Shannon entropy for intuitionistic fuzzy information

TL;DR

This paper extends Shannon entropy to intuitionistic fuzzy information by developing new formulas for distance, similarity, and information measures, introducing escort fuzzy information, and verifying the entropy's properties.

Contribution

It introduces a novel Shannon entropy formulation for intuitionistic fuzzy data, incorporating escort fuzzy information and satisfying key uncertainty conditions.

Findings

Shannon entropy for intuitionistic fuzzy information satisfies four key uncertainty conditions.

New formulas for distance and similarity of intuitionistic fuzzy information are proposed.

Measures for fuzziness and incompleteness are identified.

Abstract

The paper presents an extension of Shannon fuzzy entropy for intuitionistic fuzzy one. Firstly, we presented a new formula for calculating the distance and similarity of intuitionistic fuzzy information. Then, we constructed measures for information features like score, certainty and uncertainty. Also, a new concept was introduced, namely escort fuzzy information. Then, using the escort fuzzy information, Shannon's formula for intuitionistic fuzzy information was obtained. It should be underlined that Shannon's entropy for intuitionistic fuzzy information verifies the four defining conditions of intuitionistic fuzzy uncertainty. The measures of its two components were also identified: fuzziness (ambiguity) and incompleteness (ignorance).