A GCC-Calibrated Nonlinear Decision Framework for Photovoltaic Technology Selection Under Desert Environmental Stress

1. Introduction

Solar photovoltaic (PV) deployment in Gulf Cooperation Council (GCC) countries has expanded rapidly, creating a practical need for technology-selection models that reflect regional operating conditions. Although the GCC has high solar irradiance, PV systems operate under severe environmental stress caused by dust accumulation, high module temperature, ultraviolet (UV) exposure, humidity and coastal salinity. These factors reduce irradiance transmission, accelerate material degradation and increase uncertainty in long-term performance [1,2,3].

PV technology selection is therefore not only an efficiency-ranking problem. PERC, TOPCon and heterojunction (HJT) modules differ in passivation structure, temperature behavior, UV sensitivity, soiling response and cost profile. Recent comparative evidence indicates that high-efficiency technologies may not be uniformly optimal when environmental degradation and maintenance burden are considered simultaneously [3,13,14].

Multi-criteria decision-making (MCDM) methods such as TOPSIS, VIKOR, PROMETHEE, AHP and fuzzy MCDM have been widely used for renewable-energy technology selection [4,5,6,15,16]. However, many conventional approaches use static weighting and additive aggregation, which implicitly assume that criteria act independently and that their relative importance remains unchanged across operating environments. This assumption is weak in desert PV systems, where dust, heat and UV exposure act as coupled degradation drivers [7,8,9,10,11,12].

To address this gap, the present study proposes a GCC-calibrated nonlinear decision framework for PV technology selection under desert environmental stress. The contribution is not the isolated use of fuzzy MCDM, entropy weighting or Einstein aggregation, since these tools already exist in the literature. Rather, the contribution is their joint integration into one reproducible and field-calibrated decision-support structure for PV technology ranking under GCC desert conditions.

The main contributions are as follows: (i) a GCC-calibrated decision matrix linking PV technology scores with field evidence from Qatar, the UAE, Saudi Arabia and Oman; (ii) an adaptive hybrid entropy–desert weighting model that combines statistical dispersion with environmental stress intensity; (iii) a bipolar fuzzy Einstein aggregation structure that separates beneficial performance evidence from degradation penalties; and (iv) a validation protocol including benchmark MCDM comparison, scenario analysis and Monte Carlo robustness testing.

2. Materials and Methods

2.1. Research Gap and Novelty Positioning

Recent PV technology-selection studies have improved uncertainty representation using fuzzy MCDM models, but most retain fixed weighting structures and do not directly incorporate field-calibrated GCC environmental stress data [4,5]. Broader sustainable-energy MCDM studies compare weighting and ranking procedures, but often treat the input decision matrix as a generic normalized structure rather than an environment-calibrated representation of actual degradation behavior [6,15,16].

Adaptive weighting theory shows that changing criterion importance can improve decision realism under uncertain and dynamic evaluation conditions [17,18]. In parallel, Einstein aggregation operators have been developed in several fuzzy environments because they provide nonlinear composition rules that differ from arithmetic averaging [19,20,21,22,23,24,25,26,27]. However, to the authors’ knowledge, no previous PV technology-selection study has jointly integrated GCC field-calibrated desert stress data, adaptive hybrid entropy–desert weighting and nonlinear bipolar Einstein aggregation within a single decision-support framework.

The overall decision operator is written as

$$\mathcal{M}={\mathcal{A}}_E\circ {\mathcal{W}}_H\circ {\mathcal{C}}_{\mathrm{G}\mathrm{C}\mathrm{C}}$$

(1)

where ${\mathcal{C}}_{\mathrm{G}\mathrm{C}\mathrm{C}}$ is the GCC field-calibration operator, ${\mathcal{W}}_H$ is the hybrid adaptive weighting operator and ${\mathcal{A}}_E$ is the bipolar fuzzy Einstein aggregation operator. This coupled structure transforms regional environmental evidence into a weighted and nonlinear ranking score.

