Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model
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 <inline-for...
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MDPI AG
2020-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/7/1121 |
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| author | Shougi S. Abosuliman Saleem Abdullah Muhammad Qiyas |
| author_facet | Shougi S. Abosuliman Saleem Abdullah Muhammad Qiyas |
| author_sort | Shougi S. Abosuliman |
| collection | DOAJ |
| description | 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 <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-covering (FOF <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-covering) and fractional orthotriple fuzzy <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-neighborhood (FOF <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-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. |
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| last_indexed | 2024-03-10T18:36:08Z |
| publishDate | 2020-07-01 |
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| spelling | doaj.art-fec915817083441e8053fcf077fffec52023-11-20T06:17:13ZengMDPI AGMathematics2227-73902020-07-0187112110.3390/math8071121Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set ModelShougi S. Abosuliman0Saleem Abdullah1Muhammad Qiyas2Department of Transportation and Port Management, Faculty of Maritime Studies, King Abdulaziz University, Jeddah 21588, Saudi ArabiaDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanDepartment of Mathematics, Abdul Wali Khan University, Mardan 23200, PakistanOn 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 <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-covering (FOF <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-covering) and fractional orthotriple fuzzy <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-neighborhood (FOF <inline-formula> <math display="inline"> <semantics> <mi>β</mi> </semantics> </math> </inline-formula>-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.https://www.mdpi.com/2227-7390/8/7/1121covering-based fractional orthotriple fuzzy rough setsfractional orthotriple fuzzy <i>β</i>-covering decision-theoretic rough setsfractional orthotriple fuzzy <i>β</i>-neighborhoodmulti-attribute decision makingdecision-theoretic rough sets |
| spellingShingle | Shougi S. Abosuliman Saleem Abdullah Muhammad Qiyas Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model Mathematics covering-based fractional orthotriple fuzzy rough sets fractional orthotriple fuzzy <i>β</i>-covering decision-theoretic rough sets fractional orthotriple fuzzy <i>β</i>-neighborhood multi-attribute decision making decision-theoretic rough sets |
| title | Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model |
| title_full | Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model |
| title_fullStr | Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model |
| title_full_unstemmed | Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model |
| title_short | Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model |
| title_sort | three way decisions making using covering based fractional orthotriple fuzzy rough set model |
| topic | covering-based fractional orthotriple fuzzy rough sets fractional orthotriple fuzzy <i>β</i>-covering decision-theoretic rough sets fractional orthotriple fuzzy <i>β</i>-neighborhood multi-attribute decision making decision-theoretic rough sets |
| url | https://www.mdpi.com/2227-7390/8/7/1121 |
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