An approach toward consistency degrees of fuzzy theories

In fuzzy logic-in wider, but also in narrow sense-the problem of consistenc y has been discussed more or less occasionally from different points of vie w. Up to now, however, it has usually not been taken as really important. T his may be partly caused by a rather restricted understanding of what is to be meant by consistency or inconsistency in fuzzy logic in the wider sense -e.g, in fuzzy control as one of the main applicational fields of fuzzy log ic. In this paper we deal with fuzzy theories in the realm of the fuzzy logic i n narrow sense. Based on the fact that usually an "interactive", t-norm bas ed conjunction is considered together with the min-based conjunction one ha s in a natural way two different consistency condition. We look here at the weaker one.