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We show how noncontradiction and excluded-middle laws can hold in a fuzzy logic where the concepts of contradiction and incompatibility are clearly distinguished. However, if we want to avoid self-contradictions in fuzzy set theory then one needs to consider only Ž fuzzy sets with supremum 1 and infimum 0. We clarify in this new context on which the . applications usually take place which logical connectives make sense. Q 2000 John Wiley & Sons, Inc.

On logical connectives for a fuzzy set theory with or without nonempty self-contradictions