuzzy Set Theory, Torra [26] proposed Hesitant Fuzzy Set Theory, which provides a framework for supporting DMs in situations in which there are a set of possible values to define the membership of an element. Based on the work of Torra [26], Rodríguez et al. [14] proposed HFLTS, which differ from previous approaches because they allow DMs to use more than one linguistic term and complex linguistic expressions to represent their preferences. In this manner, HFLTSs offer greater flexibility in eliciting linguistic preferences and at the same time support expressions that are closer to natural language [27].

Considering a set of defined linguistic terms such as $S=\left\{{\mathrm{s}}_{-\mathsf{\tau }},\cdots ,{\mathrm{s}}_0,\cdots ,{\mathrm{s}}_{\mathsf{\tau }}\right\}=\left\{{\mathrm{s}}_{-2}:\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{y}\mathrm{l}\mathrm{o}\mathrm{w},{\mathrm{s}}_{-1}:\mathrm{l}\mathrm{o}\mathrm{w},{\mathrm{s}}_0:\mathrm{m}\mathrm{e}\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{m},{\mathrm{s}}_1:\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h},{\mathrm{s}}_2:\mathrm{v}\mathrm{e}\mathrm{r}\mathrm{y}\mathrm{h}\mathrm{i}\mathrm{g}\mathrm{h}\right\}$, an HFLTS defined as 𝐻_𝑆(𝜗)=$\left\{{\mathrm{s}}_{\mathrm{i}}|{\mathrm{s}}_{\mathrm{i}}\in \mathrm{S}\right\}$ consists of a finite ordered subset of linguistic terms of S. Thus, 𝐻_𝑆(𝜗)= {${\mathrm{s}}_{-2}:$very low, ${\mathrm{s}}_{-1}$:low} and 𝐻_𝑆(𝜗)= {${\mathrm{s}}_{-1}:$low, ${\mathrm{s}}_0$:medium, ${\mathrm{s}}_1$:high} are examples of HFLTS. Any other HFLTS consists of at least one of the linguistic terms in S [14]. The HFLTS approach makes it possible for DMs to use linguistic expressions that employ more than one linguistic term simultaneously in each judgement. Examples of linguistic expressions include “between very low and low" {${\mathrm{s}}_{-2}, {\mathrm{s}}_{-1}$}, “at least high” {${\mathrm{s}}_1, {\mathrm{s}}_2$}, “at most medium” {${\mathrm{s}}_{-2}, {\mathrm{s}}_{-1}, {\mathrm{s}}_0$}, and “lower than high” {${\mathrm{s}}_2$} } [8,27]..

Based on the pioneering work of Rodríguez et al. [14], other authors proposed new operators for HFLTSs [28,29,30], measures of distance and similarity [31,32], techniques that support group decision making [18,19], and consistency and consensus methods for group decision making [33], among other advances. Extensions for HFLTSs also appeared, which opened new possibilities for modeling uncertainty in decision-making processes. Table 1 presents examples of the main HFLTS extensions which are described below:

Table 1. Summary of HFLTS extensions.

ID	Approaches	Author(s)	Mathematical representation	Example
i.	EHFLTS	Wang [15]	$\left\{{\mathrm{s}}_{\mathrm{i}}|{\mathrm{s}}_{\mathrm{i}}\in \mathrm{S}\right\}$	$\left\{{\mathrm{s}}_2,{\mathrm{s}}_4,{\mathrm{s}}_5\right\}$
ii.	HIFLTS	Beg and Rashid [18]	$\left\{〈\mathrm{x},\mathrm{h}\left(\mathrm{x}\right),{\mathrm{h}}^{\mathrm{\text{'}}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$〈\left({\mathrm{s}}_1,{\mathrm{s}}_2,{\mathrm{s}}_3\left)\right({\mathrm{s}}_3,{\mathrm{s}}_4\right)〉$
iii.	IVHFLS	Wang et al. [34]	$\left\{〈\mathrm{x},{\mathrm{s}}_{\mathrm{Ѳ}\left(\mathrm{x}\right)},{\mathrm{Ґ}}_{\mathrm{A}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$〈{\mathrm{s}}_5,\left\{\right[0.4,0.5],[0.6,0.7\left]\right\}〉$
iv.	PHFLTS	Chen et al. [16]	$\left\{\left({\mathrm{s}}_{\mathrm{i}},{\mathrm{p}}_{\mathrm{i}}\right)|{\mathrm{s}}_{\mathrm{i}}\in \mathrm{S},\mathrm{i}=\mathrm{0,1},\dots ,\mathrm{g}\right\}$	$\left\{{(\mathrm{s}}_4,0.2),{(\mathrm{s}}_6,0.6)\right\}$
v.	PLTS	Pang et al. [35]	$\left\{{\mathrm{L}}^{\left(\mathrm{k}\right)}\left({\mathrm{p}}^{\left(\mathrm{k}\right)}\right)|{\mathrm{L}}^{\left(\mathrm{k}\right)}\in \mathrm{S},{\mathrm{p}}^{\left(\mathrm{k}\right)}\ge 0,\mathrm{k}=\mathrm{1,2},\dots ,\#\mathrm{L}\left(\mathrm{p}\right),\sum _{\mathrm{k}=1}^{\#\mathrm{L}\left(\mathrm{p}\right)}\mathrm{p}\right\}$	$\left\{{\mathrm{s}}_4\left(0.1\right),{\mathrm{s}}_5\left(0.65\right),{\mathrm{s}}_6\left(0.2\right)\right\}$
vi.	IVDHFLTS	Qi et al. [36]	$\left\{〈\mathrm{x},{\mathrm{s}}_{\mathrm{Ѳ}\left(\mathrm{x}\right)},\tilde{\mathrm{h}}\left(\mathrm{x}\right),\tilde{\mathrm{g}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$\left\{{\mathrm{s}}_3\left\{\right[0.4,0.4],[0.5,0.5\left]\right\},\left\{\right[0.3,0.3],[0.4,0.4\left]\right\}\right\}$
vii.	MHFLTS	Wang et al. [37]	$\left\{〈\mathrm{x},{\mathrm{h}}_{\mathrm{M}\mathrm{S}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$\left\{{\mathrm{s}}_1,{\mathrm{s}}_3,{\mathrm{s}}_{54}\right\}$
viii.	DHHFLTS	Gou et al. [38]	$S_o=\left\{S_{t<o_k>}|t=-\tau ,\dots ,-\mathrm{1,0},1,\dots ,\tau ; k=-\varsigma ,\dots ,-1, 0, 1,\dots ,\varsigma \right\}$	{${\mathrm{s}}_{2<{\mathrm{o}}_1>,}{\mathrm{s}}_{3<{\mathrm{o}}_0>}$}
ix.	HF2DLTS	Liu et al. [39]	$\left\{〈\mathrm{x},{\widehat{\mathrm{h}}}_{\mathrm{S}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$\left\{{(\dot{{\mathrm{s}}_3},\ddot{\mathrm{s}}}_4),{(\dot{{\mathrm{s}}_4},\ddot{\mathrm{s}}}_4),{(\dot{{\mathrm{s}}_5},\ddot{\mathrm{s}}}_3)\right\}$
x.	PHILTS	Malik et al. [25]	$\left\{〈\mathrm{x},\mathrm{l}\left(\mathrm{x}\right)\mathrm{p}\left(\mathrm{x}\right),{\mathrm{l}}^{\mathrm{\text{'}}}\left(\mathrm{x}\right){\mathrm{p}}^{\mathrm{\text{'}}}\left(\mathrm{x}\right)〉|{\mathrm{s}}_{\mathrm{i}}\in \mathrm{S}\right\}$	$\left\{{\mathrm{s}}_2\left(0.4\right),{\mathrm{s}}_3\left(0.1\right),{\mathrm{s}}_4\left(0.35\right)\right\},\left\{{\mathrm{s}}_4\left(0.3\right),{\mathrm{s}}_5\left(0.4\right)\right\}$
xi.	IV2THFLTS	Si et al. [17]	$\left\{〈\mathrm{x},{\mathrm{h}}_{\mathrm{s}}\left(\mathrm{x}\right),\widetilde{{\mathrm{I}}_{\mathrm{A}}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$〈\left\{{\mathrm{s}}_3,{\mathrm{s}}_4\right\},\left[0.7,0.8\right]〉$
xii.	DHFLTS	Zhang et al. [40]	$\left\{〈{\mathrm{x}}_{\mathrm{i}},{\mathrm{H}}_{\mathrm{s}}\left({\mathrm{x}}_{\mathrm{i}}\right),{\mathrm{h}}_{\mathrm{s}}\left({\mathrm{x}}_{\mathrm{i}}\right),{\mathrm{g}}_{\mathrm{s}}\left({\mathrm{x}}_{\mathrm{i}}\right)〉|{\mathrm{x}}_{\mathrm{i}}\in \mathrm{X}\right\}$	$\left\{{\mathrm{s}}_2\{0.7,0.5,0.3\}\{0.3,0.2\},{\mathrm{s}}_3\{0.6,0.4\}\{0.4,0.2\}\right\}$
xiii.	HPFLTS	Yang et al. [41]	$\left\{〈\left(s_i^k\right),\left({\mu }_i^k,{\eta }_i^k,{\nu }_i^k\right)〉|\mathrm{i}\in \mathrm{x}\left(\mathrm{0,1},\dots ,\mathrm{m}\right);\mathrm{k}=\mathrm{1,2},\dots ,\mathrm{ɑ}\right\}$	$\left\{{(\mathrm{s}}_2,(0.7,0,0)\right\}$

