Interval-Valued Fuzzy Matrices

In a conventional fuzzy set, the membership value is a single point, and it is determined by the decision maker. Obviously, it is well known that determination of membership values is a very difficult task and it completely depends on the mentality of the decision maker, time, place, and many other parameters. Sometimes, the measurement becomes impossible due to the rapid variation of the characteristics of the system whose membership values are to be determined. To make it more realistic and keeping in mind the above situations, Sambue (Fonctions ø-floues. Application l’aide au diagnostic en pathologie thyroidienne, Ph. D. Thesis, University of Marseille, France, 1975) has introduced interval-valued fuzzy sets (IVFS). The basic idea of IVFS is to replace crisp membership degrees within [0, 1] by interval in [0,1]. So, in IVFS, the membership degree is a subset of the closed interval [0,1]. For this set, the determination of membership degree becomes easy, but it increases the uncertainty.