University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 21 3 2024 06 01 Basic fuzzy logics and weak associative uninorms 123 136 8386 10.22111/ijfs.2024.47834.8417 EN Eunsuk Yang Department of Philosophy & Institute of Critical Thinking and Writing, Chonbuk National University, Rm 417, Colleges of Humanities & Social Science Blvd., Jeonju, 561-756, KOREA Journal Article 2024 01 27 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 \textbf{WA$_{\textbf{t}}$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 characterizing 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 \emph{standard} complete. https://ijfs.usb.ac.ir/article_8386_817df71eda0a2ab8e7deca04710281a6.pdf