Table 1. Summary of HFLTS extensions.

ID	Approaches	Author(s)	Mathematical representation	Example
i.	EHFLTS	Wang [15]	$\left\{{\mathrm{s}}_{\mathrm{i}}|{\mathrm{s}}_{\mathrm{i}}\in \mathrm{S}\right\}$	$\left\{{\mathrm{s}}_2,{\mathrm{s}}_4,{\mathrm{s}}_5\right\}$
ii.	HIFLTS	Beg and Rashid [18]	$\left\{〈\mathrm{x},\mathrm{h}\left(\mathrm{x}\right),{\mathrm{h}}^{\mathrm{\text{'}}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$〈\left({\mathrm{s}}_1,{\mathrm{s}}_2,{\mathrm{s}}_3\left)\right({\mathrm{s}}_3,{\mathrm{s}}_4\right)〉$
iii.	IVHFLS	Wang et al. [34]	$\left\{〈\mathrm{x},{\mathrm{s}}_{\mathrm{Ѳ}\left(\mathrm{x}\right)},{\mathrm{Ґ}}_{\mathrm{A}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$〈{\mathrm{s}}_5,\left\{\right[0.4,0.5],[0.6,0.7\left]\right\}〉$
iv.	PHFLTS	Chen et al. [16]	$\left\{\left({\mathrm{s}}_{\mathrm{i}},{\mathrm{p}}_{\mathrm{i}}\right)|{\mathrm{s}}_{\mathrm{i}}\in \mathrm{S},\mathrm{i}=\mathrm{0,1},\dots ,\mathrm{g}\right\}$	$\left\{{(\mathrm{s}}_4,0.2),{(\mathrm{s}}_6,0.6)\right\}$
v.	PLTS	Pang et al. [35]	$\left\{{\mathrm{L}}^{\left(\mathrm{k}\right)}\left({\mathrm{p}}^{\left(\mathrm{k}\right)}\right)|{\mathrm{L}}^{\left(\mathrm{k}\right)}\in \mathrm{S},{\mathrm{p}}^{\left(\mathrm{k}\right)}\ge 0,\mathrm{k}=\mathrm{1,2},\dots ,\#\mathrm{L}\left(\mathrm{p}\right),\sum _{\mathrm{k}=1}^{\#\mathrm{L}\left(\mathrm{p}\right)}\mathrm{p}\right\}$	$\left\{{\mathrm{s}}_4\left(0.1\right),{\mathrm{s}}_5\left(0.65\right),{\mathrm{s}}_6\left(0.2\right)\right\}$
vi.	IVDHFLTS	Qi et al. [36]	$\left\{〈\mathrm{x},{\mathrm{s}}_{\mathrm{Ѳ}\left(\mathrm{x}\right)},\tilde{\mathrm{h}}\left(\mathrm{x}\right),\tilde{\mathrm{g}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$\left\{{\mathrm{s}}_3\left\{\right[0.4,0.4],[0.5,0.5\left]\right\},\left\{\right[0.3,0.3],[0.4,0.4\left]\right\}\right\}$
vii.	MHFLTS	Wang et al. [37]	$\left\{〈\mathrm{x},{\mathrm{h}}_{\mathrm{M}\mathrm{S}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$\left\{{\mathrm{s}}_1,{\mathrm{s}}_3,{\mathrm{s}}_{54}\right\}$
viii.	DHHFLTS	Gou et al. [38]	$S_o=\left\{S_{t<o_k>}|t=-\tau ,\dots ,-\mathrm{1,0},1,\dots ,\tau ; k=-\varsigma ,\dots ,-1, 0, 1,\dots ,\varsigma \right\}$	{${\mathrm{s}}_{2<{\mathrm{o}}_1>,}{\mathrm{s}}_{3<{\mathrm{o}}_0>}$}
ix.	HF2DLTS	Liu et al. [39]	$\left\{〈\mathrm{x},{\widehat{\mathrm{h}}}_{\mathrm{S}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$\left\{{(\dot{{\mathrm{s}}_3},\ddot{\mathrm{s}}}_4),{(\dot{{\mathrm{s}}_4},\ddot{\mathrm{s}}}_4),{(\dot{{\mathrm{s}}_5},\ddot{\mathrm{s}}}_3)\right\}$
x.	PHILTS	Malik et al. [25]	$\left\{〈\mathrm{x},\mathrm{l}\left(\mathrm{x}\right)\mathrm{p}\left(\mathrm{x}\right),{\mathrm{l}}^{\mathrm{\text{'}}}\left(\mathrm{x}\right){\mathrm{p}}^{\mathrm{\text{'}}}\left(\mathrm{x}\right)〉|{\mathrm{s}}_{\mathrm{i}}\in \mathrm{S}\right\}$	$\left\{{\mathrm{s}}_2\left(0.4\right),{\mathrm{s}}_3\left(0.1\right),{\mathrm{s}}_4\left(0.35\right)\right\},\left\{{\mathrm{s}}_4\left(0.3\right),{\mathrm{s}}_5\left(0.4\right)\right\}$
xi.	IV2THFLTS	Si et al. [17]	$\left\{〈\mathrm{x},{\mathrm{h}}_{\mathrm{s}}\left(\mathrm{x}\right),\widetilde{{\mathrm{I}}_{\mathrm{A}}}\left(\mathrm{x}\right)〉|\mathrm{x}\in \mathrm{X}\right\}$	$〈\left\{{\mathrm{s}}_3,{\mathrm{s}}_4\right\},\left[0.7,0.8\right]〉$
xii.	DHFLTS	Zhang et al. [40]	$\left\{〈{\mathrm{x}}_{\mathrm{i}},{\mathrm{H}}_{\mathrm{s}}\left({\mathrm{x}}_{\mathrm{i}}\right),{\mathrm{h}}_{\mathrm{s}}\left({\mathrm{x}}_{\mathrm{i}}\right),{\mathrm{g}}_{\mathrm{s}}\left({\mathrm{x}}_{\mathrm{i}}\right)〉|{\mathrm{x}}_{\mathrm{i}}\in \mathrm{X}\right\}$	$\left\{{\mathrm{s}}_2\{0.7,0.5,0.3\}\{0.3,0.2\},{\mathrm{s}}_3\{0.6,0.4\}\{0.4,0.2\}\right\}$
xiii.	HPFLTS	Yang et al. [41]	$\left\{〈\left(s_i^k\right),\left({\mu }_i^k,{\eta }_i^k,{\nu }_i^k\right)〉|\mathrm{i}\in \mathrm{x}\left(\mathrm{0,1},\dots ,\mathrm{m}\right);\mathrm{k}=\mathrm{1,2},\dots ,\mathrm{ɑ}\right\}$	$\left\{{(\mathrm{s}}_2,(0.7,0,0)\right\}$

