Entropy of L-fuzzy sets

Luca, Aldo de; Termini, Settimo

doi:10.1016/s0019-9958(74)80023-9

Cited by 93 publications

(24 citation statements)

References 6 publications

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“…The Cartesian product A × B of two fuzzy sets A and B is usually defined by the membership function (x, y) → min{A(x), B(y)}. Moreover, the cardinality of a finite fuzzy set is simply the sum of its membership degrees [17]. Thus, (5) and (6) can be generalized as follows:…”

Section: Quality Measures For Fuzzy Association Rulesmentioning

confidence: 99%

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Implication-Based Fuzzy Association Rules

Hüllermeier

2001

Principles of Data Mining and Knowledge Discovery

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Abstract. Fuzzy association rules provide a data mining tool which is especially interesting from a knowledge-representational point of view since fuzzy attribute values allow for expressing rules in terms of natural language. In this paper, we show that fuzzy associations can be interpreted in different ways and that the interpretation has a strong influence on their assessment and, hence, on the process of rule mining. We motivate the use of multiple-valued implication operators in order to model fuzzy association rules and propose quality measures suitable for this type of rule. Moreover, we introduce a semantic model of fuzzy association rules which suggests to consider them as a convex combination of simple association rules. This model provides a sound theoretical basis and gives an explicit meaning to fuzzy associations. Particularly, the aforementioned quality measures can be justified within this framework.

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Section: Quality Measures For Fuzzy Association Rulesmentioning

confidence: 99%

“…Now, in some situations one might wish to modify the constraints (17), that is to weaken or to strengthen a conclusion Y ∈ B λ drawn from the condition X ∈ A λ . This leads to a collection , then a more restrictive premise X ∈ A λ (λ < λ ) justifies this conclusion all the more, that is m(λ) ≤ m(λ ).…”

Section: Pure Gradual Rulesmentioning

confidence: 99%

Implication-Based Fuzzy Association Rules

Hüllermeier

2001

Principles of Data Mining and Knowledge Discovery

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“…The Cartesian product A × B of two fuzzy sets A and B is usually defined by the membership function (x, y) → min{A(x), B(y)}. Moreover, the cardinality of a finite fuzzy set is simply the sum of its membership degrees [18]. Thus, (5) and (6) can be generalized as follows:…”

Section: Fuzzy Association Rulesmentioning

confidence: 99%

“…In fact, if the level-cuts A λ and B m(λ) of the fuzzy sets A and B are intervals, which holds true for commonly used membership functions, then (18) reduces to a class of interval-based association rules. This interpretation assigns an association rule a concrete meaning and might hence be helpful in connection with the acquisition (mining) and interpretation of such rules.…”

Section: Semantic Interpretation Of Fuzzy Association Rulesmentioning

confidence: 99%

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Fuzzy Association Rules: Semantic Issues and Quality Measures

Hüllermeier¹

2001

Computational Intelligence. Theory and Applications

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Abstract. Fuzzy association rules provide a data mining tool which is especially interesting from a knowledge-representational point of view since fuzzy attribute values allow for expressing rules in terms of natural language. So far, however, association rules of this type have not been investigated thoroughly from a semantical point of view. Particularly, the quality measures which have been proposed for assessing such rules are mostly "ad-hoc" generalizations of measures for classical rules. In this paper, we show that fuzzy association rules can be interpreted in different ways and that the interpretation has a strong influence on their assessment and, hence, on the process of rule mining. We motivate the use of multiple-valued implication operators in order to model fuzzy association rules and propose quality measures suitable for this type of rule.

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Measure of Uncertainty and Information

Klir

2005

Uncertainty and Information

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Entropy of L-fuzzy sets

Cited by 93 publications

References 6 publications

Implication-Based Fuzzy Association Rules

Implication-Based Fuzzy Association Rules

Fuzzy Association Rules: Semantic Issues and Quality Measures

Measure of Uncertainty and Information

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