Multi-granulation interval-valued fuzzy probabilistic rough sets and their corresponding three-way decisions based on interval-valued fuzzy preference relations
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In this paper, we study interval-valued fuzzy probabilistic rough sets (IVF-PRSs) based on multiple interval-valued fuzzy preference relations (IVFPRs) and consistency matrices, i.e., the multi-granulation interval-valued fuzzy preference relation probabilistic rough sets (MG-IVFPR-PRSs). First, in the proposed study, we convert IVFPRs into fuzzy preference relations (FPRs), and then construct the consistency matrix, the collective consistency matrix, the weighted collective preference relations, and the group collective preference relation (GCPR). Using this GCPR, four types of MG-IVFPR-PRSs are founded in terms of different constraints on parameter. Finally, to find a suitable way of explaining and determining these parameters in each model, three-way decisions are studied based on Bayesian minimum-risk procedure, i.e., the multi-granulation interval-valued fuzzy preference relation decision-theoretic rough set approach. An example is included to show the feasibility and potential of the theoretic results obtained.
KeywordsInterval-valued fuzzy probabilistic rough set Interval-valued fuzzy preference relation Multi-granulation Three-way decisions
The authors would like to thank the Editor-in-Chief and reviewers for their thoughtful comments and valuable suggestions.
Compliance with ethical standards
Conflict of interest
Prasenjit Mandal and A. S. Ranadive declare that there is no conflict of interest.
This article does not contain any study performed on humans or animals by the authors.
Informed consent was obtained from all individual participants included in the study.
- Lee LW, Chen SM (2008) Fuzzy multiple attributes group decision-making based on the extension of TOPSIS method and interval type-2 fuzzy sets. In: Proceedings of the 2008 international conference on machine learning and cybernetics, Kunming, China, vol 6, pp 3260–3265Google Scholar
- Lv Y, Chen Q, Wu L (2013) Multi-granulation probabilistic rough set model. Int Conf Fuzzy Syst Knowl Discov 10:146–151Google Scholar
- Tsai PW, Pan JS, Chen SM, Liao BY, Hao SP (2008) Parallel cat swarm optimization. In: Proceedings of the 2008 international conference on machine learning and cybernetics, Kunming, China, vol 6, pp 3328–3333Google Scholar
- Wang JY, Xu LM (2002) Probabilistic rough set model. Comput Sci 29(8):76–78Google Scholar
- Xu W, Wang Q, Zhang X (2012) A generalized multi-granulation rough set approach. Lect Notes Bioinf 1(6840):681–689Google Scholar