(T′,N)-Fuzzy Soft Implications, Fuzzy Soft Uninorms and (N′,T,N)-Fuzzy Soft Implications in Fuzzy Soft Logic

In 1999, Molodtsov first proposed soft set theory as an effective approach for dealing with uncertainties. Fuzzy soft set theory is developed vastly over time, combining ideas from soft set theory and fuzzy set theory to enhance decision-making. Recently, in fuzzy soft set theory, Acharjee and Medhi presented several advanced concepts regarding logical connectives. Here, we extend the findings of Acharjee and Medhi to address new developments in fuzzy soft logic, building on Molodtsov’s original concepts. In particular, we introduce the ideas of [Formula: see text]-fuzzy soft implication, [Formula: see text]-fuzzy soft implication, fuzzy soft uninorm, and [Formula: see text]-fuzzy soft operation in the context of fuzzy soft logic. Later, we study their various fundamental properties.