Complex numbers can capture compound features and convey multifaceted information; thereby providing means for solving complicated problems. In this paper, we combine the degree of membership and a degree of non-membership of members of Intuitionistic Fuzzy Sets via complex numbers to characterize these fuzzy sets. This approach enables extending several concepts such as classical fuzzy sets, P...

Multi-criteria group decision-making is a process in which decision makers assess the performance of alternatives on the basis of conflicting criteria to opt the most worthy alternative as solution. TOPSIS and ELECTRE are effective and commonly used methods to solve multiple criteria decision-making problems. The aim of this study is to propose two new models, namely, complex Pythagorean fuzzy ...

Abstract The similarity measures are essential concepts to discuss the closeness between sets. Fuzzy and intuitionistic fuzzy dealt with incomplete inconsistent data more efficiently. With time in decision-making theory, a complex frame of environment that occurs cannot be specified entirely by these A generalization like Pythagorean set can handle such situation applicability this attracted re...

Recently, a new model based on Pythagorean fuzzy set (PFS) has been presented to manage the uncertainty in real-world decision-making problems. PFS has much stronger ability than intuitionistic fuzzy set to model such uncertainty. In this paper, we define some novel operational laws of PFSs and discuss their desirable properties. For the multicriteria decision-making problems with PFSs, we prop...

In this paper we present a short but important summary of Pythagorean fuzzy sets. Especially we discuss several basic and important definitions of Pythagorean fuzzy sets, several operations on Pythagorean fuzzy sets, several algebraic laws of Pythagorean fuzzy sets. In the last we also present the concept of modal operators and normalization on Pythagorean fuzzy sets.

Dimensional analysis under linguistic Pythagorean fuzzy set (DA-LPFS) is a technique to handle qualitative (intangible) as well the interactions between criteria, by combining dimensional (DA) and (PFS) with variables. In this paper, novel DA method proposed for LPFSs based in PFS extension, order consider mutual relationship among criteria (fuzzy) quantitative (crisp) information usually invol...

In this paper, we present two Pythagorean fuzzy averaging aggregation operators such as, Pythagorean fuzzy weighted averaging (PFWA) operator, Pythagorean fuzzy ordered weighted averaging (PFOWA) operator and also introduce some of their basic properties.

Pythagorean fuzzy sets provide stronger ability than intuitionistic fuzzy sets to model uncertainty information and knowledge, but little effort has been paid to conflict analysis of Pythagorean fuzzy information systems. In this paper, we present three types of positive, central, and negative alliances with different thresholds, and employ examples to illustrate how to construct the positive, ...

With respect to multi-attribute group decision making (MAGDM) problems in which the attribute values take form of Pythagorean fuzzy numbers, a new Pythagorean fuzzy aggregation operator called Pythagorean fuzzy induced generalized ordered weighted averaging (PFIGOWA) operator is proposed. Some desirable properties and families of the proposed operator are discussed. Furthermore, based on the pr...