Bipolar picture fuzzy sets and relations with applications

Abstract

The notions of both the bipolar fuzzy sets and picture fuzzy sets have been studied by many authors, the bipolar picture fuzzy set is the nice combination of these two notions. Basically, the concepts we present in our study are the direct extensions of both the bipolar fuzzy sets and picture fuzzy sets. In this study, we add few more operations and results in the theory of the bipolar picture fuzzy sets. We also initiate the notion of bipolar picture fuzzy relations along with their applications. We present numerous basic operations along with the algebraic sums, bounded sums, algebraic product, bounded difference on bipolar picture fuzzy sets. Different types of distances between two bipolar picture fuzzy sets are also addressed. We provide the application of bipolar picture fuzzy sets towards decision making theory along with its algorithm. Afterward, we introduce different types of bipolar picture fuzzy relations like bipolar picture fuzzy reflexive, symmetric and transitive relations. Subsequently, we introduce the concepts of the bipolar picture fuzzy equivalence relation and partition. We also produce numerous interesting results based on these relations. Finally, we establish the criteria for the detection of covid-19 at the base of bipolar picture fuzzy relations.

Keywords

• bipolar picture fuzzy sets
• ring sum of bipolar picture fuzzy sets
• bipolar picture fuzzy equivalence relation
• bipolar picture fuzzy partition
• distances between bipolar picture fuzzy sets