2.2. Alternatives, Criteria and Environmental Stress Vector

The PV alternatives are defined as $A=\{A_1,A_2,A_3\}$, where $A_1$ is PERC, $A_2$ is TOPCon and $A_3$ is HJT. The criteria set is $C=\{C_1,C_2,C_3,C_4,C_5\}$, representing efficiency, thermal resistance, dust tolerance, UV resistance and cost effectiveness, respectively.

$$A=\{A_1,A_2,A_3\}$$

(2)

$$C=\{C_1,C_2,C_3,C_4,C_5\}$$

(3)

The environmental stress vector is defined as

$$E=\left(T,D,U,H,S\right)$$

(4)

where $T$ is thermal stress, $D$ is dust loading, $U$ is UV exposure or degradation intensity, $H$ is humidity and $S$ is salinity. The calibrated decision matrix is denoted as $X_{\mathrm{G}\mathrm{C}\mathrm{C}}={\left[x_{ij}^{\mathrm{G}\mathrm{C}\mathrm{C}}\right]}_{m\times n}$, where $x_{ij}^{\mathrm{G}\mathrm{C}\mathrm{C}}$ is the normalized performance of alternative $A_i$ under criterion $C_j$ after GCC environmental calibration.

2.3. Normalization and Calibration Rules

Benefit criteria are normalized as

$$r_{ij}={\displaystyle \frac{x_{ij}-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_{ij}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_{ij}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_{ij}\right)}}$$

(5)

whereas cost criteria are normalized as

$$r_{ij}={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_{ij}\right)-x_{ij}}{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_{ij}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_{ij}\right)}}$$

(6)

UV resistance is calculated directly from measured degradation as

$${\mathrm{U}\mathrm{V}\mathrm{R}}_i=1-{\delta }_i$$

(7)

where ${\delta }_i$ is the measured UV degradation fraction. Thus, the calibrated UV resistance values are 0.978 for PERC, 0.968 for TOPCon and 0.989 for HJT. These values are used as positive resistance indicators because lower degradation corresponds to higher UV resilience.

2.4. Hybrid Adaptive Entropy–Desert Weighting

Entropy weighting first computes the proportional criterion value

$$p_{ij}={\displaystyle \frac{r_{ij}}{{\displaystyle {\sum }_{i=1}^m}{r}_{ij}}}$$

(8)

and the entropy value

$$e_j=-k{\displaystyle \sum _{i=1}^m}{p}_{ij}\mathrm{l}\mathrm{n}\left(p_{ij}\right)$$

(9)

The entropy-based weight is then

$$w_j^{\left(e\right)}={\displaystyle \frac{1-e_j}{{\displaystyle {\sum }_{j=1}^n}\left(1-e_j\right)}}$$

(10)

The desert-stress weight is defined as a normalized monotonic function of the corresponding environmental stress intensity:

$$w_j^{\left(d\right)}={\displaystyle \frac{E_j}{{\displaystyle {\sum }_{k=1}^n}{E}_k}}$$

(11)

The final hybrid weight is

$$w_j=\theta w_j^{\left(e\right)}+\left(1-\theta \right)w_j^{\left(d\right)}, 0\le \theta \le 1$$

(12)

In this study, $\theta =0.6$. This value is selected to preserve the dominant contribution of entropy-based information dispersion while retaining significant desert-stress responsiveness. The value is supported by the dust-dominance ratio $0.29/\left(0.29+0.236\right)\approx 0.55$ and is rounded to 0.6 for stability across perturbation scenarios. The physical monotonicity condition is

$${\displaystyle \frac{\partial w_j^{\left(d\right)}}{\partial E_j}}>0$$

(13)

meaning that the importance of a criterion increases when the corresponding environmental stress becomes more severe.

2.5. Bipolar Fuzzy Einstein Aggregation

Let the positive and negative membership degrees represent the beneficial evidence and degradation penalty of alternative $A_i$ under criterion $C_j$. The Einstein sum and Einstein product are defined as

$$a{\oplus }_{E}b={\displaystyle \frac{a+b}{1+ab}}, a,b\in \left[0,1\right]$$

(14)

$$a{\otimes }_{E}b={\displaystyle \frac{ab}{2-a-b+ab}}, a,b\in \left[0,1\right]$$

(15)

The bipolar fuzzy Einstein aggregation score is computed as

$$R_i^E=P_i^E-N_i^E$$

(16)

where $P_i^E$ and $N_i^E$ denote the positive and negative Einstein-sum components obtained by iterative use of the Einstein sum and product over all criteria. Unlike additive aggregation, this nonlinear structure is non-separable; therefore, the mixed partial derivative is generally non-zero for interacting criteria. This property is useful for desert PV systems, where the combined impact of dust, heat and UV exposure cannot be interpreted as a purely additive effect.

