In the era of sustainable development, green supplier selection has become a key component of supply chain management, as it considers criteria such as carbon footprint, water usage, energy usage and recycling capacity. Since the green supplier selection problem involves subjective criteria and uncertainty in preferences, it is well suited to using multi-criteria decision-making methods (MCDM). Although few researchers have investigated MCDM for green supplier selection under uncertainty using intuitionistic and Pythagorean fuzzy sets. Still, the newly developed fermatean fuzzy can handle greater data uncertainty than intuitionistic and Pythagorean fuzzy sets. Since interval extension of fuzzy theory provides more accurate modeling, in this paper, we propose an interval extension of fermatean fuzzy set and discuss its fundamental set operations, arithmetic operations and related properties. We propose the Hamming distance function and the score function of the interval-valued fermatean fuzzy numbers. The recently developed Multi-attribute Border Approximation Area Comparison (MABAC) method is also considered due to its stable and simple computation compared to other conventional MCDM methods. Therefore, an interval-valued fermatean fuzzy MABAC method is proposed and solved to select a green supplier based on multiple criteria. The proposed method's comparative analysis and sensitivity analysis validate the proposed method's effectiveness and robustness.

Multi-stakeholder based construction projects are subject to various risk factors due to dynamic business environments. These risks affect project activities which indirectly impact construction costs, resulting in delays and poor building quality. So, managing these project risks requires suitable risk mitigation strategies to evaluate and analyse their severity. Hence, risk evaluation and assessment of construction projects is a multi-criteria decision making (MCDM) problem. In present real-life problems, evaluation of project risks is often uncertain and even incomplete, and the prevailing methodologies fail to handle such situations. To address the problem, this paper extends the analytical network process (ANP) methodology in the D number domain to handle three types of ambiguous evaluations, viz. complete, uncertain, and incomplete, and assesses the weight of risk criteria. The D number based approach overcomes the deficiencies of the exclusiveness hypothesis and completeness constraint of Dempster-Shafer (D-S) theory. Here, preference ratings of the decision matrix for each decision-maker are determined using a D number extended consistent fuzzy preference relation (D-CFPR). An extended multi-attributive border approximation area comparison (MABAC) method in D number is then developed to rank and select the best alternative risk response strategy. Finally, an illustrative example from construction sector is presented to check the feasibility of the proposed approach. For checking the reliability of alternative ranking, a comparative analysis is performed with different MCDM approaches (D-COPRAS, D-ARAS, D-MABAC, and D-TOPSIS). Based on different criteria weights, a sensitivity analysis of obtained ranking of the hybrid D-ANP-MABAC model is performed for verify the robustness of the proposed method.