A Novel Similarity Measure for Generalized Nonlinear Trapezoidal Fuzzy Numbers with Applications to Multi-Attribute Decision Making

There are several similarity measure techniques for generalized trapezoidal fuzzy numbers. However, no similarity measure technique has yet been proposed for generalized non-linear trapezoidal fuzzy numbers. In the present work, a new similarity measure approach for two generalized non-linear trapezoidal fuzzy numbers is proposed based on distance and center of gravity (COG) measures. Several propositions related to the proposed method are also discussed. Furthermore, a comparative analysis with existing methods is carried out through illustrative examples, demonstrating that the proposed method is applicable to both generalized non-linear and generalized linear trapezoidal fuzzy numbers. Finally, a multi-attribute decision-making problem is considered, and a new algorithm is introduced to identify the best alternative for a decision maker using the proposed similarity measure method.