Basic fuzzy logics and weak associative uninorms

Micanorm-based logics with a weak form of associativity are introduced and their completeness results are addressed. More concretely, first the basic wa_t-uninorm logic WA_t BUL and its axiomatic extensions are introduced as [0, t]-continuous wa_t-uninorm analogues of the logics based the [0, 1)-continuous uninorms. Next algebraic structures char-acterizing the logics are introduced along with algebraic completeness results. Third, wa_t-uninorms are introduced as uninorms with weak t-associativity instead of associativity and associated properties are discussed. Finally, by virtue of Yang–style construction, it is verified that the logics based on wa_t-uninorms are complete on unit real interval [0, 1], i.e., so called standard complete.