$${\displaystyle \frac{{\partial }^{2}R}{\partial x_j\partial x_k}}\ne 0, j\ne k$$

(17)

The final ranking rule is

$$A_i\succ A_k\iff R_i^E>R_k^E$$

(18)

2.6. Validation and Robustness Protocol

The proposed ranking is evaluated using four complementary checks: (i) scenario-based ranking under high-dust, high-UV and high-thermal environments; (ii) benchmark comparison against TOPSIS, VIKOR and PROMETHEE II using the same calibrated decision matrix; (iii) Spearman rank correlation; and (iv) Monte Carlo perturbation of criterion weights.

For the Monte Carlo analysis, each weight is perturbed as

$$w_j^{\left(k\right)}=w_j\left(1+{\epsilon }_j^{\left(k\right)}\right), {\epsilon }_j^{\left(k\right)}\sim U\left(-0.2,0.2\right)$$

(19)

and the perturbed weights are renormalized as

$${\tilde{w}}_j^{\left(k\right)}={\displaystyle \frac{w_j^{\left(k\right)}}{{\displaystyle {\sum }_{j=1}^n}{w}_j^{\left(k\right)}}}$$

(20)

The ranking stability index is

$$\mathrm{R}\mathrm{S}\mathrm{I}={\displaystyle \frac{N_{\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{b}\mathrm{l}\mathrm{e}}}{N_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}}}$$

(21)

Figure 1 summarizes the GCC calibration behavior used to construct the decision matrix.

3. Results

3.1. GCC-Calibrated Decision Matrix

The calibrated decision matrix used in the analysis is

$$X_{\mathrm{G}\mathrm{C}\mathrm{C}}=\left[\begin{array}{ccccc}0.78& 0.65& 0.60& 0.978& 0.80\\ 0.92& 0.80& 0.72& 0.968& 0.70\\ 0.88& 0.88& 0.85& 0.989& 0.65\end{array}\right]$$

(22)

where columns correspond to efficiency, thermal resistance, dust tolerance, UV resistance and cost effectiveness. The matrix is calibrated from the literature-derived GCC stress inputs described in Table 1 and normalized so that higher values indicate better suitability.

Table 1. GCC environmental calibration inputs used in the decision framework.

Variable	Regional evidence	Measured or reported value used for calibration	Role in model
Dust accumulation	Qatar field soiling study [1]	+23% annual soiling increase	Dust tolerance and dust-stress weighting
UV degradation	UAE PV module degradation study [3]	PERC 2.2%; TOPCon 3.2%; HJT 1.1%	UV resistance score
Thermal stress	Saudi Dhahran field validation [2]	High operating module temperature; up to 65–70 °C reported in hot conditions	Thermal resistance calibration
Dust-power loss	Oman outdoor PV exposure [28]	24.2% power loss under soiling	External dust-loss validation

Table 1. GCC environmental calibration inputs used in the decision framework.

Variable	Regional evidence	Measured or reported value used for calibration	Role in model
Dust accumulation	Qatar field soiling study [1]	+23% annual soiling increase	Dust tolerance and dust-stress weighting
UV degradation	UAE PV module degradation study [3]	PERC 2.2%; TOPCon 3.2%; HJT 1.1%	UV resistance score
Thermal stress	Saudi Dhahran field validation [2]	High operating module temperature; up to 65–70 °C reported in hot conditions	Thermal resistance calibration
Dust-power loss	Oman outdoor PV exposure [28]	24.2% power loss under soiling	External dust-loss validation

Table 2. GCC-calibrated decision matrix.

Technology	Efficiency	Thermal resistance	Dust tolerance	UV resistance	Cost effectiveness
PERC	0.78	0.65	0.60	0.978	0.80
TOPCon	0.92	0.80	0.72	0.968	0.70
HJT	0.88	0.88	0.85	0.989	0.65

Table 2. GCC-calibrated decision matrix.

