Homomorphisms-based attribute reduction of dynamic fuzzy covering information systems

Abstract

Information system homomorphisms have made a substantial contribution to attribute reduction of covering information systems. However, the efforts made on homomorphisms are far from sufficient. This paper further studies homomorphisms for attribute reduction of dynamic fuzzy covering information systems. First, the concepts of neighbourhood and induced fuzzy covering are proposed and their properties are discussed in detail. Then, we introduce the concepts of consistent functions and fuzzy covering mappings providing a basic theoretical foundation for compressing fuzzy covering information systems. Afterwards, the notion of homomorphisms is presented to reveal the relationship between fuzzy covering information systems. We show how large-scale fuzzy covering information systems and dynamic fuzzy covering information systems can be compressed into smaller ones by means of homomorphisms. Finally, illustrative examples are employed to show that attribute reduction can be simplified significantly by our proposed approach.

Keywords:

• rough set
• fuzzy covering
• fuzzy covering information system
• homomorphism
• attribute reduction

Acknowledgements

We would like to thank the anonymous reviewers very much for their helpful comments and valuable suggestions. This work was supported by the National Natural Science Foundation of China (No. 11201490, 11371130, 11401052, 11401195) and the Scientific Research Fund of Hunan Provincial Education Department (No.14C0049).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 11201490], [grant number 11371130], [grant number 11401052], [grant number 11401195]; the Scientific Research Fund of Hunan Provincial Education Department [grant number 14C0049].