• Extended HFLTS (EHFLTS): makes it possible to create sets of non-consecutive ordered terms based on a combination of HFTLS data for a group of DMs. The values are computed as a function of the possible terms in each group [15]. An EHFLTS can be especially useful in situations in which the DMs are divided into subgroups, and there is no consensus among the DMs which therefore leads to the need to represent evaluations in non-consecutive terms [42];
• Hesitant Intuitionistic Fuzzy Linguistic Term Set (HIFLTS): this approach deals with situations in which the DMs evaluate each alternative using a possible linguistic interval and an impossible linguistic interval. Each HIFLTS is composed of the functions h and h’ which return finite ordered subsets of consecutive linguistic terms. h(x) and h’(x) indicate the respective possible membership degrees and non-membership degrees of element x and an HIFLTS [18]
• Interval-Valued Hesitant Fuzzy Linguistic Set (IVHFLS): is an HFLTS extension based on Interval-Valued HFSs. IVHFLSs incorporate the possible interval-valued membership degrees that an alternative has in relation to a linguistic term. These membership degrees are quantified by finite numbers of closed intervals which are defined in (0, 1] [34]
• Proportional HFLTS (PHFLTS): is formed by the union of the HFLTSs that correspond to the individual assessments of the DMs, which can contain consecutive or non-consecutive linguistic terms. This approach is different, because it takes into account proportional information for each generalized linguistic term. Each linguistic term which makes up an PHFLTS is associated with a $p_l$ value, which denotes the degree of possibility that the alternative carries an assessment value $s_l$ provided by a group of DMs [16]. The values are computed as a function of the terms and values of $p_l$;
• Probabilistic Linguistic Term Set (PLTS): this approach adds probability distributions to an HFLTS in order to prevent the loss of any linguistic information provided by the DMs. Thus, PLTSs allow DMs to attribute possible linguistic values to an alternative or criterion at the same time that they reflect the probabilistic information of a group of attributed values. In each PLTS, $L\left(k\right)\left(p\left(k\right)\right)$ is made up of the linguistic term $L\left(k\right)$ which is associated with the probability $p\left(k\right)$, and # $L\left(p\right)$ is the total number of different linguistic terms in $L\left(p\right)$ [35];
• Interval-Valued Dual Hesitant Fuzzy Linguistic Set (IVDHFLTS): considers a function for the possible membership degrees and another function for the possible degrees which do not belong to the $s_{Ѳ\left(x\right)}$ terms selected by the DMs. $\tilde{h}$(x) is a set of closed interval values defined in [0,1], which denote the possible membership degrees of $s_{Ѳ\left(x\right)}$; $\tilde{g}$(x) is a set of closed interval values defined in [0,1] which represent the possible non-membership degrees [36];
• Multi-Hesitant Fuzzy Linguistic Term Set (MHFLTS): is an extension based on HFLTS and HFL elements, in which each set can contain repeated and non-consecutive linguistic terms. Considering the sets of terms $\widehat{S}=\left\{{\mathrm{s}}_{\mathrm{k}}|k\in [0,\mathrm{l}]\right\}$ and X as the reference set, an MHFLTS in X is represented by a function ${\mathrm{H}}_{\mathrm{M}\mathrm{S}}$ which generates a finite ordered multi-subset of $\widehat{S}$. $H_{MS}\left(x\right)$ indicates the possible membership degrees of element x in X [37];
• Double Hierarchy Hesitant Fuzzy Linguistic Term Set (DHHFLTS): is composed of two independent hierarchies of linguistic terms. Considering ${S=\{s}_t | t=-\tau ,\dots ,-\mathrm{1,0},1,\dots ,\tau \}$ as the first hierarchy and $O=\left\{o_k \right| k=-\varsigma ,\dots ,-1, 0, 1,\dots ,\varsigma \}$ as the second, $s_{t<0_k>}$ is defined as a DHHFLTS in which $o_k$ is the second term of the hierarchy when the first term is $s_t$. The use of this approach makes it possible for DMs to use expressions such as “very very good”, “medium or just right”, and “medium or between a little bad and very bad” [38];
• Hesitant Fuzzy 2-Dimension Linguistic Term Set (HF2DLTS): was proposed based on the concept of two-dimensional linguistic variables. Each set is made up of possible linguistic terms which represent a DM’s assessment of an alternative, with each term having a degree of importance denoted by a linguistic term. If X is a fixed set and ${S^{\left(1\right)}=\{\dot{s}}_0,{\dot{s}}_1, {\dot{s}}_1,\dots ,{\dot{s}}_{g-1}\}$ and ${S^{\left(2\right)}=\{\ddot{s}}_0,{\ddot{s}}_1, {\ddot{s}}_1,\dots ,{\ddot{s}}_{t-1}\}$ two sets of linguistic terms, each HF2DLTS has a function ${\widehat{h}}_s\left(x\right)={\bigcup }_{\left({\dot{s}}_a\left(x\right), { \ddot{s}}_b\left(x\right)\right) є {\widehat{h}}_s\left(x\right)}\left\{({\dot{s}}_a\left(x\right), {\ddot{s}}_b\left(x\right))\right\}$, ${\dot{s}}_a\left(x\right)$ is a set of consecutive terms in $S^{\left(1\right)}$, and ${\ddot{s}}_b\left(x\right)$ is a two-dimensional piece of linguistic information which expresses a DM’s assessment of the importance of ${\dot{s}}_a\left(x\right)$. The adoption of this approach enables DMs to use linguistic expressions such as “it is certain (${\ddot{s}}_4$) that (${\dot{s}}_3$) is fair”, and “it is uncertain (${\ddot{s}}_2$) whether (${\ddot{s}}_4$) is very good” [39];
• Probabilistic Hesitant Intuitionistic Linguistic Term Set (PHILTS): arose from the combination of HIFLTS and PLTS to reflect the probabilities of DM assessments. Thus, this approach takes into account membership probability data ($l\left(x\right)p\left(x\right)$) and non-membership probability data ($l^{\text{'}}\left(x\right)p^{\text{'}}\left(x\right))$, with these probabilities being considered independent [25];
• Interval-Valued 2-Tuple HFLTS (IV2THFLTS): is a combination of HFLTS with interval numbers. Each IV2THFLTS has a function ${\tilde{I}}_A$(x), defined in a closed subinterval of [0, 1], which denotes the possible interval-valued membership degrees of x in h_s(x). This approach helps DMs avoid a loss of information and improves the accuracy of the decision-making results [17];
• Dual HFLTS (DHFLTS): is the result of a combination of HFLTSs and Dual HFSs. DHFLTS includes the possible membership and non-membership degrees of h_s(x_i) in the set S. It is useful in very risky decision-making situations, in which DMs consider not only the advantages of a decision, but also the risks of taking this decision [40];
• Hesitant Picture Fuzzy Linguistic Set (HPFLTS): is based on Picture 2-Tuple Linguistic Term Sets and arose to avoid the loss of DM information. In this representation, each term selected by the DM $\left(s_i^k\right)$ is accompanied by the crisp values of the positive membership degrees $\left({\mu }_i^k\right)$, of the undetermined membership degrees $\left({\eta }_i^k\right)$, and the negative membership degrees (${\nu }_i^k)$ [41]. Another distinguishing characteristic of it is that this approach takes into account the refusal information concerning DMs for each assessment.

