Some New Approaches to Solve Decision Making Problems under Pythagorean Fuzzy Set Environment

Abstract

The objective of this thesis entitled, Some New Approaches to Solve Decision Making Problems Under Pythagorean Fuzzy Set Environment , is to study new notions of Pythagorean Fuzzy soft matrices and information measures with their applications in decision making processes. The way we think, we process information, we make our decision and particularly in our language, fuzziness can be found everywhere. In real world scenario, decision making is the biggest challenge now a days due to its significance and importance everywhere such as in companies, in industries, in institutions and many more. Thus it is the need of the hour to handle uncertainty, vagueness and impreciseness involved in the decision making problems by developing some new techniques. The reported work in the thesis is classified into two categories: one is related to the notion of soft matrices and other is related to the information measures.The main goal of the thesis is to deal with the uncertainty,vagueness and impreciseness available in the informational data and solve the multi-criteria decision making problems. For handling such circumstances, we have utilized the several extensions of fuzzy set theory as Pythagorean fuzzy set. The work related to the thesis is described as, We have presented the preliminaries related to the proposed work, which covers all the basic definitions related to the extensions of fuzzy set theory to Pythagorean fuzzy set along with the literature reviewed on the soft matrices and information measure such as entropy, divergence. we have developed the new kind of soft matrix called Pythagorean fuzzy soft matrix with its different possible types and also presented binary operations satisfying various properties with the proof of their validity. Some new kinds of matrices such as choice matrix, weighted choice/score matrix, and utility matrix have also been proposed in a modified format.