A Novel Approach of Picture Fuzzy Sets with Unknown Degree of Weights based on Schweizer-Sklar Aggregation Operators.

Abstract

This work aims to present some new aggregation operators (AOs) by generalizing the theory of Schweizer-Sklar (SS) aggregation tools. The picture fuzzy set (PFS) is the modified version of intuitionistic fuzzy sets and fuzzy sets. The PFS can handle such situations with three components of human opinion to mitigate the impact of insufficient information on human opinions. By utilizing concepts of prioritization, several mathematicians proposed different AOs. Some realistic operations of SS are presented under the picture fuzzy (PF) information system. We develop a class of new approaches based on picture fuzzy information, including picture fuzzy Schweizer-Sklar prioritized average (PFSSPA) and picture fuzzy Schweizer-Sklar prioritized geometric (PFSSPG) operators. Moreover, we also proposed a series of AOs with specific degrees of weights, such as picture fuzzy Schweizer-Sklar prioritized weighted average (PFSSPWA) and picture fuzzy Schweizer-Sklar prioritized weighted geometric (PFSSPWG) operators. Some realistic characteristics and special cases of currently developed approaches are also presented. To demonstrate the solution to complicated real-life problems, an algorithm for the MADM problem is established under a system of picture-fuzzy information. To check the potential of proposed aggregation approaches, we gave a numerical example to select desirable optimal options by using invented approaches. To reveal the flexibility and applicability of invented approaches, sensitive analysis, and comparative analysis are illustrated by contrasting the findings of existing approaches with currently developed approaches.