%0 Journal Article
%T A note on divisible discrete triangular norms
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Kouchakinejad, F.
%A Stupnanova, A.
%A Seliga, A.
%D 2022
%\ 02/01/2022
%V 19
%N 1
%P 73-81
%! A note on divisible discrete triangular norms
%K Discrete I-semigroup
%K divisible t-norm
%K divisible t-conorm
%K finite chain
%R 10.22111/ijfs.2022.6552
%X Triangular norms and conorms on [0,1] as well as on finite chains are characterized by 4 independent properties, namely by the associativity, commutativity, monotonicity and neutral element being one of extremal points of the considered domain (top element for t-norms, bottom element for t-conorms). In the case of [0,1]domain, earlier results of Mostert and Shields on I-semigroups can be used to relax the latest three properties significantly, once the continuity of the underlying t-norm or t-conorm is considered. The aim of this short note is to show a similar result for finite chains, we significantly relax 3 basic properties of t-norms and t-conorms (up to the associativity) when the divisibility of a t-norm or of a t-conorm is considered.
%U https://ijfs.usb.ac.ir/article_6552_212cf3ae3695a65bcb7510f17d629c1d.pdf