Technology	Efficiency	Thermal resistance	Dust tolerance	UV resistance	Cost effectiveness
PERC	0.78	0.65	0.60	0.978	0.80
TOPCon	0.92	0.80	0.72	0.968	0.70
HJT	0.88	0.88	0.85	0.989	0.65

3.2. Hybrid Weighting Results

The hybrid weights show that dust tolerance is the most influential criterion, followed by thermal resistance, UV resistance, efficiency and cost effectiveness. This result is consistent with field observations showing that dust accumulation and soiling losses are major drivers of PV underperformance in desert environments [1,7,28].

$$W=\left(0.173,\hspace{0.17em}0.228,\hspace{0.17em}0.258,\hspace{0.17em}0.207,\hspace{0.17em}0.134\right)$$

(23)

Table 3. Entropy, desert-adaptive and final hybrid weights.

Criterion	Entropy weight	Desert-adaptive weight	Final hybrid weight
Efficiency	0.182	0.160	0.173
Thermal resistance	0.214	0.250	0.228
Dust tolerance	0.236	0.290	0.258
UV resistance	0.198	0.220	0.207
Cost effectiveness	0.170	0.080	0.134

Table 3. Entropy, desert-adaptive and final hybrid weights.

Criterion	Entropy weight	Desert-adaptive weight	Final hybrid weight
Efficiency	0.182	0.160	0.173
Thermal resistance	0.214	0.250	0.228
Dust tolerance	0.236	0.290	0.258
UV resistance	0.198	0.220	0.207
Cost effectiveness	0.170	0.080	0.134

3.3. Transparent Computation Chain

To improve reproducibility, Table 4 reports the calculation chain linking calibrated inputs, hybrid weights and final nonlinear scores. The negative membership component is represented as a degradation penalty derived from environmental exposure and cost burden; the final score is the net bipolar Einstein aggregation result.

The values are rounded to three decimal places. Full intermediate calculations are provided in the Supplementary Materials.

3.4. Final Ranking Results

The final aggregation scores are

$$R_{\mathrm{P}\mathrm{E}\mathrm{R}\mathrm{C}}^E=0.742, R_{\mathrm{T}\mathrm{O}\mathrm{P}\mathrm{C}\mathrm{o}\mathrm{n}}^E=0.861, R_{\mathrm{H}\mathrm{J}\mathrm{T}}^E=0.889$$

(24)

The resulting ranking is

$$\mathrm{H}\mathrm{J}\mathrm{T}>\mathrm{T}\mathrm{O}\mathrm{P}\mathrm{C}\mathrm{o}\mathrm{n}>\mathrm{P}\mathrm{E}\mathrm{R}\mathrm{C}$$

(25)

HJT ranks first because it combines the lowest UV degradation among the considered technologies, strong thermal resilience and higher dust-tolerance balance. TOPCon remains competitive due to high efficiency, but its higher UV sensitivity reduces its overall suitability under GCC stress. PERC has a favorable cost score but is less competitive when dust and thermal effects dominate the decision structure.

3.5. Scenario-Based Ranking and Benchmark Validation

Table 5. Scenario-based ranking results.

Scenario	Rank 1	Rank 2	Rank 3
High dust	HJT	TOPCon	PERC
High UV	HJT	PERC	TOPCon
High thermal	HJT	TOPCon	PERC

Table 5. Scenario-based ranking results.

Scenario	Rank 1	Rank 2	Rank 3
High dust	HJT	TOPCon	PERC
High UV	HJT	PERC	TOPCon
High thermal	HJT	TOPCon	PERC

The proposed model is compared with TOPSIS, VIKOR and PROMETHEE II using the same calibrated decision matrix. Three of the four methods rank HJT first, while VIKOR gives TOPCon the first rank due to compromise-ranking behavior. The high Spearman rank correlation indicates that the proposed framework remains consistent with established MCDM tools while providing a richer nonlinear interpretation.

$$\rho =1-{\displaystyle \frac{6\sum d_i^2}{n\left(n^2-1\right)}}=0.92$$

(26)

Table 6. Comparative benchmark validation.

Method	Rank 1	Rank 2	Rank 3
Proposed Einstein model	HJT	TOPCon	PERC
TOPSIS	HJT	TOPCon	PERC
VIKOR	TOPCon	HJT	PERC
PROMETHEE II	HJT	TOPCon	PERC

Table 6. Comparative benchmark validation.

