Abstract
This paper investigates the cutability of the fuzzy relational compositions: the sup- T composition, the triangular compositions of Bandler and Kohout and their improved versions. The theoretical and practical importance of (fuzzy) α-cuts is illustrated by means of a careful selection of results from the fuzzy literature. Some new potential properties of fuzzy implications operators and triangular norms that play an important role in this cutability study are introduced and discussed extensively. The paper concludes with a study of the fuzzy cutability of the sup- T composition.
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