Generalized rough set models determined by multiple neighborhoods generated from a similarity relation
- 269 Downloads
Rough set theory is widely used to deal with uncertainty. Original rough set model is mainly based on equivalence relations. To extend the application scope, classical rough set model based on equivalence relations is generalized to rough set model based on similarity relations. In the present paper, we propose and investigate three new generalized rough set models by introducing new definitions of lower and upper approximations based on multiple neighborhoods generated from a similarity relation. The characteristics of the proposed approximations are investigated. Theoretically, analysis indicates the monotonicity of the corresponding uncertainty measures including accuracy, roughness and approximation accuracy. Experiments indicate that the constructed monotonic measures can be used in attribute reduction.
KeywordsRough set model Similarity relation Roughness Accuracy measure Attribute reduction
This work was partially supported by the National Natural Science Foundation of China (Nos. 61473259, 61070074, 60703038), the Zhejiang Provincial Natural Science Foundation (No. LY14F020029), the National Science and Technology Support Program of China (2015BAK26B00, 2015BAK26B01, 2015BAK26B02) and the PEIYANG Young Scholars Program of Tianjin University (2016XRX-0001).
Compliance with ethical standards
Conflict of interest
All authors declare that they have no conflict of interest.
This article does not contain any studies with human participants or animals performed by any of the authors.
- Blake C, Merz C (2016) UCI repository of machine learning databases. In: http://www.ics.uci.edu/mlearn/mlrepository.html
- Dai J, Wang W, Xu Q, Tian H (2012a) Uncertainty measurement for interval-valued decision systems based on extended conditional entropy. Knowl Based Syst 27:443–450Google Scholar
- Dai J, Han H, Zhang X, Liu M, Wan S, Liu J, Lu Z (2016) Catoptrical rough set model on two universes using granule-based definition and its variable precision extensions. Inf Sci 390:70–81Google Scholar