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Keywords = covering-based fractional orthotriple fuzzy rough sets

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31 pages, 920 KB  
Article
Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model
by Shougi S. Abosuliman, Saleem Abdullah and Muhammad Qiyas
Mathematics 2020, 8(7), 1121; https://doi.org/10.3390/math8071121 - 9 Jul 2020
Cited by 32 | Viewed by 3793
Abstract
On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional [...] Read more.
On the basis of decision-theoretical rough sets (DTRSs), the three-way decisions give new model of decision approach for deal with the problem of decision. This proposed model of decision method is based on the loss function of DTRSs. First, the concept of fractional orthotriple fuzzy β -covering (FOF β -covering) and fractional orthotriple fuzzy β -neighborhood (FOF β -neighborhood) was introduced. We combined loss feature of DTRSs with covering-based fractional orthotriple fuzzy rough sets (CFOFSs) under the fractional orthotriple fuzzy condition. Secondly, we proposed a new FOF-covering decision-theoretical rough sets model (FOFCDTRSs) and developed related properties. Then, based on the grade of positive, neutral and negative membership of fractional orthotriple fuzzy numbers (FOFNs), five methods are established for addressing the expected loss expressed in the form of FOFNs and the corresponding three-way decisions are also derived. Based on this, we presented a FOFCDTRS-based algorithm for multi-criteria decision making (MCDM). Then, an example verifies the feasibility of the five methods for solving the MCDM problem. Finally, by comparing the results of the decisions of five methods with different loss functions. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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