A new integrated methodology for constructing linguistic pythagorean fuzzy statements for decision making problems

Abstract

As a combining concept of Pythagorean fuzzy sets (PFSs) and linguistic fuzzy sets (FSs), linguistic PFSs (LPFSs) has been suggested in the literature to deal with the uncertain and inconsistent information in multi-criteria decision making (MCDM) process. The LPFSs based procedure has been built by assuming that the experts make assessments suitable with PFS. It does not provide a mechanism to ensure the suitability of the assessments with theory of PFSs but there are other type of non-standard fuzzy sets such as Neutrosophic sets (NSs) used for modeling with inconsistent information. The main motivation of this study is to offer an assessment collection method to guarantee that the input statements will be Pythagorean fuzzy linguistic expressions. As a second motivation, it is aimed to extend the PFS method for the fuzzy modeling of the other type of decision-making problems apart from MCDM which do not require aggregation and comparison operations and continue with precise fuzzy modeling (PFM). The third motivation of this study is to offer enhancements on the LPFSs method to increase the sensitivity of the modeling while protecting the interpretability. For these purposes, a new methodology based on LPFSs has been proposed and applied on a decision-making problem in a comparative way.