IVIF-PROMETHEE outranking methods for multiple criteria decision analysis based on interval-valued intuitionistic fuzzy sets

This paper attempts to develop an interval-valued intuitionistic fuzzy preference ranking organization method for enrichment evaluations (IVIF-PROMETHEE) and attempts to apply it to multiple criteria decision analysis. The theory of interval-valued intuitionistic fuzzy sets is useful for modeling impressions and quantifying the ambiguous nature of subjective judgments in a convenient manner. PROMETHEE is a well-known and widely used outranking method, but it has not been investigated in depth within the interval-valued intuitionistic fuzzy environment. Based on the concepts of inclusion comparison possibilities, this paper proposes inclusion-based generalized criteria to determine preference functions and global preference indices for acquiring leaving flows, entering flows, and net flows of alternative actions. Using the score functions and accuracy functions of the flows, this paper develops IVIF-PROMETHEE I and IVIF-PROMETHEE II, which are methods for the partial ranking and complete ranking, respectively, of alternatives. The feasibility and applicability of the proposed methods are illustrated through a problem on the selection of bridge construction methods. Finally, a comparative discussion of other decision-making methods is conducted to demonstrate the advantages of the proposed IVIF-PROMETHEE methods.