The Correct Structures in Fuzzy Soft Set Theory

Santanu Acharjee and Sidhartha Medhi ()
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Santanu Acharjee: Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India
Sidhartha Medhi: Department of Mathematics, Gauhati University, Guwahati 781014, Assam, India

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 01, 353-378

Abstract: In 1999, Molodtsov introduced soft set theory as a useful tool for handling uncertainty. Over time, it has been combined with fuzzy set theory to address complex problems involving vagueness. However, earlier attempts to define fuzzy soft sets contained errors that weakened the concept. This paper revisits Molodtsov’s ideas and presents a correct framework for fuzzy soft set theory. We refine key operations, such as union, intersection, complement, and various kinds of approximates; study their properties; and utilize matrix-based representations. The effectiveness of this improved framework is demonstrated through a practical example in decision-making.

Keywords: Fuzzy soft set; soft set (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005726500420

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