Mathematical analysis of interval-valued fuzzy relations: Application to approximate reasoning

In this paper, interval-valued fuzzy relations between sets X and Y are introduced as fuzzy subsets of the cartesian product X x Y, and t-norms and t-conorms are chosen in such a way that as many properties of relations in 2-valued logic are preserved. Besides, we will see that if we require certain reasonable properties, including distributivity, then we end up with the only possible choice: min and max. Finally, as an example, a method of inference in approximate reasoning for the one-dimensional case based on interval-valued fuzzy sets is considered and discussed using the idea of interval-valued fuzzy relations. (C) 2000 Elsevier Science B.V. All rights reserved.