Enhancing PROMETHEE method with intuitionistic fuzzy soft sets

Abstract

The notion of intuitionistic fuzzy soft sets (IFSSs) provides an effective tool for solving multiple attribute decision making with intuitionistic fuzzy information. The most crucial issue in decision making based on IFSSs is how to derive the ranking of alternatives from the information quantified in terms of intuitionistic fuzzy values. In this study, we propose a new extension of the preference ranking organization method for enrichment evaluation (PROMETHEE), by taking advantage of IFSSs. In addition to presenting a myriad of new notions, such as intuitionistic fuzzy membership (or nonmembership) deviation matrices, intuitionistic fuzzy membership (or nonmembership) preference matrices, and aggregated intuitionistic fuzzy preference matrices, we put more emphasis on the construction of three distinct preference structures and related utility functions on the corresponding weakly ordered sets by considering the positive, negative, and net flows of the alternatives based on the aggregated intuitionistic fuzzy preference matrix. We present a new algorithm for solving multiple attribute decision-making problems with the extended PROMETHEE method based on IFSSs. Moreover, a benchmark problem concerning risk investment is investigated to give a comparative analysis and show the feasibility of our approach. K E Y W O R D S decision making, intuitionistic fuzzy set, outranking, PROMETHEE, soft set | INTRODUCTIONDecision making is a ubiquitous activity in daily life, which can be seen as a process of ranking a collection of alternatives or selecting the optimal one(s) from them based on the provided decision information. Multiple attribute decision making (MADM) refers to the decisionmaking process in which alternatives are evaluated by virtue of several attributes, reflecting the performance of alternatives from independent perspectives. In the MADM process, it is of vital importance to reconcile the contradictory goals, make decisions with many criteria, and strive for compromise solutions. 1 Up to now, researchers around the world have paid much attention to MADM problems and have attained fruitful results in diverse aspects. 2 For instance, Liu et al 3 proposed a model for evaluating and selecting a transport service provider based on singlevalued neutrosophic numbers. Using linguistic neutrosophic numbers, Pamučar et al 4 presented an enhanced combinative distance-based assessment (CODAS) decision-making approach and a pairwise model for determining the weights of criteria. Pamučar et al 5 defined the normalized weighted geometric Bonferroni mean operator of interval rough numbers and developed a hybrid decision-making method involving interval rough decision-making trial and evaluation laboratory (DEMATEL) and complex proportional assessment (COPRAS) models. With the integrated use of the full consistency method (FUCOM) and fuzzy multiattributive border approximation area comparison (MABAC) method, Božanić et al 6 developed a decision-making model for selecting the most favorable location in single-span Baile...

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