Properties of models of fuzzy attribute implications

Radim Belohlavek; Vilem Vychodil

doi:10.14864/softscis.2006.0.291.0

SCIS & ISIS 2006

Session ID : TH-C3-1

DOI https://doi.org/10.14864/softscis.2006.0.291.0

Conference information

Host: Japan SOciety for Fuzzy Theory and intelligent informatics

Co-host: The Korea Fuzzy Logic and Intelligent Systems Society, IEEE Computational Intelligence Society, The International Fuzzy Systems Association, 21th Century COE Program "Creation of Agent-Based Social Systems Sciences"

TH-C3 Mathematics and Theory (1)

Properties of models of fuzzy attribute implications

Radim Belohlavek, *Vilem Vychodil

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Keywords: fuzzy logic, fuzzy attribute, fuzzy attribute implication

CONFERENCE PROCEEDINGS FREE ACCESS

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Abstract

This paper deals with closure properties of models of fuzzy attribute implications. Fuzzy attribute implications are particular IF-THEN rules which can be interpreted in data tables with fuzzy attributes and/or ranked data tables over domains with similarity relations. We show that models of any set of fuzzy attribute implications form a fuzzy closure system with hedge. Conversely, we show that each fuzzy closure system with hedge can be seen as a system of models of some set of fuzzy attribute implications. Furthermore, we show applications of the closure properties: we describe semantic entailment from fuzzy attribute implications using least models and show a method for generating of non-redundant sets of dependencies which are true in a given data table with fuzzy attributes.

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