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Novel classes of coverings based multigranulation fuzzy rough sets and corresponding applications to multiple attribute group decision-making

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Abstract

The notion of covering based multigranulation fuzzy rough set (CMGFRS) models is a generalization of both granular computing and covering based fuzzy rough sets. Therefore it has become a powerful tool for coping with vague and multigranular information in cognition. In this paper we introduce three kinds of CMGFRS models by means of fuzzy β-neighborhoods and fuzzy complementary β-neighborhoods, and we investigate their axiomatic properties. We investigate three respective types of coverings based CMGFRS models, namely, optimistic, pessimistic and variable precision setups. In particular, by using multigranulation fuzzy measure degrees and multigranulation fuzzy complementary measure degrees, we derive three types of coverings based γ-optimistic (γ-pessimistic) CMGFRSs and E (F, G)-optimistic and E (F, G)-pessimistic CMGFRSs, respectively. We discuss the interrelationships among these three types of CMGFRS models and covering based Zhan-CMGFRS models. In view of the theoretical analysis for these three types of CMGFRS models, we put forward a novel methodology to multiple attribute group decision-making problem with evaluation of fuzzy information. An effective example is fully developed, hence concluding the applicability of the proposed methodology.

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Notes

  1. From the point of view of group decision-making, this accuracy parameter in the model of 1-CMGFRS can account for the consistency consensus threshold among the group of decision-makers.

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Acknowledgements

The authors are extremely grateful to the editors and three reviewers for their valuable comments and helpful suggestions which helped to improve the presentation of this paper. The first and the second authors were supported by the NNSFC of China (61866011; 11961025; 11561023). The third author was partly supported by the NNSFC of China (71571090), the National Science Foundation of Shaanxi Province of China (2017JM7022), the Fundamental Research Funds for the Key Strategic Research of Central Universities (JBZ170601).

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Authors and Affiliations

  1. Department of Mathematics, Hubei Minzu University, Enshi, 445000, China

    Xueling Ma & Jianming Zhan

  2. School of Economics and Management, Xidian University, Xi’an, 710071, China

    Bingzhen Sun

  3. BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, 37007, Salamanca, Spain

    José Carlos R. Alcantud

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  1. Xueling Ma
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  4. José Carlos R. Alcantud
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Correspondence to Jianming Zhan.

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Ma, X., Zhan, J., Sun, B. et al. Novel classes of coverings based multigranulation fuzzy rough sets and corresponding applications to multiple attribute group decision-making. Artif Intell Rev 53, 6197–6256 (2020). https://doi.org/10.1007/s10462-020-09846-1

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