More information about HFLTS extensions can be consulted in the references indicated in Table 1. It is important to emphasize that even though the research presented in Table 1 provides an overview of HFLTS extensions, it is not exhaustive, given that there are other variations that have recently appeared based on the presented approaches.

The following section will present the methodological procedures adopted in this systematic review of the literature.

3. Methodological Procedures

This systematic review of the literature was developed using the PRISMA^TM methodology. According to Page et al. [43], literature review studies “can provide a synthesis of the status of knowledge in a field, from which future priorities can be identified”. The PRISMA^TM methodology provides a guide for the preparation of transparent, complete, and concise reviews. It provides an evidence-based minimum set of items which help ensure the robustness and reliability of systematic literature review studies [43]

Table 3 presents the research protocol developed based on the PRISMA^TM methodology used to conduct this study. The Parsifal software was used to support the planning and conducting steps. Later, during the reporting step, MS Excel software was used to prepare our graphs to summarize the findings. A set of research questions was defined by the authors to present information which makes it possible to provide an overview of the use of HFTLS and HFLTS extension techniques in SCM. The research questions RQ1.1 to RQ1.4 deal with information related to the origin of the selected studies, while RQ2.1 to RQ2.4 investigate questions related to SCM, and RQ3.1 to RQ3.8 are focused on questions about HFLTSs and decision making.

The keywords used in the search string were defined to cover studies which involve the application of HFLTSs in various subareas of SCM. The databases utilized were the ACM Digital Library, EBSCO, El Compendex, Emerald Insight, the Google Scholar tool, IEEE Digital, Science Direct, Scopus, Springer, Taylor & Francis, Web of Science, and the Wiley Online Library. The time frame considered in our search ranged from 2012 to 2023, given that the first publication about HFLTS dates from 2012 [14]. The searches were performed in March 2023. During the selection of our study sample, we only included journal articles published in English which presented real HFLTS or HFLTS extension applications used in SCM problems. We excluded books, book chapters, proceedings, literature review articles, and works that did not present real HFLTS applications in SCM, as well as other studies which were not within the scope of this review of the literature. In addition to the cited databases, we also selected studies using citation searching and searches of the Research Gate website (https://www.researchgate.net/).

Figure 1 presents the results obtained through the search and selection of articles from the databases. In Step 1, using the search string in our database search we obtained a total of 1,085 results. 173 duplicates were excluded. Considering the remaining 912 studies, the initial selection was performed by the two authors in an independent manner by reading the titles, keywords, and abstracts. The goal of this step was to only select articles which are within the scope of this review. Later, in the evaluation of the quality of the articles, the two authors read the complete articles to confirm that they perform real applications, are written in English, and have been peer-reviewed. After the eligibility criteria were applied and after the quality evaluation, we included 28 studies from these databases. In Step 2, several more studies were collected through a search of the Research Gate website and a search for citations referenced in the studies selected in Step 1. These studies were also evaluated in terms of their eligibility and quality, which made it possible to identify 6 studies which were included in our review. Thus, a total of 34 studies were included.

In Step 3 in Figure 1, the studies were classified according to the factors and categories presented in Table 4. These factors were defined based on systematic literature review studies dealing with SCM [6,13], supplier selection [7], supply management [44], group decision making [45], and the modeling of complex linguistic expressions [12]. The categories related to each factor were defined initially based on the such studies. Then the categories were reviewed and updated according to the findings based on a thorough reading of the selected articles. After the extraction of the data and the classification of the studies in accordance with Table 4, a set of graphs was prepared to better visualize the results. Finally, the information was summarized to answer the research questions presented in Table 2 and identify research gaps and opportunities in terms of this subject.

4. Results and Discussion

4.1. Presentation of the Selected Studies

4.1.1. HFLTS-Based Studies

This section presents the selected studies which are based on HFLTS applications. Among them, there are six studies which proposed models focused on supply management. Liao et al. [47] combined HFLTSs with the Best Worst Method (BWM) and Additive Ratio Assessment (ARAS) methods to support supplier selection in a digital supply chain. Dolatabad et al. [48] also proposed a supplier selection model for a digital supply chain, however they used a fuzzy cognitive map combined with the HFLTS-VIKOR (Vlsekriterijumska Optimizacija I KOmpromisno Resenje, in Serbian) method. Liu et al. [49] developed a method which combines HFLTS with Dempster–Shafer evidence theory to achieve consensus in group decision making problems. The application was realized in a supplier selection problem for chemical products in a retail supermarket. Lima-Junior and Hsiao [50] developed a model to monitor supplier performance in an automobile factory. In this study, the HFLTS-TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method was utilized to classify suppliers in a bi-dimensional matrix based on operational performance and supply costs.

Another HFLTS-TOPSIS model based on a bi-dimensional matrix was proposed by Borges et al. [4] to support the segmentation of sustainable suppliers. In this study, the application involved the classification of suppliers in a hydroelectric plant. Finger and Lima-Junior [8] developed an approach based on Quality Function Deployment (QFD) and HFLTS to support decision making during the elaboration of programs to develop sustainable suppliers. The application took place in an automotive firm considering criteria related to the economic, environmental, and social performance of the suppliers. In addition to the studies by Borges et al. [4] and Finger and Lima-Junior [8], we identified two other studies focused on the promotion of sustainable supply chains. Osiro et al. [19] proposed a method which combines HFLTS with QFD to select evaluation measures for sustainable supply chains. Erol et al. [51] applied the HFLTS-QFD, HFLTS-Delphi, HFLTS-ANP (Analytic Network Process), and HFLTS-TOPSIS methods to analyze barriers to the adoption of circular economics.

There are four studies which involve the application of HFLTSs to performance management. Tüysüz and Şimşek [52] applied HFLTS-based AHP (Analytic Hierarchy Process) to evaluate the factors which affect the performance of a transport company’s affiliates. Pérez-Domínguez et al. [53] evaluated the impact of using lean tools for organizational performance using a combination of AHP and HFLTS-TOPSIS methods. Through a combination of the HFLTS-AHP and HFLTS-MULTIMOORA (Multi-Objective Optimization on the basis of Ratio Analysis Multiplicative Forms) methods, Büyüközkan and Güler [54] created a methodology to support managers in evaluating supply chain analytics tools. Zheng et al. [55] present a Hesitant Fuzzy Linguistic DEMATEL (Decision Making Trial and Evaluation Laboratory) model to evaluate the importance of critical success factors in a health company.

In terms of risk management in supply chains, we found three related applications. Wu et al. [56] presented a new approach to risk evaluation in supply chains which integrates HFLTSs, the fuzzy synthetic method, and the eigenvalue method. A pilot application of this approach was realized to evaluate risks in electric vehicle supply chains. Chang et al. [57] combined the Failure Mode and Effect Analysis (FMEA), DEMATEL and HFLTS methods to analyze risks that failures will occur in an electronic company’s production processes. More recently, Qin et al. [9] integrated the swaps method based on the prospect theory with HFLTS. The objective of the application of this proposal was to help select emergency logistics plans during the COVID-19 pandemic.

