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.

Intuitionistic fuzzy sets (IFSs) have advantage over fuzzy sets and made it possible to describe imprecise information considering its positive and negative aspects simultaneously. In an information system mass assignment and possibility theory are very useful to assign membership grades to elements in a fuzzy set. Unfortunately the situation differs for IFSs in assigning membership function (MF) and nonmembership function (NMF). In this paper, it is shown that the above-mentioned theories fail to produce the MF and NMF for IFSs. Aim of this paper is to present an alternate algorithm to generate these grading functions based on q-rung orthopair fuzzy set. Consequently, it will be extremely convenient to model imprecise and vague information using this approach.

Molodtsov investigated the pioneer notion of soft set (SfS) which provides a general framework for mathematical problems by affix parameterization tools during the analysis as compared to fuzzy set and q-rung orthopair fuzzy set (q-ROFS). The aim of this manuscript is to investigate the notion of q-rung orthopair fuzzy soft set (q-ROFSfS), which provide a lay of foundation for those difficulties and complexities which the contemporary theories face during the study of uncertainty. Therefore, our main contribution in this manuscript is to investigate the q-rung orthopair fuzzy soft weighted averaging, q-rung orthopair fuzzy soft ordered weighted averaging and q-rung orthopair fuzzy soft hybrid averaging operators in q-ROF soft (q-ROFSf) environment. Further, the fundamental properties of these aggregation operators are studied. On the base of developed approach an algorithm for multicriteria decision making method is being presented. An application of medical diagnosis problems is solved on the proposed algorithm under the q-ROFSf environment. Finally, comparison between the developed operators with some existing operators are being presented showing the superiority and efficiency of the developed approach than the existing literature.

Many different types of ranking methods based on the score and accuracy functions of intuitionistic fuzzy values (IFVs) exist in the literature. The notion of knowledge bases, as in the case of rough set theory, is very handy to show that every ranking technique produces a unique classification of IFVs with a unique order among the classes. This means these rankings give rise to unique knowledge bases. Therefore, ranking of IFVs by two or more distinct techniques may produce different results. In this study, a graphical ranking method based on the uncertainty index and entropy is proposed. This approach is tested on several numerical examples existing in the literature and shown to be intuitive and convenient for applications in real-life scenarios.

In this paper, two new approaches have been presented to view q-rung orthopair fuzzy sets. In the first approach, these can viewed as L-fuzzy sets, whereas the second approach is based on the notion of orbits. Uncertainty index is the quantity , which remains constant for all points in an orbit. Certain operators can be defined in q-ROF sets, which affect when applied to some q-ROF sets. Operators , , and have been defined. It is studied that how these operators affect when applied to some q-ROF set A.