Abstract
In fuzzy logic-in wider, but also in narrow sense-the problem of consistency has been discussed more or less occasionally from different points of view. Up to now, however, it has usually not been taken as really important. This 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 logic. In this paper we deal with fuzzy theories in the realm of the fuzzy logic in narrow sense. Based on the fact that usually an "interactive", r-norm based conjunction is considered together with the min-based conjunction one has in a natural way two different consistency condition. We look here at the weaker one.
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