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An Ontological and Epistemological Perspective of Fuzzy Set Theory by I. Burhan Türksen

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Chapter 9

CONTAINMENT OF FDCF IN FCCF

On the basis of ontological and epistemological assumption, in previous chapters, it was shown that the equivalence between canonical forms break down in fuzzy set and logic theory, i.e., FDCF ⊆ FFCF.

However, we have stated that for particular classes of t-norms and t-conorms FDCF(.)⊆FCCF(.) holds for all sixteen combination of concepts that are formed with De Morgan triples. This is now developed in this chapter in detail with the application of generating functions for strict and nilpotent Archimedean t-norms and t-conorms. For this purpose, we next review the generators of continuous t-norms and t-conorms and other relevant concepts in addition to the properties of t-norms and t-conorms stated in Appendix ...

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