The compromise solution of the multi-criteria decision-making (MCDM) problem by the existing VIKOR method for Pythagorean fuzzy sets (PyFSs) is not closest to the positive ideal solution. This is because the defining function for VIKOR does not obey the axioms for a dissimilarity measure. Thus in this context, the existing notion of dissimilarity measures and the VIKOR method are controversial. This study aims to provide a new dissimilarity measure and refine the VIKOR method for PyFSs accordingly. We define a new dissimilarity measure for PyFSs and refine the existing VIKOR method. We discuss the additional properties of dissimilarity measures and improve the ideas of remoteness and ranking indexes. We provide numerical examples to support the analysis and findings of our study. Finally, we solve the MCDM problems to illustrate the proposed method.

Despite the importance of divergence measures, the literature has not provided a satisfactory formulation for the case of q-rung orthopair fuzzy set. This paper criticizes the existing attempts in terms of respect of the basic axioms of a divergence measure. Then new improved, axiomatically supported divergence measures for qROFSs are proposed. Additional properties of the new divergence measures are discussed to guarantee their good performance. The transformation relationships with entropy and dissimilarity measures are debated. The multiattribute border approximation area comparison decision method is extended based on the suggested divergence measures, and it is applied to the selection of all-rounder cricketer for a team.

The q-rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set and Pythagorean fuzzy sets. In this paper, we define the knowledge measure for qROFS by using the tangent inverse function. This is the first approach to quantify the knowledge associated with qROFS. The membership and nonmembership functions as well as the hesitancy margin are used to define the knowledge measure which makes it capable of considering both knowledge and fuzziness. The entropy measure which is the dual of the knowledge measure is also defined. The properties of the proposed knowledge measure with graphical explanations are discussed. An application of the proposed knowledge measure in multiattribute group decision making problem under confidence level approach is given.