A Survey on Generalized Fuzzy Parameter-Based Fractional Programming Problem

Vaishaly Verma () and Pitam Singh
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Vaishaly Verma: Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Paryagraj (UP), 211004, India
Pitam Singh: Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, Paryagraj (UP), 211004, India

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 01, 281-321

Abstract: In fuzzy sets, the elements of a universal set may belong to that set completely, may not belong to that set, or may belong partially. Therefore, fuzzy sets are called generalizations of crisp sets. Due to the diverse nature of problems in real-world situations, fuzzy set theory is found to be unable to address some of the other features of ambiguity. Therefore, researchers extended fuzzy sets to picture fuzzy sets, orthopair, intuitionistic, Pythagorean, Fermatean, neutrosophic, spherical fuzzy sets, etc. Real-world problems can be solved using the method of fractional programming. Decision-makers are trying to get good results using generalized fuzzy numbers in fractional programming problems; hence, this review paper provides a specific framework for generalized fuzzy sets and generalized fuzzy fractional programming problems. Furthermore, it is a platform for researchers who want to work on generalized fuzzy parameter-based fractional programming problems. This research paper summarizes all the basic concepts and prior research on fractional programming and generalized fuzzy linear fractional programming problems.

Keywords: Fuzzy set; basic concepts of fuzzy sets; linear fractional programming problem; fuzzy numbers; generalized fuzzy sets (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500152

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