Affiliations: College of Mathematics and Information Science, Shaanxi Normal University, Xi’an, P.R. China
Correspondence:
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Corresponding author. Hongjun Zhou, College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710119, P.R. China. E-mail: [email protected].
Abstract: Fuzzy implications play important roles in both theoretic and applied communities of fuzzy set theory and have been extensively investigated. Fuzzy coimplications, as the dual operators of fuzzy implications, have received, however, little attention in the literature and, to the best of our knowledge, (T, N)-coimplications and residual coimplications are the only well-studied classes. On the other hand, many studies show that not all properties of fuzzy implications can be dualized in the standard way to fuzzy coimplications while fuzzy coimplications play key roles in quantum B-algebras, BCK-algebras, Heyting-Brouwer logic, fuzzy expert systems, etc. The present paper chooses to stand in the line of research on fuzzy coimplications. The notion of (O, N)-coimplication, obtained by relaxing the t-norm T in a (T, N)-coimplication to be an overlap function O that is used to model the degree to which an object is simultaneously supported by two different classes in decision making and image processing, is introduced, and basic properties and characterizations of some subclasses of (O, N)-coimplications are obtained.
Keywords: Fuzzy coimplication, (O, N)-coimplication, overlap function
