| Disjunctive and Conjunctive Normal Forms in Fuzzy Logic (2008) | |||||||||||||||
Abstract | |||||||||||||||
| When performing set-theoretical operations, such as intersection and union, on fuzzy sets, one can opt not to consider exact formula, but to leave the results less specific (in particular, interval-valued) by using both disjunctive and conjunctive representations (normal forms) of the underlying logical operations. We investigate which De Morgan triplets are suitable for this transformation (i.e. really yield intervals) and reveal the importance and unique role of the ̷Lukasiewicz-triplet in the theory of fuzzy normal forms. To conclude we extend binary fuzzy normal forms to higher dimensions. Keywords: Fuzzy normal form, Interval-valued fuzzy set. 1 | |||||||||||||||
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