Finally, we identified two studies related to location selection, one for human resources management and another for packaging design selection. More recently, Wu et al. [58] developed a new method that combines HFLTS, TODIM (Tomada de Decisão Interativa Multicritério, in Portuguese), and DEA. The method was applied for the selection of the most appropriate location a new health management center. Another model for location selection was developed by Ren et al. [33] based on Incomplete Hesitant Fuzzy Linguistic Preference Relations, which was applied to selecting the location of hydroelectric plants. Yalçın and Pehlivan [59] proposed a personnel selection model for a manufacturing company. The use of the Fuzzy Combinative Distance-based Assessment (CODAS) Method Based on Fuzzy Envelopes for HFLTS proved effective in dealing with this problem.

Lima et al. [8] developed a method which combines HFLTS, AHP, QFD, and Preference Ranking Organization Method for Enriched Evaluation (PROMETHEE) for packaging design selection. The application was applied in an automotive firm and the results were compared with other multicriteria decision methods.

4.1.2. Studies Based on HFLTS Extensions

Among the 15 studies based on extensions of HFLTS, we have identified the use of seven distinct approaches. The use of DHHFLTS has predominated, and it is present in seven of these studies. Krishankumar et al. [60] presented a framework for supplier selection based on DHFLTS, which is focused on situations in which the weights of the criteria are unknown. Krishankumar et al. [61] proposed a DHHFLTS-based framework for green supplier selection with partial weight information. Krishankumar et al. [62] applied DHHFLTS to generate a ranking of sustainable suppliers.

In addition to these three studies regarding supply management, we found three applications of DHHFLTS for risk analysis. Shen and Liu [63] evaluated the risk of logistics firms based on a combination of DHHFLTS and FMEA. Dai et al. [64] evaluated the risk of failures in an electronic products firm utilizing DHHFLTS, FMEA, and the K-means algorithm. Similarly, Duan et al. [65] combined DHHFLTS, FMEA, and the K-means algorithm to analyze the risk of failures in a firm in the energy sector. Finally, we have a study which uses DHHFLTS and ORESTE (Organísation, Rangement et Synthèse de Données Relarionnelles, in French) to evaluate traffic congestion [66].

The use of PLTSs has also emerged in SCM problems. Li et al. [67] developed a methodology which integrates PLTS with DEMATEL to evaluate sustainable recycling partners. Zhang et al. [68] proposed the use of PLTSs to deal with sustainable logistics suppliers. Zhang et al. [69] applied PLTSs to supplier selection for a construction company. In this application, the authors also used the BWM and Combined Compromise Solution (CoCoSo) methods based on rough boundary intervals.

The other identified extensions appear in only one application apiece. Wang et al. [70] proposed an MHFLTS model to support the outsourcing of logistics services, which is especially useful in situations in which the weight information for the criteria is incomplete. Based on the performance indicators of the Supply Chain Operations Reference (SCOR) model, Divsalar et al. [71] created a model to evaluate the supply chain performance which integrates the EHFLTS-VIKOR, Fuzzy Delphi, Interval-valued Hesitant Fuzzy, and DANP (DEMATEL-ANP) methods. A distinguishing characteristic of this model is that it combines criteria, paradigms and LARG (Lean, Agile, Resilient, and Green) practices to improve supply chain performance.

Qu et al. [72] developed a stochastic method based on DHFLTS and HFLTS for sustainable supplier selection in a high-tech manufacturing center. Wu et al. [73] combined HPLTSs with the Weighted Cross-Entropy TOPSIS method to support the decision-making process for personnel selection in a firm in the automotive sector. Zolfaghari and Mousavi [73] created a risk evaluation methodology based on FMEA, MULTIMOORA, Technique of Precise Order Preference (TPOP), and IVHFLTS. A pilot application of this methodology was created to manage failures in a healthcare company.

Based on the characterizations of the studies presented in Section 4.1.1 and 4.1.2, it was possible to answer the research questions displayed in Table 2. Section 4.2 to 4.4 will discuss the obtained results.

4.2. Information about the Origins of These Studies

This section is dedicated to answering the research questions RQ1.1 to RQ1.4, presenting the classification results for these studies in terms of year of publication, journal, country, and most cited articles. Figure 2 presents the distribution of the number of articles by year of publication (RQ1.1). This figure demonstrates that our subject is quite emergent in the literature, given that the first publication we found occurred in 2017. Roughly 58.8% of the studies were published within the past three years (beginning with 2021). In addition, the trend line of Figure 2 indicates a growth trend in terms of the number of publications about this subject. It is important to mention that the results displayed in the last column of the graph only include studies published in the first few months of 2023, given that our study sample was selected in March 2023.

Figure 3a presents the distribution of publications classified according to the first author’s affiliated institution for each study (RQ1.2). China has the largest number of publications with 17 studies, which represented 50% of our analyzed sample. It was followed by Brazil (5 studies), Turkey (4 studies), India (3 studies), and Iran (3 studies). As shown in Figure 3b, production related to this subject was concentrated in Asia (24 studies), South America (5 studies), and Europe (4 studies).

Table 4 presents the journals in which the selected studies were published (RQ1.3). A wide variety of journals published articles about this subject, with there being a total of 27 distinct journals. The journal which most published articles on this subject was IEEE Transactions on Engineering Management. Following it there was a tie between the journals Applied Soft Computing, Computers & Industrial Engineering, Environmental Science and Pollution Research, the Journal of Intelligent & Fuzzy Systems, and Symmetry, each with two publications. The other 21 journals had one publication apiece.

Table 4. List of the Most Cited Articles.

Journal	2017	2018	2019	2020	2021	2022	2023	Total
IEEE Transactions on Engineering Management						3		3
Applied Soft Computing				1	1			2
Computers & Industrial Engineering						2		2
Environmental Science and Pollution Research						1	1	2
Journal of Intelligent & Fuzzy Systems		1				1		2
Symmetry			1			1		2
Applied Sciences			1					1
Aslib Journal of Information Management							1	1
Complex & Intelligent Systems	1							1
Complexity				1				1
DYNA					1			1
Energy			1					1
Fuzzy Optimization and Decision Making				1				1
International Journal of Computational Intelligence Systems				1				1
International Journal of Environmental Research and Public Health				1				1
International Journal of Information Technology & Decision Making					1			1
International Journal of Production Economics						1		1
International Journal of Strategic Property Management				1				1
International Transactions in Operational Research		1						1
Journal of Cleaner Production						1		1
Journal of Contemporary Administration						1		1
Journal of Mathematics					1			1
Journal of the Operational Research Society						1		1
Knowledge-Based Systems					1			1
Kybernetes					1			1
Neural Computing & Applications					1			1
Technological and Economic Development of Economy			1					1

Table 4. List of the Most Cited Articles.

Journal	2017	2018	2019	2020	2021	2022	2023	Total
IEEE Transactions on Engineering Management						3		3
Applied Soft Computing				1	1			2
Computers & Industrial Engineering						2		2
Environmental Science and Pollution Research						1	1	2
Journal of Intelligent & Fuzzy Systems		1				1		2
Symmetry			1			1		2
Applied Sciences			1					1
Aslib Journal of Information Management							1	1
Complex & Intelligent Systems	1							1
Complexity				1				1
DYNA					1			1
Energy			1					1
Fuzzy Optimization and Decision Making				1				1
International Journal of Computational Intelligence Systems				1				1
International Journal of Environmental Research and Public Health				1				1
International Journal of Information Technology & Decision Making					1			1
International Journal of Production Economics						1		1
International Journal of Strategic Property Management				1				1
International Transactions in Operational Research		1						1
Journal of Cleaner Production						1		1
Journal of Contemporary Administration						1		1
Journal of Mathematics					1			1
Journal of the Operational Research Society						1		1
Knowledge-Based Systems					1			1
Kybernetes					1			1
Neural Computing & Applications					1			1
Technological and Economic Development of Economy			1					1

By collecting the number of citations in Google Scholar, it was possible to identify the most influential articles. Table 5 presents the number of citations received by the 11 most cited studies within our analyzed sample (RQ1.4). The article which had the greatest number of citations was Osiro et al. [19], with a total of 86 citations. The works of Wang et al. [70], Yalçın and Pehlivan [70], Tüysüz and Şimşek [52], and Liu et al. [49] followed with 84, 72, 71, and 65 citations respectively.

