Construction of intuitionistic fuzzy relations with predetermined properties

In this paper we present different theorems that allow us to build intuitionistic fuzzy relations on a set with predetermined properties, i.e. theorems that allow us to build reflexive, 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 define 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 reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations from fuzzy relations. (C) 2000 Elsevier Science B.V. All rights reserved.