Title：Micanorm aggregation operators
Abstract: Yager introduced a generalization of uninorms, a variant of the concept of uninorm obtained by removing the associativity condition in its definition: he (1994a; 1994b) introduced a class of MICA (Monotonic Identity Commutative Aggregation) operators, and claimed that MICA operators constitute the basic operators needed for aggregation in fuzzy system modeling. Recently, Yang (2015) introduced micanorms as binary MICA operations. In particular, he (2009; 2016; 2017) has introduced micanorms with three weak forms of associativity and micanorm analogues of the Lukasiewicz, Goedel, and Product t-norms. Note that Yang's investigations in Yang (2009; 2015; 2016; 2017) concentrate on introducing logical systems based on such micanorms and their corresponding standard algebraic semantics, whereas his works do not concentrate on introducing good examples for such micanorms and their algebraic properties.
The main purpose of the paper is to provide more thorough investigation of basic algebraic properties of micanorms introduced by Yang. For this, we organize the paper as follows. In Section 2, we first recall the definitions of micanorms in general, micanorms with three weak forms of associativity, and Lukasiewicz, Goedel, and Product weak e-associative (wea-) uninorms. In Section 3, we introduce micanorm analogues of the Lukasiewicz, Goedel, and Product t-norms and investigate some characteristic algebraic properties of those analogues.
Department of Philosophy
Jeonbuk National University
Jeonju, 54896, South Korea
Eunsuk Yang received his Ph.D. in Department of Philosophy from Yonsei University in 1997, visited Indiana University (Bloomington), IN, USA, in 2001-2002 as a postdoctoral researcher, and is an Associate Professor of Philosophy Department at Jeonbuk National University, Jeonju, South Korea. His research interests include non-classical logics, in particular, fuzzy logic, substructural logic, relevance logic, and algebraic logic. He has published many articles in journals and conference proceedings in these research areas.