4.3. Aspects Related to SCM

To answer the research questions RQ2.1 to RQ2.4, this section will present the results regarding the objectives of HFLTS applications in SCM processes, their industrial sector, and the company’s type of SCM strategy. In order to identify what has been the focus of HFLTS and HFLTS extension techniques as applied to SCM problems, the selected studies have been organized in accordance with the objective of the application. Based on this, to elucidate which SCM processes have received the greatest attention in these applications each study has been classified as dealing with one of the following SCM processes: Source, Plan, Make, Deliver, Return, and Enable. These are the six main SCM processes according to the SCOR model (Supply Chain Operations Reference), which is an SCM reference that has been widely adopted by practitioners and researchers [46]. Table 6 displays the results of the classification of our studies in terms of the objectives of their applications and the associated SCM processes (RQ2.1). Studies dealing with supplier selection have been the most frequent, totaling 23.5% of the sample. It has been followed by failure evaluations (11.8%) and performance evaluations (8.8%).

According to the results displayed in Figure 4a, the source process had the most associated applications and represented 38.2% of the studies. This process is dedicated to acquiring goods and hiring external services which are necessary to meet actual or planned demand. It was followed by the enable process with 29.4% of the studies. This process involves activities related to managing supply chain structure, such as risk and performance management, defining its locations, and personnel selection, among other activities [46]. The plan process appeared in 14.7% of the applications. This process encompasses planning activities to create the actions that will best achieve the requirements of the make, delivery, and return processes. The studies dealing with the make process totaled 11.8% of the sample, including activities dealing with the transformation of products or the execution of services. Finally, the delivery process, which involves order, transportation, and distribution management appears with just one application (2.9%). Similarly, the return process, related to receiving products that are returned for any reason [46], was also associated with just a single application.

Figure 4b displays the results of the classification of these studies by the type of SCM strategy adopted by the company where the model was applied (RQ2.3). While 58.8% of the studies did not clearly identify the type of SCM strategy employed, 20.6% of the studies involved companies which adopted a sustainable strategy. In general, sustainable SCM studies are based on triple bottom line dimensions and include decision-making criteria related to economic, environmental, and social aspects. Applications in companies employing green supply chains represented 8.8% of the sample and are oriented towards minimizing environmental pollution and improving the environmental performance of products and processes. They were followed by 5.9% of the companies with digital (or smart) supply chains, which are focused on promoting digitalization, automation, and the integration of operations throughout the supply chain. The lean strategy, which focuses on the reduction of costs and the elimination of waste, was represented by one application (2.9%). Similarly, the LARG strategy, which combines aspects of the Lean, Agile, Resilient, and Green strategies, was also represented by just one application. We did not find applications devoted exclusively to agile or resilient supply chains.

Finally, Figure 5 displays the classification of these studies according to the sector of the participating company (RQ2.4). The automotive sector stands out with 10 applications (29.4%). It was followed by the health and electro-electronic sectors with 5 and 4 applications respectively. The food, glass, high-technology, infrastructure, manufacturing, retail, and transportation sectors were represented by just one application apiece. Five of the studies did not specify the company’s sector.

4.4. Aspects Related to Decision Making and HFLTSs

This section deals with subjects related to research questions RQ3.1 to RQ3.8. In the graph displayed in Figure 6, the selected studies are classified according to the main decision-making problem that they deal with (RQ3.1). The results indicate that half of the applications are devoted to ranking problems, or in other words, problems with ranking alternatives by global preference. This was followed by 32.4% of the applications, which deal with choice problems, in which there is a desire to choose a subgroup of alternatives within the available options. Finally, with 17.6% of the applications, we have studies which deal with sorting issues, or in other words, problems in which the objective is to classify each alternative in a predetermined category.

In Figure[MT3] 7a the studies are classified according to the adopted HFLTS approach (RQ3.2). The HFLTS approach was used in 23 studies (67.6%), while 15 studies (44.1%) adopted an HFLTS extension. Among the 13 HFLTS extensions displayed in Table 1, we found applications based on just seven of them: DHHFLTS (seven studies), PLTS (three studies), and DHFLTS, EHFLTS, HPFLS, IVHFLTS, and MHFLTS (with one study apiece). Four studies combined HFLTSs with an HFLTS extensions, such as PLTSs and DHFLTSs. These results underline the fact that this subject is emergent and presents many opportunities for research. The great frequency of the HFLTS approach originally proposed by Rodríguez et al. [14] may be related to its ease of use by DMs and the ease of calculations. Meanwhile, the use of DHHFLTSs may be associated with the possibility of using complex linguistic expressions, which combine two scales of linguistic terms in each judgement. In addition to increasing the flexibility of DM preferences, the use of DHHFLTSs increases the possibilities of values that can be attributed to the evaluated object.

Table 7 displays the techniques that were applied in each of the analyzed studies. It also describes how the criteria weights were determined and which techniques were employed in calculating these weights. In terms of research question RQ3.3, we verified that all of the studies propose the integration of HFLTS or HFLTS extension techniques with other techniques, which include Multicriteria Decision-Making (MCDM) methods, quality management, and statistical techniques. Integration occurs through the hybridization or sequential application of these techniques.

Figure 8 presents the frequency with which each technique was utilized in the integrated methods. We identified 36 distinct techniques. The most frequently utilized methods are FMEA and TOPSIS, which are present in five of the studies. These are followed by AHP, DEMATEL and QFD with four applications apiece. We believe that the great frequency of the use of FMEA is related to the fact that this method is recognized worldwide as an efficient risk evaluation tool. In FMEA, failures are prioritized according to the criteria of gravity, occurrence, and detection. Combining it with HFLTS techniques makes it possible to overcome deficiencies in the original version of FMEA, such as the inability to attribute weights to the criteria and the need to review occasional erroneous evaluations of failures utilizing exact numerical values [63]. The TOPSIS method, on the other hand, is a multicriteria decision method which is well-known for its simplicity and versatility. This method classifies the alternatives according to their proximity to the positive and negative ideal solutions. The methods resulting from the combination of TOPSIS and HFLTSs and HFLTS extensions made it possible to deal with different types of uncertainty offering greater flexibility to the alternative evaluation process [4].

In addition to the approaches used to model DM preferences, another factor which directly influences decision making is the weights (degrees of relative importance) attributed to the criteria. The definition of these weights allows DMs to decide which aspects should have priority in evaluating alternatives for the solution of a problem. The literature features various ways of obtaining the values of criteria weights. As shown in Table 7, in most of the studies (31), the weights were calculated by a decision-making technique, or an aggregation operator based on the DM judgements (RQ3.4). The most often applied techniques to accomplish this were HFLTS-QFD, HFLTS-AHP, and HFLTS-BWM. In two studies, the weights were attributed directly by the DMs. One study did not attribute weights to the criteria.

Table 8 presents the classification of the studies based on factors related to their support of group decision making (RQ3.5). We found that all of the studies applied methods support group decision making, even though the application presented by Finger and Lima-Junior [8] considered only one DM. The average number of participating DMs in the analyzed applications was 6.4 and the mode was 3. In nine studies, the weights of the DMs were taken into account in obtaining the results (RQ3.6). Among these, seven studies used methods to make this calculation, and two studies attributed numerical values to arrive at their weights.

