Micanorm aggregation operators: basic logico-algebraic properties

This paper investigates basic logico-algebraic properties of micanorms. For this, as preliminaries, we first introduce micanorms and consider their logic related properties such as conjunctiveness, left-continuity, and continuity. We then give a characterization of left-continuous micanorms and consider two kinds of micanorm analogues of the Ł ukasiewicz, Gödel, and product t-norms and their residuated implications. We finally generalize basic algebraic concepts of t-norms and t-conorms to those of micanorms and investigate related properties, along with those of the micanorm analogues.