β Scribed by H. Bustince
No coin nor oath required. For personal study only.
In this paper we present di erent theorems that allow us to build intuitionistic fuzzy relations on a set with predetermined properties, i.e. theorems that allow us to build re exive, symmetric, antisymmetric, perfect antisymmetric and transitive intuitionistic fuzzy relations from fuzzy relations with the same properties. We begin by recalling the intuitionistic fuzzy relations and their most important properties. We then recall the opposite process, i.e. the manner of obtaining fuzzy relations by means of Atanassov's operator from intuitionistic fuzzy relations. This problem leads us to deΓΏne partially included relations and important properties of these are presented. Next we enunciate the three most important intuitionistic fuzzy set construction theorems. We conclude the paper applying these theorems to the construction of re exive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations from fuzzy relations.
π SIMILAR VOLUMES
Fuzzy relations are able to model vagueness, in the sense that they provide the degree to which two objects are related to each other. However, they cannot model uncertainty: there is no means to attribute reliability information to the membership degrees. Intuitionistic fuzzy sets, as deΓΏned by Ata
The problem of information generalization in multicriteria decision making is considered in this paper. The information is uniΓΏed by fuzzy relations and the generalization is realized with the help of aggregation operators. Some of the most oftenly used operators are presented and their properties d
At the early stages of design process, several design concepts are proposed as potential solutions. The selection of the most appropriate one is based on their evaluation with respect to several con icting criteria. In this paper, we consider the case where the evaluations of design concepts with re