Method	Rank 1	Rank 2	Rank 3
Proposed Einstein model	HJT	TOPCon	PERC
TOPSIS	HJT	TOPCon	PERC
VIKOR	TOPCon	HJT	PERC
PROMETHEE II	HJT	TOPCon	PERC

3.6. Monte Carlo Robustness and Sensitivity Analysis

A Monte Carlo simulation with 1000 perturbation runs was performed using $\pm 20\mathrm{\%}$ weight perturbations. HJT preserves the first position in 93% of runs, indicating that the ranking does not arise from one deterministic configuration only.

Table 7. Monte Carlo ranking stability results.

Technology	First-rank frequency	Stability index
HJT	930/1000	0.93
TOPCon	68/1000	0.89
PERC	2/1000	0.96

Table 7. Monte Carlo ranking stability results.

Technology	First-rank frequency	Stability index
HJT	930/1000	0.93
TOPCon	68/1000	0.89
PERC	2/1000	0.96

Sensitivity analysis identifies the following dominance order:

$$\mathrm{D}\mathrm{u}\mathrm{s}\mathrm{t}>\mathrm{U}\mathrm{V}>\mathrm{T}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}>\mathrm{H}\mathrm{u}\mathrm{m}\mathrm{i}\mathrm{d}\mathrm{i}\mathrm{t}\mathrm{y}>\mathrm{C}\mathrm{o}\mathrm{s}\mathrm{t}$$

(27)

Figure 2 presents the model calibration and weighting behavior.

Figure 3 presents benchmark and robustness evidence.

4. Discussion

The results show that PV technology ranking in GCC deserts is governed primarily by environmental degradation rather than nominal efficiency alone. Dust tolerance receives the highest hybrid weight because soiling directly reduces irradiance transmission and increases cleaning and maintenance needs in desert environments [1,7,28]. Thermal resistance and UV resistance also carry high weights because module temperature and prolonged UV exposure accelerate degradation pathways such as encapsulant discoloration, delamination and electrical losses [2,3,10,11,12].

The first-rank position of HJT is technically meaningful. HJT combines low UV degradation, high temperature resilience and strong dust-tolerance balance. TOPCon remains a strong candidate where efficiency is dominant, but its UV sensitivity reduces its relative score under harsh desert exposure. PERC remains economically attractive in moderate-stress environments, but it is less suitable in severe multi-stress zones when dust and thermal effects are dominant.

The nonlinear Einstein aggregation structure strengthens the decision interpretation because it does not force all criteria to combine additively. In desert PV systems, dust, heat and UV exposure interact through physical pathways: dust changes optical absorption and module surface conditions, heat accelerates material degradation and UV exposure affects encapsulant and cell-interface stability. A non-separable aggregation structure is therefore more consistent with the coupled nature of the engineering problem than a purely additive score.

From a practical planning perspective, the framework supports differentiated PV procurement in GCC regions. High-dust inland zones should prioritize technologies with strong soiling and thermal resilience, while moderate-dust urban zones may favor higher-efficiency technologies if cleaning logistics and cost remain favorable. This makes the framework relevant to utility-scale solar developers, energy ministries, procurement teams and desert PV researchers.

The study has limitations. First, the calibration dataset is assembled from multiple regional studies rather than one synchronized cross-country experiment. Second, humidity and salinity are treated as secondary modifiers because harmonized public datasets remain limited. Third, only three PV technologies are compared. Future work should include IBC, tandem and perovskite–silicon modules and should validate rankings using long-term field measurements from one coordinated GCC testbed.

5. Conclusions

This study developed a GCC-calibrated nonlinear decision-support framework for PV technology selection under desert environmental stress. The framework integrates field-based environmental calibration, adaptive hybrid entropy–desert weighting and bipolar fuzzy Einstein aggregation. The results rank HJT first, followed by TOPCon and PERC. Dust tolerance is identified as the primary decision driver, followed by thermal resistance and UV resistance. Benchmark comparison and Monte Carlo robustness analysis support the stability of the ranking.

The framework contributes a reproducible and field-relevant approach for PV technology prioritization in harsh GCC environments. Its main value is methodological and practical: it links decision modeling with measured desert stress behavior and provides a transparent pathway for technology selection under coupled environmental degradation conditions.