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Intuitionistic fuzzy \(\beta \)-covering-based rough sets

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Abstract

Covering-based rough set is an important extended type of classical rough set model. In this model, concepts are approximated through substitution of a partition in classical rough set theory with a covering in covering-based rough set theory. Various generalized covering-based rough sets have been investigated, however, little work has been done on extending four classical covering-based rough set to intuitionistic fuzzy (IF) settings. In this study, four novel IF covering-based rough set models are developed by combining an IF \(\beta \)-covering with four classical covering-based rough set models. First, we present the concept of IF \(\beta \)-minimal description, and then construct four order relations on IF \(\beta \) approximation space. Second, we propose four IF \(\beta \)-covering-based rough set models and derive that they are generalizations of four existing covering-based rough sets in IF settings. We also discuss the properties of these IF \(\beta \)-covering-based rough sets and reveal their relationships. We use the existing distance between two IF sets to characterize the uncertainty of the presented IF \(\beta \)-covering-based rough sets. Third, we define the reducts of IF \(\beta \)-covering decision systems and examine their discernibility-function-based reduction methods for these IF \(\beta \)-covering-based rough sets. Fourth, we present four optimistic and pessimistic multi-granulation IF \(\beta \)-covering-based rough sets and analyze their properties and uncertainty measures from multi-granulation perspective. Fifth, we study the discernibility-function-based reduction methods for the presented multi-granulation IF \(\beta \)-covering-based rough sets. Finally, we discuss another two neighborhood-based IF covering-based rough sets. This study can provide a covering-based rough set method for acquiring knowledge from IF decision systems.

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Acknowledgements

We would like to thank the EssayStar Company (http://essaystar.com/) for their assistance in improving the English language of this paper. We appreciate the support provided by the Natural Science Foundation of China (Grant nos. 61473157, 71671086, 61170105, and 71201076) and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

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Authors and Affiliations

  1. School of Information Engineering, Nanjing Audit University, Nanjing, 211815, People’s Republic of China

    Bing Huang & Guofu Feng

  2. School of Management Engineering, Nanjing University, Nanjing, 210093, People’s Republic of China

    Huaxiong Li

  3. School of Business, Sichuan University, Chengdu, 610064, People’s Republic of China

    Chunxiang Guo

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  1. Bing Huang
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  2. Huaxiong Li
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  3. Guofu Feng
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  4. Chunxiang Guo
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Correspondence to Bing Huang or Chunxiang Guo.

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Huang, B., Li, H., Feng, G. et al. Intuitionistic fuzzy \(\beta \)-covering-based rough sets. Artif Intell Rev 53, 2841–2873 (2020). https://doi.org/10.1007/s10462-019-09748-x

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