Integrating Intuitionistic Fuzzy Diamond-Shaped Sets with Combinative Distance-Based Assessment Method for Multi-Criteria Decision-Making

Abstract

In diverse decision values may find it difficult to offer a coherent and truthful viewpoint in situations with multiple decision makers. In order to overcome the limitation, this work introduces the Diamond Intuitionistic Fuzzy Set (Dia-IFS). The Dia-IFS model, an extended version of the Intuitionistic Fuzzy Set (IFS) model, provides better performance by extending intuitionistic fuzzy sets to Interval-Valued Intuitionistic Fuzzy Set (IVIFS). By describing its components using Diamond Intuitionistic Fuzzy Values (Dia-IFVs), the Dia-IFS framework improves the IFS. The main features of fundamental algebraic and arithmetic operations, including union, intersection, addition, multiplication, and scalar multiplication, are examined and codified for Dia-IFVs. Additionally, new Diamond Intuitionistic Fuzzy (Dia-IF) weighted average and geometric aggregation operators are presented, and their special features are thoroughly examined. Using t-norms and t-conorms, algebraic procedures between Dia-IFVs are devised. Specialized weighted aggregation operators are suggested in order to combine input values represented by Dia-IFVs into a single output. Additionally, by utilizing both Euclidean and Hamming distances, the Dia-IF framework incorporates the "Combinative Distance-based Assessment" (CODAS) methodology. Through comparison analysis and instructive instances, the Dia-IF model's usefulness is illustrated. The outcomes demonstrate the framework's viability and efficiency in assessing and choosing the best options, expanding its possible uses in challenging decision-making situations.