On the composition of intuitionistic fuzzy relations

✍ Scribed by Glad Deschrijver; Etienne E. Kerre

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 343 KB
• Volume: 136
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(02)00269-5

✦ Synopsis

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 deÿned by Atanassov (Instuitionistic Fuzzy Sets, Physica-Verlag, Heidelberg, New York, 1999), give us a way to incorporate uncertainty in an additional degree. Intuitionistic fuzzy relations are intuitionistic fuzzy sets in a cartesian product of universes.

One of the main concepts in relational calculus is the composition of two relations. Burillo and Bustince (Fuzzy Sets and Systems 78 (1996) 293; Soft Comput. 2 (1995) 5) have extended the sup-T composition of fuzzy relations to a composition of intuitionistic fuzzy relations. In this paper, we present an intuitionistic fuzzy version of the triangular compositions of Bandler and Kohout (in: