Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model

Shougi S. Abosuliman, Saleem Abdullah and Muhammad Qiyas
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Shougi S. Abosuliman: Department of Transportation and Port Management, Faculty of Maritime Studies, King Abdulaziz University, Jeddah 21588, Saudi Arabia
Saleem Abdullah: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Muhammad Qiyas: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan

Mathematics, 2020, vol. 8, issue 7, 1-31

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 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.

Keywords: covering-based fractional orthotriple fuzzy rough sets; fractional orthotriple fuzzy ? -covering decision-theoretic rough sets; fractional orthotriple fuzzy ? -neighborhood; multi-attribute decision making; decision-theoretic rough sets (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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