Information measures for <i>q</i> ‐rung orthopair fuzzy sets

TLDR

The q‑rung orthopair fuzzy set (q‑ROFS) extends Pythagorean fuzzy sets, offering greater capability for handling real‑world uncertainty. This study aims to explore the interrelations among distance, similarity, entropy, and inclusion measures for q‑ROFSs and to systematically transform these information measures. The authors derive new formulae for these measures and validate the similarity metric through applications in pattern recognition, clustering, and medical diagnosis. Illustrative examples confirm the validity and practical usefulness of the proposed similarity measure between q‑ROFSs.

Abstract

The q-rung orthopair fuzzy set (q-ROFS), originally developed by Yager, is more capable than that of Pythagorean fuzzy set to deal uncertainty in real life. The main goal of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for q-ROFSs. The primary purpose of the study is to develop the systematic transformation of information measures (distance measure, similarity measure, entropy, and inclusion measure) for q-ROFSs. For obtaining this goal, some new formulae for information measures of q-ROFSs are presented. To show the validity of the explored similarity measure, we apply it to pattern recognition, clustering analysis, and medical diagnosis. Some illustrative examples are given to support the findings, and also demonstrate their practicality and availability of similarity measure between q-ROFSs.