Covering-based intuitionistic fuzzy rough sets and applications in multi-attribute decision-making

  • Jianming ZhanEmail author
  • Bingzhen Sun


Covering based intuitionistic fuzzy (IF) rough set is a generalization of granular computing and covering based rough sets. By combining covering based rough sets, IF sets and fuzzy rough sets, we introduce three classes of coverings based IF rough set models via IF\(\beta \)-neighborhoods and IF complementary \(\beta \)-neighborhood (IFC\(\beta \)-neighborhood). The corresponding axiomatic systems are investigated, respectively. In particular, the rough and precision degrees of covering based IF rough set models are discussed. The relationships among these types of coverings based IF rough set models and covering based IF rough set models proposed by Huang et al. (Knowl Based Syst 107:155–178, 2016). Based on the theoretical analysis for coverings based IF rough set models, we put forward intuitionistic fuzzy TOPSIS (IF-TOPSIS) methodology to multi-attribute decision-making (MADM) problem with the evaluation of IF information problem. An effective example is to illustrate the proposed methodology. Finally, we deal with MADM problem with the evaluation of fuzzy information based on CFRS models. By comparative analysis, we find that it is more effective to deal with MADM problem with the evaluation of IF information based on CIFRS models than the one with the evaluation of fuzzy information based on CFRS models.


Covering based IF rough sets IF\(\beta \)-neighborhood IFC\(\beta \)-neighborhood IF-TOPSIS methodology MADM 



The authors are extremely grateful to the editor and four anonymous referees for their valuable comments and helpful suggestions which helped to improve the presentation of this paper. The first author was supported by the NNSFC (11461025, 11561023). The second author was supported by the NNSFC (71571090), the National Science Foundation of Shaanxi Province of China (2017JM7022), the Key Strategic Project of Fundamental Research Funds for the Central Universities (JBZ170601).


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of MathematicsHubei University for NationalitiesEnshiChina
  2. 2.School of Economics and ManagementXidian UniversityXi’anChina

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