Pythagorean Fuzzy Information Measures and Their Applications

• Published in: International journal of intelligent systems Vol. 32; no. 10; pp. 991 - 1029
• Main Authors: Peng, Xindong, Yuan, Huiyong, Yang, Yong
• Format: Journal Article
• Language: English
• Published: New York Hindawi Limited 01-10-2017
• Subjects: Cluster analysis; Clustering; Diagnosis; Entropy; Fuzzy sets; Intelligent systems; Pattern recognition; Similarity; Similarity measures
• ISSN: 0884-8173; 1098-111X
• DOI: 10.1002/int.21880

Pythagorean fuzzy set (PFS), originally proposed by Yager, is more capable than intuitionistic fuzzy set (IFS) to handle vagueness in the real world. The main purpose of this paper is to investigate the relationship between the distance measure, the similarity measure, the entropy, and the inclusion measure for PFSs. The primary goal of the study is to suggest the systematic transformation of information measures (distance measure, similarity measure, entropy, inclusion measure) for PFSs. For achieving this goal, some new formulae for information measures of PFSs are introduced. To show the efficiency of the proposed 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 effectiveness of similarity measure between PFSs.