Logical connectives of fuzzy soft set theory

Abstract: Soft set theory, introduced by Molodtsov [Molodtsov, D. (1999). Soft set theory-first results. Comput. Math. Appl., 37(4-5), 19-31], provides a flexible framework for managing uncertainty and vagueness, addressing limitations in traditional approaches such as fuzzy set theory, rough set theory, and probability theory. Over time, fuzzy soft set theory has emerged as a significant extension, blending the principles of fuzzy set theory and soft set theory to support applications in various decision-making processes. This study revisits fuzzy soft set theory, addressing conceptual errors and inaccuracies in the definitions of t-norm, t-conorm, strong negation, and implication that deviated from Molodtsov's foundational principles. Corrected definitions-fuzzy soft t-norm, fuzzy soft t-conorm, fuzzy soft negation, and fuzzy soft implication-are proposed to ensure theoretical rigor. The paper rectifies conceptual errors in prior work by Ali and Shabir [Ali, M. I., Shabir, M. (2013). Logic connectives for soft sets and fuzzy soft sets. IEEE Transactions on Fuzzy Systems, 22(6), 1431-1442] and introduces refined results to strengthen the logical framework, providing a consistent foundation for future research and hybrid model development in this domain.