WSEAS Transactions on Mathematics


Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 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 17, 2018


On Equivalences Between Fuzzy Dependencies and Fuzzy Formulas’ Satisfiability for Yager’s Fuzzy Implication Operator

AUTHORS: Nedzad Dukic, Dzenan Gusic, Nermana Kajmovic

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ABSTRACT: In this paper we consider fuzzy functional and fuzzy multivalued dependencies introduced by Sozat and Yazici. We appropriately relate these dependencies to fuzzy formulas. In particular, we relate any subset of the universal set of attributes to fuzzy conjunction of its attributes. Thus, being in the form of implication between such subsets, we naturally relate a fuzzy dependency to fuzzy implication between corresponding fuzzy conjunctions. In this paper we choose standard min, max as well as Yager’s fuzzy implication operator for definitions of fuzzy conjunction, fuzzy disjunction and fuzzy implication, respectively. If any two-element fuzzy relation instance on a given scheme, known to satisfy some set of fuzzy functional and fuzzy multivalued dependencies, satisfies some fuzzy functional or fuzzy multivalued dependency f which is not member of the given set of fuzzy dependencies, then, we prove that satisfiability of the related set of fuzzy formulas yields satisfiability of the fuzzy formula related to f and vice versa. A methodology behind the proofs of our results is mainly based on an application of definitions of the introduced fuzzy logic operators. Our results can be verified for various choices of fuzzy logic operators however.

KEYWORDS: Fuzzy functional and multivalued dependencies, Fuzzy formulas, Fuzzy relation instances

REFERENCES:

[1] M. Baczynski and B. Jayaram, ´ Fuzzy Implications, Springer–Verlag, Berlin–Heidelberg 2008

[2] R.–P. Buckles and F.–E. Petry, A fuzzy representation of data for relation databases, Fuzzy Sets and Systems 7, 1982, pp. 231–216.

[3] R.–P. Buckles and F.–E. Petry, Fuzzy databases and their applications, Fuzzy Inform. Decision Processes 2, 1982, pp. 361–371.

[4] R.–P. Buckles and F.–E. Petry, Uncertainity models in information and database systems, J. Inform. Sci. 11, 1985, pp. 77–87.

[5] G. Chen, Fuzzy Logic in Data Modeling. Semantics, Constraints, and Database Design, Kluwer Academic Publishers, MA 1998

[6] R.–C.–T. Lee, Fuzzy Logic and the Resolution Principle, J. Assoc. Comput. Mach. 19, 1972, pp. 109–119.

[7] Y. Shi, A Deep Study of Fuzzy Implications, Ph.D. dissertation, Faculty of Science, Ghent University, Ghent, 2009.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #6, pp. 35-43


Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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