Similarity, Cardinality and Entropy for Bipolar Fuzzy Set in the Framework of Penta-valued Representation

TL;DR

This paper introduces new similarity, cardinality, and entropy measures for bipolar fuzzy sets and their variants within a penta-valued logic framework, along with a new distance measure for bounded real intervals.

Contribution

It presents novel measures for bipolar fuzzy sets based on multi-valued logic, expanding the tools for fuzzy set analysis in a penta-valued logic context.

Findings

New similarity, cardinality, and entropy measures introduced.

A new distance measure for bounded real intervals developed.

Framework applicable to various fuzzy set types like intuitionistic and paraconsistent.

Abstract

In this paper one presents new similarity, cardinality and entropy measures for bipolar fuzzy set and for its particular forms like intuitionistic, paraconsistent and fuzzy set. All these are constructed in the framework of multi-valued representations and are based on a penta-valued logic that uses the following logical values: true, false, unknown, contradictory and ambiguous. Also a new distance for bounded real interval was defined.