Abstract
An extension of fuzzy implications and coimplications, called fuzzy boundary weak implications (shortly, fuzzy bw-implications), is introduced and discussed in this paper. Firstly, by weakening the boundary conditions of fuzzy implications and coimplications, we introduce the concept of fuzzy bw-implications. And then, we investigate some of their basic properties. Next, the concept of fuzzy pseudo-negations is introduced and the natural pseudo-negations of fuzzy bw-implications are investigated. Finally, the fuzzy bw-implications generated, respectively, by aggregation operators and generator functions are discussed in details. This work is motivated by the fact that in real applications there are used some operators which are not fuzzy implications. We hope that such an extension of fuzzy (co)implications can provide a certain theoretical foundation for the real applications.
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