Affiliations:
School of Cyber Security and Computer, Hebei University, Baoding, P.R. China
Correspondence:
[*]
Corresponding author. Yifan Zhao, School of Cyber Security and Computer, Hebei University, Baoding, 071002, P.R. China, E-mail: wmk6905@sina.com.
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 etย 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
๐(X,โ๐(X,โY))โคY
(GOC), where
๐
is an interval fuzzy implication and
๐
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
R๐-,โ(๐พ,โโ)-,โ(๐,โ๐พ,โโ)-
and
(๐พ,โ๐,โโ)-
implications. Finally, we further analyze the generalized law of O-conditionality for these four classes of interval fuzzy implications.
Keywords: Interval fuzzy implications, O-conditionality, interval overlap and grouping functions
