Picture Logic Operators and Implications on Fermatean Picture Fuzzy Sets
V. Chitra
Department of Mathematics, Nallamuthu Gounder Mahalingam College, (Affiliated to Bharathiar University), Pollachi, Tamil Nadu 642001, India.
B. Maheswari *
Department of Mathematics, Dr. Mahalingam College of Engineering and Technology, (Affiliated to Anna University), Pollachi, Tamil Nadu 642003, India.
*Author to whom correspondence should be addressed.
Abstract
Fermatean Picture Fuzzy sets (FPFS) represent an advanced extension of Picture Fuzzy sets and Pythagorean Picture Fuzzy sets, aimed at enhancing uncertainty modeling through the principles of Fermatean geometry. FPFS deliver heightened precision and adaptability rendering them highly applicable to complex decision-making, voting analysis and computational intelligence tasks. This work details the mathematical formulation of FPFS which explores their fundamental operations and demonstrates their practical relevance via numerical examples. The results highlight the efficacy of FPFS as a dynamic framework for resolving complex fuzzy logic challenges.
Keywords: Fermatean picture fuzzy sets, fuzzy logic, decision-making processes, membership functions, fuzzy set operations