Complex probabilistic fuzzy set and their aggregation operators in group decision making extended to TOPSIS

Abstract

Randomness and fuzziness create uncertainty in the system at the same time. To combine randomness and cognitive uncertainty into a single paradigm and incorporate more data, this article focuses on developing complex probabilistic fuzzy set. The main intention of this article is to develop a method that can solve both statistical and non-statistical uncertainties. Statistical uncertainty depicts the type of uncertainty concerning the possibility of a future event occurring and non-statistical uncertainties denote the concept of partial truth and imprecise reason. Here, statistical uncertainty is given through probability and non-statistical uncertainty is denoted via the complex fuzzy sets and are incorporated together to form the complex probabilistic fuzzy set. This combination summarizes the importance of this article as they could depict the real life situations more precisely. Proposing the complex probabilistic fuzzy set and studying its basic operations are the article’s main contributions. Also, various aggregation operators are developed for the same and their essential properties are duely explained. Further on, these operators are extended to TOPSIS which is utilized for a group decision making problem with data obtained in the form of complex probabilistic fuzzy number to find the best site for construction of ethanol plant to produce biofuel. The main reason for considering TOPSIS here is because it is a concept that formulates a scalar value taking into consideration both the best and worst alternatives, it represents the rationale of human choice in a more simplistic and straightforward logic and also, it takes less computation time.