Issue Details
SIGNIFICANCE AND PRACTICAL APPLICATIONS OF FUZZY SET EXTENSIONS
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Page No. : 55-70
ABSTRACT
Fuzzy sets are a powerful tool for coping with uncertainty and imprecision in a variety of disciplines, but their basic implementations are limited in their ability to represent complex and ambiguous data. This paper investigates the significance and practical applications of fuzzy set extensions, such as Intuitionistic Fuzzy Sets, Pythagorean Fuzzy Sets, and Fermatean Fuzzy Sets, which surmount these limitations and permit more complex analysis. In addition, we discuss operators on Intuitionistic Fuzzy Sets, establish theorems regarding their relationships, and introduce a new distance measure that takes into account both membership and non-membership functions, demonstrating its significance through a pattern recognition problem. The results demonstrate the potential of fuzzy set extensions, operators, and distance measures for obtaining a deeper understanding of complex real-world systems and making informed decisions in a variety of fields.
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