Preserving T-transitivity

This contribution deals with the problem of aggregating T-equivalence relations, in the sense that we are looking for functions that preserve reflexivity, symmetry and transitivity with respect to a given t-norm T. Under any extra condition on the t-norm, we obtain a complete description of those functions in terms of that we call T-triangular triplets.Peer ReviewedPostprint (author's final draft

Computing a T-transitive lower approximation or opening of a proximity relation

Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Fuzzy Sets and Systems. IMPACT FACTOR: 1,181. Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the more number of elicitations, the more probable inconsistency is. This is mostly the case within a fuzzy framework, even when the number of alternatives or object to be classified is relatively small. In this paper we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, being T any left-continuous t-norm. The computed approximation we propose will take O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors¿ knowledge, there are no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties

T-Funtions of several variables: New Criteria for Transitivity

The paper presents new criteria for transitivity of T-functions of several variables. Our approach is based on non-Archimedean ergodic theory. The criteria: for any 1-lipschitz ergodic map $F:\, \mathbb{Z}^{k}_{p} \mapsto \mathbb{Z}^{k}_{p},\;k>1\in\mathbb{N},$ there are 1-lipschitz ergodic map $G:\, \mathbb{Z}_{p} \mapsto \mathbb{Z}_{p}$ and two bijection $H_k$, $T_{k,\;P}$ that $$G = H_{k} \circ T_{k,\;P}\circ F\circ H^{-1}_{k} \text{and} F = H^{-1}_{k} \circ T_{k,\;P^{-1}}\circ G\circ H_{k}.$$Comment: arXiv admin note: text overlap with arXiv:1112.5089 by other author