Summary: | 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.
|