2006
DOI: 10.1007/11671404_3
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Attribute Implications in a Fuzzy Setting

Abstract: Abstract. The paper is an overview of recent developments concerning attribute implications in a fuzzy setting. Attribute implications are formulas of the form A ⇒ B, where A and B are collections of attributes, which describe dependencies between attributes. Attribute implications are studied in several areas of computer science and mathematics. We focus on two of them, namely, formal concept analysis and databases.

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Cited by 66 publications
(68 citation statements)
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“…In the future, we will compare the introduced size reduction method with the existing ones, and, using Theorem 10, a classification in the set of attributes will be studied and its applicability in the attribute implications framework [4].…”
Section: Discussionmentioning
confidence: 99%
“…In the future, we will compare the introduced size reduction method with the existing ones, and, using Theorem 10, a classification in the set of attributes will be studied and its applicability in the attribute implications framework [4].…”
Section: Discussionmentioning
confidence: 99%
“…An if-then rule A ⇒ B, where A, B ∈ L Y is called a fuzzy attribute implication. Fuzzy attribute implications have two basic interpretations as (i) if-then attribute dependencies extracted from object-attribute data with graded attributes [9], and (ii) similarity-based functional dependencies in a relational database model extended by domain similarities and ranks [10]. Since both (i) and (ii) have the same notion of semantic entailment, we use here the first interpretation: given M ∈ L Y , the degree to which A ⇒ B is satisfied by M, written A ⇒ B M , is defined by…”
Section: Illustrative Examplementioning
confidence: 99%
“…In fact, in Ref. [1][2][3][4][5]20 and Ref. 24, fuzzy implications or fuzzy decision implications are only considered by taking as a whole in fuzzy attribute logic.…”
Section: The Semantical Characteristics Of Fuzzy Decision Implicationsmentioning
confidence: 99%