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International Journal of Machine Learning and Cybernetics
Erschienen in: International Journal of Machine Learning and Cybernetics 5/2013

01.10.2013 | Original Article

Independence of axiom sets on intuitionistic fuzzy rough approximation operators

verfasst von: Xiaoping Yang, Yu Yang

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 5/2013

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Abstract

Algebraic approach is widely used in the study of rough sets. In the algebraic approach, one defines a pair of dual approximation operators and states axioms that must be satisfied by the operators. Axiomatic approaches have been used in the study of intuitionistic fuzzy rough sets. Intuitionistic fuzzy rough approximation operators are defined by axioms, and different axiom sets of lower and upper intuitionistic fuzzy rough approximation operators guarantee the existence of different types of intuitionistic fuzzy relations. However, the independence of the axioms in each of those axiom sets has not been proved. If the axioms are not independent, one of the axioms is redundant. In this paper, we prove that no axioms can be derived from other axioms, which means the axioms in the axiom set are independent. For each axiom set, we examine the independence of axioms and present the independent axiom sets characterizing intuitionistic fuzzy rough approximation operators. Thus, we improve the intuitionistic fuzzy rough set theory.
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Metadaten
Titel
Independence of axiom sets on intuitionistic fuzzy rough approximation operators
verfasst von
Xiaoping Yang
Yu Yang
Publikationsdatum
01.10.2013
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 5/2013
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-012-0116-6

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