Archimedean components of triangular norms
نویسندگان
چکیده
The Archimedean components of triangular norms (which turn the closed unit interval into an abelian, totally ordered semigroup with neutral element 1) are studied, in particular their extension to triangular norms, and some construction methods for Archimedean components are given. The triangular norms which are uniquely determined by their Archimedean components are characterized. Using ordinal sums and additive generators, new types of left-continuous triangular norms are constructed. 2000 Mathematics subject classification: primary 20M05; secondary 03E72.
منابع مشابه
Associativity of Triangular Norms in Light of Web Geometry
The aim of this paper is to promote web geometry and, especially, the Reidemeister closure condition as a powerful and intuitive tool characterizing associativity of the Archimedean triangular norms. In order to demonstrate its possible applications, we provide the full solution to the problem of convex combinations of nilpotent triangular norms. Keywords— Archimedean triangular norm, web geome...
متن کاملTriangular norms. Position paper III: continuous t-norms
This third and last part of a series of position papers on triangular norms (for Parts I and II see [25, 26]) presents the representation of continuous Archimedean t-norms by means of additive generators, and the representation of continuous t-norms by means of ordinal sums with Archimedean summands, both with full proofs. Finally some consequences of these representation theorems in the contex...
متن کاملOn the Distributivity of Fuzzy Implications over Continuous Archimedean Triangular Norms
Recently, the distributivity of fuzzy implications over t-norms, t-conorms and uninorms was studied in many articles. In this paper we characterize functions which satisfy one of the four generalized distributivity equations of classical implication in the case when t-conorms are continuous and Archimedean. Using the obtained characterizations we describe some solutions which are fuzzy implicat...
متن کاملTriangular norms. Position paper I: basic analytical and algebraic properties
We present the basic analytical and algebraic properties of triangular norms. We discuss continuity as well as the important classes of Archimedean, strict and nilpotent t-norms. Triangular conorms and De Morgan triples are also mentioned. Finally, a brief historical survey on triangular norms is given. Submitted for publication Johannes Kepler Universität Linz Fuzzy Logic Laboratorium Linz-Hag...
متن کاملOn computation of the compositional rule of inference under triangular norms
This paper is devoted to the derivation of exact calculation formulas for the compositional rule of inference under Archimedean t-norms, when both the observation and the relation parts are given by Hellendoorn’s φ-function [6].
متن کامل