In terms of the approaches adopted to manipulate the individual preferences of the DMs (RQ3.7), 31 (88.2%) applied a decision-making technique or a mathematical operator to aggregate DM preferences, such as for example, VHFLPWA, Interval Weighed Geometric Aggregation (IWGA), OWA, HFLWA, DHHLWA, GWOWA, and GMSM. Three studies (11.8%) presented a decision making matrix obtained by consensus, without specifying how this consensus among the various DM evaluations was achieved. Only four studies (11.8%) applied iterative methods in the search for consensus. These methods make it possible to suggest modifications to the DM evaluations by calculating measures of consensus during the evaluation rounds. Examples of iterative methods seeking consensus are presented in Liu et al. [49], Wu et al. [73], Divsalar et al. [71], and Erol et al. [51].

Finally, another important aspect of these applications has to do with how their results were validated. As presented in Figure 9, in 12 studies (35.3%) the results were validated by comparing them with the results of other decision-making methods applied to the same problem (RQ3.8). In general, this comparison is based on the ranking or categorization (sorting) supplied for each analyzed method. In 11 studies (23.5%) the authors compared the obtained results with those furnished by other methods and also conducted sensitivity analysis tests. Sensitivity analysis was utilized in an isolated manner in four studies (11.8%). The main purpose of sensitivity analyses is to verify alterations in the outputs furnished by the model when the input parameter values are varied. In three studies (8.8%) the results were validated through a combination of sensitivity analysis, comparisons with other methods, and statistical tests. In addition, three studies featured just one application without specifying how the results were validated. Just one study validated the results by comparing them with real data.

4.5. Comparison of the Results of Previous Studies

The results of this study were compared to those of previous literature review studies on subjects related to our objective. Thus, as in Yu et al. [22], which analyzed 1,080 studies based on HFS and HFS extensions, this study finds that the HFLTS approach proposed by Rodríguez et al. [14] has been the most utilized in the analyzed studies. In terms of the type of SCM strategy, our results are similar to the study by Lima-Junior and Carpinetti [6] which investigates decision-making models to evaluate supply chain performance. Both studies indicate the predominance of sustainable and green supply chains. In terms of the procedures adopted to validate their results, Lima-Junior and Carpinetti [6] related the prevailing use of sensitivity analysis, followed by statistical techniques and comparisons with other methods, while our study has concluded that comparisons with other methods have been the most utilized validation procedure, followed by sensitivity analysis combined with comparisons with other methods.

The results of this study indicate that the most frequently adopted techniques in integrated models have been TOPSIS, FMEA, AHP, DEMATEL and QFD, while in Lima-Junior and Carpinetti’s study [6] the AHP and Data Envelopment Analysis (DEA) techniques and linear programming predominated. In terms of the SCM processes which had the most applications, in analyzing artificial intelligence techniques in SCM, Yang et al. [5] found that the return and make processes had fewer applications, while our study has found that the least studied processes have been return and delivery. On the other hand, while Yang et al. [5] found that the enable and plan processes had the most applications, this study has found that the source and enable processes have had the most applications.

Finally, in terms of the economic sectors of the participating companies which have received these applications, Yang et al.’s study [5] noted the predominance of retail, food, and manufacturing, while our study showed a prevalence in the automotive, health, and electro-electronic industries. These results are somewhat similar to those found by Lima-Junior and Carpinetti [6], who related that the sectors that received the most applications of decision-making models were the automotive, food, and electro-electronic industries.

5. Recommendations for Future Research

The results of our systematic review of the literature have identified various gaps in the research on this subject. Based on the such gaps, as well as in SCC [46], Lima Junior and Carpinetti [6], Wang et al. [11], Kabak [45], and Yang et al. [5], we propose a framework which seeks to help researchers and managers develop future studies on this subject. The framework presented in Figure 10 encompasses pertinent recommendations regarding the following topics: innovative applications of techniques; new combinations of decision-making techniques; comparative studies of decision-making techniques; group decision-making issues, and validation procedures for new decision-making support models.

5.1. Innovative Applications

The results of this study indicate that the use of HFLTS and HFLTS extension techniques has still not been tested in various decision-making problems which are important to ensure effective SCM. Problems related to the delivery and return processes have been less studied up till now. There are also various types of industries which have not participated in HFLTS and HFLTS extension applications.

As Figure 10 illustrates, SCM processes span various business areas that present multiple criteria decision-making problems for which few or no applications have been applied. The use of HFLTS and HFLTS extension techniques has great potential to contribute to applications dealing with these problems due to the capacity of these techniques to provide support for group decision making under conditions of uncertainty. Based on the research opportunities that we have identified, here is a list of SCM problems which involve selecting, ordering, and categorizing that can be explored in future works. It includes problems associated with various business areas which involve strategic, tactical, and/or operational decision making:

• Asset management: prioritization of asset management investments, strategic asset allocation, selecting the location of new installations, and layout selection;
• CRM (Customer relationship management) and marketing: marketplace selection, marketing strategy selection, market segmentation, customer satisfaction analysis, and customer relationship management software selection;
• Finance: credit risk evaluation, corporate financial performance analysis, investment appraisal, budget allocations, and the evaluation of financial plans;
• IT (Information Technology): information system selection, computer workstation selection, software quality evaluation, IT service provider selection, and disruptive industry 4.0 technology evaluation;
• Maintenance: maintenance strategy selection, maintenance service provider selection, maintenance machine selection, and the prioritization of maintenance activities;
• Occupational safety & health: accident risk evaluation, the selection of key indicators for improving the occupational safety system, the prioritization of emergency plans, individual protection equipment selection, and system reliability evaluation;
• Order management: prioritization of production orders, order delivery evaluation, and the prioritization of plans to improve order management;
• Performance evaluation: performance indicator selection, performance measurement system evaluation, and organizational performance evaluation;
• Product development: product development strategy selection, new product material selection, prototype evaluation, and product portfolio evaluation;
• Project management: project proposal selection, project risk evaluation, project performance indicator selection, project management practice maturity evaluation, and program and/or project success evaluation;
• Quality management: six sigma project selection, benchmarking, product or service requirement prioritization, the selection of the certifying body for the implementation of ISO 9001 certification, and the prioritization of continual improvement actions;
• Risk management: risk evaluation tool selection, organizational risk evaluation, and supply chain risk evaluation;
• Stock management: stock management strategy selection, ABC classification of stocks, warehouse location selection, and warehouse structure selection;
• Supply management: make or buy, supplier performance monitoring; supplier segmentation, and supplier development program evaluation;
• Personnel management: organizational climate evaluation, personnel selection, position evaluation, and skills and qualifications evaluation;
• Sustainability: waste treatment alternative evaluation, prioritization of sanitary landfill location selection actions, prioritization of actions designed to promote sustainability, evaluation of the barriers to the adoption of sustainable practices, and product lifecycle evaluation;
• Transportation: route selection, modes of transport evaluation, logistics service provider selection, vehicle selection, and geographic information system selection.

The suggested applications open a gamut of possibilities for new studies. On one hand, one can explore problems which still have not been addressed with applications, such as those related to asset management, finance, IT, maintenance, marketing, occupational safety & health, order management, and stock management, among other areas. On the other, one can test the use of techniques which still have not been applied to problems that have received more attention, such as supplier selection, failure evaluation, and performance evaluation. These applications can involve companies in sectors that have not been very studied up until now, or firms in sectors that have not had any applications, such as aerospace, agriculture, education, entertainment, fashion, finance, hospitality, media and news, mining, pharmaceuticals, and telecommunications. It is also important to take SCM strategies into account in each case. Applications related to agile, flexible, and resilient supply chains have received less attention in recent studies. Different combinations of SCM strategies could also be studied in future studies.

