Abstract
On the basis of ontological and epistemological assumption, this chapter demonstrates that the equivalence between canonical forms breaks down in fuzzy set and logic theory. Archimedean t-norms and t-conorms admit an additive representation on the extended non-negative real numbers. The results of the representation of continuous t-norms by means of ordinal sums can be derived from results in the context of I-semigroups. are important in the sense that, the interval-valued fuzzy set construction does not yield higher order fuzziness than second order. If a t-norm, a t-conorm, and a negation function, n are related to each other, then such a triple is called a De Morgan Triple. The concern is whether the containment of FDCF in FCCF still holds in the fuzzy logic under a similar construction. If a valued relation is constructed from other valued relations by means of linguistic connective, then it is defined as an interval-valued fuzzy relation.
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