A Hybrid Method for Pythagorean Fuzzy Multiple-Criteria Decision Making

Abstract

As a generalization of intuitionistic fuzzy set, the Pythagorean fuzzy set is interesting and very useful in modeling uncertain information in real-world decision-making problems. In this paper, we develop a new method for Pythagorean fuzzy multiple-criteria decision-making (MCDM) problems with aggregation operators and distance measures. First, we present the Pythagorean fuzzy ordered weighted averaging weighted average distance (PFOWAWAD) operator. The main advantage of the PFOWAWAD operator is that it uses distance measures in a unified framework between the ordered weighted averaging (OWA) operator and weighted average (WA) that considers the degree of importance of each concept in the aggregation. Some of its main properties and special cases are studied. Then, based on the proposed operator, a hybrid TOPSIS method, called PFOWAWAD-TOPSIS is introduced for Pythagorean fuzzy MCDM problem. Finally, a numerical example is provided to illustrate the practicality and feasibility of the developed method.

Intuitionistic Linguistic Multiple Attribute Decision-making Based on Heronian Mean Method and Its Application to Evaluation of Scientific Research Capacity

“…It generalizes a wide range of aggregation operators such as the generalized mean, the OWA and the ordered weighted geometric (OWG) operator. The GOWA operator has been studied by various authors (Beliakov, Pradera and Calvo, 2007;Merigo and Yager, 2013;Peng, Gao and Gao, 2013;Zeng, Chen and Li, 2016). Another interesting aggregation operator is the Heronian mean (HM), which is developed to deal with the exact numerical values (Beliakov, Pradera and Calvo, 2007).…”

Some Generalized Pythagorean Fuzzy Bonferroni Mean Aggregation Operators with Their Application to Multiattribute Group Decision-Making

“…Table 2 presents further details. Table 2 shows that the aggregation operators introduced in [23][24][25][26] cannot consider the interrelationship among PFNs. Although PFCIA and PFCIG can capture the interrelationship among all PFNs, they only focus on changing the weight vector of the aggregation operators.…”

“…Ma and Xu [24] introduced new score and accuracy functions of PFNs and developed the symmetric Pythagorean fuzzy weighted averaging (SPFWA) operator and the symmetric Pythagorean fuzzy weighted geometric (SPFWG) operator. Zeng et al [25] introduced the Pythagorean fuzzy ordered weighted averaging weighted average distance (PFOWAWAD) operator, from which a hybrid TOPSIS method was proposed for the Pythagorean fuzzy MAGDM problems. Garg [26] introduced the Pythagorean fuzzy Einstein operations and developed a few new Pythagorean fuzzy aggregation operators.…”

Fuzzy decision making: A bibliometric-based review

“…We can point out Intuitionistic fuzzy sets [36], Decision-making in a fuzzy environment [3], Multiple attribute decision-making [11], On ordered weighted averaging aggregation operators in multi-criteria decision-making [15], Families of OWA operators [37], Fuzzy sets [1], The concept of a linguistic variable and its application to approximate reasoning-I-II-III [4][5][6], Fuzzy sets as a basis for a theory of possibility [9], Results of empirical studies in fuzzy set theory [38], Fuzzy sets and decision analysis [39], Fuzzy sets, decision-making and expert systems [7], Fuzzy preference orderings in group decision-making [40], Group decision-making with a fuzzy linguistic majority [41], The analytic hierarchy process [42][43][44], Aggregation methods for decision-making [45], Intuitionistic fuzzy information aggregation [46], Linguistic information context [47], Intuitionistic fuzzy with probabilistic and OWA operator [48], New extension of OWAD operator [49] and Hybrid method for fuzzy decision making [50].…”