Building a class of fuzzy equivalence relations

International audienceIn this paper, we propose a practical method, given a strict triangular norm with a convex additive generator, for deriving a fuzzy equivalence relation whose reflexivity condition generalizes Ruspini's definition of fuzzy partitions. The properties of the relations, their comparison, their transitivity, the construction of fuzzy equivalence relations on cartesian products are presented. A large part of the paper is devoted to applications with fuzzy partitions defined on the real line. Several examples, including the fairy-tale problem from De Cock and Kerre [On (un)suitable fuzzy relations to model approximate equality, Fuzzy Sets and Systems 133 (2) (2003) 137-153], the comparison of colored objects and comfort situations are proposed

Characteristic of partition-circuit matroid through approximation number

Rough set theory is a useful tool to deal with uncertain, granular and incomplete knowledge in information systems. And it is based on equivalence relations or partitions. Matroid theory is a structure that generalizes linear independence in vector spaces, and has a variety of applications in many fields. In this paper, we propose a new type of matroids, namely, partition-circuit matroids, which are induced by partitions. Firstly, a partition satisfies circuit axioms in matroid theory, then it can induce a matroid which is called a partition-circuit matroid. A partition and an equivalence relation on the same universe are one-to-one corresponding, then some characteristics of partition-circuit matroids are studied through rough sets. Secondly, similar to the upper approximation number which is proposed by Wang and Zhu, we define the lower approximation number. Some characteristics of partition-circuit matroids and the dual matroids of them are investigated through the lower approximation number and the upper approximation number.Comment: 12 page

Graph ambiguity

In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved

ε-partitions and α-equivalences

The aim of this paper is to study a special type of fuzzy relations, the α-equivalences, as well as to consider the relation that connects these with the family of ε-partitions of the referential. Some classic equivalences between set, partitions and fuzzy relations are also studied