ON NORMAL FORM BASED INTERVAL-VALUED FUZZY SETS AND THEIR APPLICATIONS TO APPROXIMATE REASONING

Abstract

In this paper, normal form based interval-valued fuzzy sets, which is initiated by Turksen in 1986, are investigated. It is shown that DNF(•) ⊆ CNF(•) holds for a newly introduced family, called g-family, of conjugate pairs of t-norms and t-conorms. Interval-valued fuzzy set (IVFS) based approximate reasoning is also studied. The generalized compositional rule of inference (GCRI) is applied into interval-valued reasoning. It is proved that Modus Ponens and Syllogism hold for IVFS based GCRI, and we conclude that using GCRI with respect to the g-family is quite reasonable for IVFS based approximate reasoning.