A New Approach to Rank Generalized Type-1 Fuzzy Numbers Using Cost-Benefit Analysis

This study introduces a novel approach for ranking fuzzy numbers by integrating Cost-Benefit Analysis with vector normalization. In this method, a generalized fuzzy number is preferred when it yields higher benefits and lower costs. The left area of the fuzzy number, representing benefit, is more desirable when larger, whereas the right area, considered a cost, is more favorable when smaller. To ensure a balanced evaluation, a Profit Index is computed, incorporating both horizontal and vertical dimensions for a comprehensive ordering of fuzzy numbers. This ensures that all relevant information of the generalized fuzzy numbers is taken into account, leading to consistent and reliable rankings. The proposed technique is well-suited for application in various fuzzy multi-criteria decision-making (MCDM) frameworks, offering enhanced support for decision-makers in practical, real-world contexts.