From Fuzzy Dependences to Fuzzy Formulas and Vice Versa, for Kleene-Dienes Fuzzy Implication Operator
WSEAS Transactions on Systems and Control archive(2018)
摘要
To prove that a fuzzy dependency follows from a set of fuzzy dependences can be a very demanding
task. As far as we know, an algorithm or an application that generally and automatically solves the problem, does
not exist. The main goal of this paper is to offer such an algorithm. In order to achieve our goal we consider
fuzzy dependences as fuzzy formulas. In particular, we fix fuzzy logic operators: conjunction, disjunction and
implication, and allow only these operators to appear within fuzzy formulas. Ultimately, we prove that a fuzzy
dependency follows from a set of fuzzy dependences if and only if the corresponding fuzzy formula is a logical
consequence of the corresponding set of fuzzy formulas. To prove an implication of the last type, one usually uses
the resolution principle, i.e., the steps that can be fully automated. Our methodology assumes the use of soundness
and completeness of fuzzy dependences inference rules as well as the extensive use of active fuzzy multivalued
dependences fulfillment
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