Attributes Reduction Based on Interval-Valued Fuzzy Rough Sets

Abstract

Aims: This paper provides a systematic study on attribute reduction with interval-valued fuzzy rough sets. Study Design: The interval-valued fuzzy rough sets are an important improvement of traditional rough set model to deal with both fuzziness and vagueness in data which the traditional one cannot handle. Place and Duration of Study: The existing researches on interval-valued fuzzy rough sets mainly focus on the establishment of lower and upper approximation operators by using constructive and axiomatic approaches. Less effort has been put on the attributes reduction of databases based on interval-valued fuzzy rough sets. Methodology: After introducing some concepts and theorems of attributes reduction with interval-valued fuzzy rough sets, we study the structure of the attributes reduction with interval-valued fuzzy rough sets and present an algorithm by using discernibility matrix to find all the attributes reductions with interval-valued fuzzy rough sets. Results: Finally, we propose an example to demonstrate our idea and method in this paper. Conclusion: With these discussions we construct a basic foundation for attributes reduction based on interval-valued fuzzy rough sets.