5.2. Technique Integration

There are various combinations of HFLTS and HFLTS extension techniques, and other types of methods that still have not been tested in SCM problems. Given the low frequency of applications that employ the DHFLTS, EHFLTS, HPFLS, IVHFLTS, and MHFLTS techniques, as well as the absence of applications based on HIFLTS, PHFLTS, IVDHFLTS, HF2DLTS, PHILTS, IV2THFLTS techniques, future studies could test new combinations of these approaches with MCDM methods, quality management techniques, risk evaluation techniques, optimization methods, and/or artificial intelligence techniques.

More specifically, new hybrid methods can be created based on MCDM methods, which have great potential for integration with HFLTS approaches, but have rarely or never been used, such as ORESTHE, ARAS, CODAS, CoCoSo, Delphi, ELECTRE (ÉLimination Et Choix Traduisant la REalité, in French), Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS), Measuring Attractiveness by a Categorical Based Evaluation Technique (MACBETH), ORESTE, PROMETHEE, Qualitative Flexible Multiple Criteria Method (QUALIFLEX), Simple Multi-Attribute Rating Technique (SMART), and SWARA.

There are also quality management techniques such as QFD, Service Quality Measurement (SERVQUAL), and the GUT matrix (a process prioritization matrix based on Gravity, Urgency, and Tendency) which are multicriteria in nature and can be integrated with HFLTS extensions to create new MCDM methods. Similarly, FMEA, risk matrix, and fault tree analysis can be combined with these approaches to generate new methodologies for risk evaluation.

In cases in which a problem step seeks to order, select or sort alternatives, while another step seeks to optimize resources, one can use combinations with optimization methods such as linear programming, non-linear programming, stochastic programming, and dynamic programming. On the other hand, for problems which seek to classify patterns or predictions and/or group values, and/or require the analysis of a large quantity of data, HFLTS approaches can be combined with AI methods such as artificial neural networks, neuro-fuzzy systems, genetic algorithms, and case-based logic.

5.3. Comparison of Techniques

The results of our study also demonstrate the need to conduct comparative studies involving MCDM techniques based on HFLTSs and HFLTS extensions. Even though some of the analyzed studies have compared the numeric outputs of distinct techniques when applied to the same problem, the literature offers few comparative studies which discuss the benefits and limitations of HFLTS and HFLTS extension techniques in specific problem domains.

The realization of these comparative studies would contribute to a greater understanding of the technical characteristics being compared and could assist researchers and practitioners in choosing the most appropriate techniques for given SCM problems. In addition to comparing the outputs generated by each technique, it is recommended that these studies take into account comparison factors such as computational complexity, limitations in terms of the number of input variables, the effect of variations in criteria and alternatives, support for group decision making, and agility in the decision-making process [24].

The realization of studies which compare various HFLTS extensions could also be valuable in mapping the advantages in use, as well as the similarities and differences among these approaches. These comparative studies could take into account factors such as the complexity of modeling and processing, the effect of differences in the representation of DM preferences, and the appropriateness of each approach in dealing with various types of uncertainty. The behavior of various aggregation operators for HFLTS and HFTLS extension information could also be analyzed.

5.4. Group Decision-Making Issues

There are some topics related to group decision making in SCM that have been little studied and deserve more attention. Even though all of the analyzed studies provide support for group decision making, we have verified that there are few methods which make it possible to attribute weights to the DMs. This may be especially useful when one wants to weight the opinion of DMs based on their level of experience, positions, and/or knowledge of a problem. In addition, since methods that allow the attribution of weights to DMs using linguistic expressions were not found, we suggest the development of methods which make this possible to deal appropriately with uncertainty in the definition of DM weights.

An important emergent research topic is large group decision-making problems. These problems are a special case in terms of group decision-making processes in which the opinions of a large number of people are collected. There are various large group decision-making problems inherent in SCM which could be investigated in future works, for example, strategic decisions which involve DMs from various departments or organizations, or product or service evaluations made by a gamut of customers. In cases in which the number and diversity of DMs are large, we recommend the adoption of EHFLTS techniques which make it possible to organize DMs in subgroups and avoid losses of information in situations in which there is no consensus among the DMs.

Finally, another relevant topic regarding group decision making which requires more investigation has to do with models based on the consensus reaching process. There are a variety of opportunities to develop new models of this type which can be explored through a combination of iterative methods with HFLTS and/or HFLTS extension techniques. One of them consists of the development of new approaches that combine the Delphi method with HFLTS extensions. In addition, it would be interesting to test new consensus models that propose modifications in DM preferences, as well as models based on adaptive consensus strategies which automatically update DM weights with each iteration.

5.5. Validation of New Decision-Making Models

Future studies could use validation procedures which have been little explored to evaluate the reliability of the results of new decision-making models. Given that most studies currently conduct sensitivity analysis tests and compare their results with other methods, it is plausible to adopt statistical techniques that analyze the obtained results such as hypothesis tests, variance analysis, and error measurements. The use of similarity measures is also a useful way to compare the results generated by different techniques. In addition, the realization of factor analysis experiments would make it possible to identify which input variables have the greatest influence over the results.

To verify the consistency of the obtained results, it is important to conduct tests considering a larger number of application cases, in order to evaluate the performance of these techniques under distinct scenarios, varying the number of alternatives, criteria, and linguistic terms. We also recommend verifying the usability of HFLTS and HFLTS extension techniques by users who are not specialists in dealing with these techniques. To accomplish this, we suggest that future studies develop software with graphic interfaces based on these techniques to verify their usability in various organization areas.

6. Conclusions

This study has presented a systematic review of the literature on applications of HFLTS and HFLTS extension techniques in SCM decision-making problems. In order to answer a series of research questions regarding this subject, the selected studies have been characterized in accordance with a group of factors related to their origin, SCM, HFLTSs and decision making. The results demonstrate that this research subject is quite recent and there has been substantial growth in the number of publications about this topic. The applications we have identified provide support for a wide variety of decision-making problems, with their main focuses being on supplier selection, failure evaluation, and performance evaluation.

We have verified the predominance of the use of HFLTS, TOPSIS and FMEA techniques. Among HFLTS extensions, we can highlight DHHFLTS and PLTS applications. Applications in automotive firms and sustainable supply chains have received the most attention. It has been confirmed that all of the analyzed models are appropriate for providing support for group decision making, even though few of them permit the attribution of distinct weights to DMs. There are also few models designed to obtain a consensus among DMs.

The results of this study demonstrate that even though there is a wide variety of HFLTS extensions, we did not find SCM applications for around half of them. There are also various types of SCM strategies, industries, and decision-making problems which deserve greater attention from researchers and practitioners.

The main contribution of this study consists of presenting an overview of the use of HFLTSs and HFLTS extensions in SCM in practice, highlighting trends and research opportunities. Our study presents a wide array of directions for future studies which encompass topics related to innovative applications, combinations of techniques, comparisons of techniques, group decision-making issues, and validation procedures for new decision-making models. To further our knowledge this is the first study to present a systematic review which focuses on real applications of HFLTS and HFLTS extension techniques. It is also the first study to analyze applications of decision techniques that deal with uncertainty and hesitation in SCM. That being said, we believe that this study will contribute to the dissemination of the use of HFLTS and HFLTS extensions to solve real SCM problems to minimize the effects of uncertainty on the results and contribute to the promotion of more structured and rational decision-making processes.

Finally, a limitation of this study is that there may be works which present HFLTS or HFLTS extension applications that were not identified in our searches. Even though we consulted various databases, this list is not exhaustive. In addition, we opted to include just articles in English and did not include gray literature or non-realistic numerical applications. Future studies can complement the results of this systematic review of the literature by including new works in the study sample. Other reviews can also be conducted that consider applications of techniques derived from HFSs and HFS extensions in various areas of knowledge such as the engineering, health, construction, and energy fields.