On the generalized law of O-conditionality for interval fuzzy implications

Abstract

Interval fuzzy implications play an important role in both theoretical and applied communities of interval-valued fuzzy sets and have been widely studied. Recently, Dimuro et al. analyzed the law of O-conditionality for fuzzy implications in general. However, there is no corresponding researches about the interval extension. To fill the gap, in this paper, we introduce the generalized law of O-conditionality 𝕆 ( X , 𝕀 ( X , Y ) ) ≤ Y (GOC), where 𝕀 is an interval fuzzy implication and 𝕆 is an interval overlap function. Meanwhile, we discuss the advantages one may get using it. Moreover, we consider the conditional antecedent boundary condition (CABC) for interval fuzzy implications derived from interval overlap and grouping functions, including, interval R 𝕆 - , ( 𝔾 , ℕ ) - , ( 𝕆 , 𝔾 , ℕ ) - and ( 𝔾 , 𝕆 , ℕ ) - implications. Finally, we further analyze the generalized law of O-conditionality for these four classes of interval fuzzy implications.