WSEAS Transactions on Systems and Control


Print ISSN: 1991-8763
E-ISSN: 2224-2856

Volume 13, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.


Volume 13, 2018



From Fuzzy Dependences to Fuzzy Formulas and Vice Versa, for Kleene-Dienes Fuzzy Implication Operator

AUTHORS: Nedzad Dukic, Dzenan Gusic, Amela Muratovic-Ribic, Adis Alihodzic, Edin Tabak, Haris Dukic

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ABSTRACT: 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

KEYWORDS: - Fuzzy multivalued dependences, Fuzzy functional dependences, Fuzzy relation instances, Fuzzy formulas, Fuzzy logic

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WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 13, 2018, Art. #33, pp. 285-297


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