Transitive Closure of Interval-valued Fuzzy Relations

Abstract

In this paper are introduced some concepts of interval-valued fuzzy relations and some of their properties: reflexivity, symmetry, T-transitivity, composition and local reflexivity. The existence and uniqueness of T-transitive closure of interval-valued fuzzy relations is proved. An algorithm to compute the T-transitive closure of finite interval-valued fuzzy relations is showed. Some properties and some examples is given for t-representable and t-pseudo representable generalized t-norms.

Keywords

• Generalized t-norms
• Interval-valued Fuzzy Relations
• Interval-valued Fuzzy Sets
• t-norms
• t-representable t-norms
• T-transitive closure