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A computational algorithm for the FFD transitive closure and a complete axiomatization of fuzzy functional dependence (FFD)
Author(s) -
Chen Guoqing,
Kerre Etienne E.,
Vandenbulcke Jacques
Publication year - 1994
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.4550090503
Subject(s) - transitive closure , soundness , correctness , transitive relation , rule of inference , algorithm , computer science , inference , mathematics , axiom , completeness (order theory) , closure (psychology) , axiomatic system , theoretical computer science , artificial intelligence , discrete mathematics , programming language , mathematical analysis , geometry , combinatorics , economics , market economy
This article focuses on the axiomatization of fuzzy functional dependency (FFD) in a fuzzy relational data model, which is considered as a fundamental issue towards building a theory of fuzzy relational database design. As an inference basis, the FFD axiomatic system composed of four FFD inference rules is established, and proven to be correct in terms of FFD logical implication with respect to the relation scheme. Consequently, the concept of the FFD transitive closure is defined, and correspondingly a computational algorithm is developed. This helps to tell whether a specific FFD can be derived from a given FFD set using those inference rules. In addition, some details of the algorithm as well as the aspects of the computational complexity and correctness are investigated. Finally, the soundness and completeness of the axiomatic system are discussed. It is proven that the system is both sound and complete. Importantly, this result enables us to “equate” the concept of FFD logical implication to the concept of FFD derivation using the inference rules. © 1994 John Wiley & Sons, Inc.