Document Type : Research Paper
Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Bahonar University of Kerman, Kerman, Iran
Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, Radlinskeho 11, 810 05 Bratislava, Slovakia
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.