From Fuzzy Sets to Deep Learning: Exploring the Evolution of Pattern Recognition Techniques
Suhail Ahmad Ganai, Nitin Bhardwaj, Riyaz Ahmad Padder · Zenodo (CERN European Organization for Nuclear Research) · 2023
Fuzzy sets are a powerful tool for dealing with uncertainty and imprecision in various fields but their basic versions have limitations in representing complex and ambiguous information. This paper explores the significance and practical applications of fuzzy set extensions, including Intuitionistic Fuzzy Sets, Pythagorean Fuzzy Sets, and Fermatean Fuzzy Sets, among others, which overcome these limitations and enable more complex analysis. We also discuss operators on Intuitionistic Fuzzy Sets, establish theorems on their relations, and introduce a new distance measure which consider both membership and non-membership functions, highlighting its importance through a pattern recognition problem. The results showcase the potential of fuzzy set extensions, operators, and distance measures in gaining deeper insights into complex real-world systems and making informed decisions in various fields.