Algebraic Properties of Adjunction-Based Fuzzy Rough Sets

Authors:
Tingquan Deng;Yanmei Chen;Guanghong Gao
Affiliations:
College of Science, Harbin Engineering University, Harbin 150001, P.R. China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, P.R. China
Venue:
RSFDGrC '07 Proceedings of the 11th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing
Year:
2009

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Abstract

A fuzzy rough set is a fuzzy generalization of rough set. There are already several definitions for it, and most of them are given with reference to a t-norm *, a fuzzy (*-)similarity relation and the duality principle. In this paper, a generalization of fuzzy rough sets is investigated regarding a general fuzzy relation and a lower semi-continuous fuzzy conjunction logical operator in its second argument. The generalized fuzzy rough approximation operators are established by using the adjunction between the fuzzy conjunction operator and a fuzzy implication operator. Algebraic properties of the generalized fuzzy rough approximation operators are discussed. It has been shown that information with much more necessity measure and with less probability measure for a fuzzy set can be mined in comparison with existing methods of fuzzy rough sets.