Multi-Attribute Group Decision Making Based on a New Ranking of Positive and Negative Interval Type-۲ Fuzzy Numbers

This paper addresses multi-attribute group decision-making (MAGDM) where linguistic assessments are represented by both positive and negative interval type-۲ fuzzy numbers (IT۲FNs)‎, ‎capturing the intrinsic uncertainty of group evaluations more accurately. ‎We introduce a novel ranking method for IT۲FNs that simultaneously utilizes the mean and standard deviation of the upper and lower membership functions‎, ‎ as well as the IT۲FN's height‎. ‎This enhances its discriminatory capability‎. ‎The theoretical foundations of this ranking— encompassing zero‎, ‎unity‎, ‎and symmetry properties— are rigorously established‎, ‎and its superiority over existing techniques is demonstrated through comparative analyses on seven benchmark datasets‎. ‎Building on this ranking‎, ‎we develop an integrated fuzzy MAGDM framework that can handle both positive and negative IT۲FN assessments for criteria and weights‎. ‎The framework’s practicality and effectiveness are validated through two case studies‎: ‎one with exclusively positive linguistic terms and another with mixed positive and negative scales‎. ‎Results indicate that the proposed ranking and decision framework yield more rational and robust group decisions under substantial uncertainty‎. ‎They outperform conventional fuzzy methods and offer a nuanced solution for real-world MAGDM scenarios‎.

کلیدواژه ها:

Multi-attribute group decision making‎ ، Fuzzy ، ‎Ranking method‎ ، Linguistic assessment ، Uncertainty