Abstract
In this paper new notions of fuzzy equivalences interpreted as fuzzy connectives are introduced. One of the axioms of such fuzzy equivalences is transitivity defined by the use of a fuzzy conjunction or both a fuzzy conjunction and a parameter α from the unit interval, that is why they are called fuzzy α–C-equivalences. In particular, fuzzy C-equivalences, fuzzy semi-C-equivalences as well as fuzzy weak C-equivalences are considered. Dependencies between the new types of fuzzy equivalences are presented. Moreover, the problem of preservation of axioms of such defined fuzzy equivalences by aggregation functions is examined. As a conclusion, ways of generating new fuzzy equivalences of the considered type from given ones are indicated.
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