Willmott Fuzzy Implication in Fuzzy Databases

Author:

Nesimovic Sanela1,Gusic Dzenan2

Affiliation:

1. University of Sarajevo, Faculty of Educational Sciences, Skenderija 72, 71000 Sarajevo, Bosnia and Herzegovina

2. University of Sarajevo, Faculty of Sciences and Mathematics, Department of Mathematics, Zmaja Od Bosne 33-35, 71000 Sarajevo, Bosnia and Herzegovina

Abstract

The object of the research are fuzzy functional dependencies on given relation scheme, and the question of their obtaining using the classical and innovated techniques. The attributes of the universal set are associated to the elements of the unit interval, and are turned into fuzzy formulas in this way. We prove that the dependency (which is treated as a fuzzy formula with respect to appropriately chosen valuation) is valid whenever it agrees with the attached two-elements fuzzy relation instance. The opposite direction of the claim is proven to be incorrect in this setting. Generalizing things to sets of attributes, we prove that particular fuzzy functional dependency follows form a set of fuzzy dependencies (in both, the world of two-element and the world of arbitrary fuzzy relation instances) if and only if the dependency is valid with respect to valuation anytime the set of fuzzy formulas agrees with the valuation. The results derived in paper show that the classical techniques in the procedure for generating new fuzzy dependencies may be replaced by the resolution ones, and hence automated. The research is conducted with respect to Willmott fuzzy implication operator

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Generalization of Possibilistic Fuzzy C-Means Method for Statistical Clustering of Data;International Journal of Circuits, Systems and Signal Processing;2021-12-17

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