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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shougi S. Abosuliman & Saleem Abdullah & Muhammad Qiyas, 2020. "Three-Way Decisions Making Using Covering Based Fractional Orthotriple Fuzzy Rough Set Model," Mathematics, MDPI, vol. 8(7), pages 1-31, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1121-:d:382285
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    References listed on IDEAS

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    1. Rula Ghandour & Azza Shoaibi & Rana Khatib & Niveen Abu Rmeileh & Belgin Unal & Kaan Sözmen & Bülent Kılıç & Fouad Fouad & Radwan Al Ali & Habiba Ben Romdhane & Wafa Aissi & Balsam Ahmad & Simon Capew, 2015. "Priority setting for the prevention and control of cardiovascular diseases: multi-criteria decision analysis in four eastern Mediterranean countries," International Journal of Public Health, Springer;Swiss School of Public Health (SSPH+), vol. 60(1), pages 73-81, January.
    2. Shouzhen Zeng & Muhammad Munir & Tahir Mahmood & Muhammad Naeem, 2020. "Some T-Spherical Fuzzy Einstein Interactive Aggregation Operators and Their Application to Selection of Photovoltaic Cells," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-16, June.
    3. Guiwu Wei, 2016. "Picture fuzzy cross-entropy for multiple attribute decision making problems," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 17(4), pages 491-502, July.
    4. Jurgita Antucheviciene & Madjid Tavana & Mehrbakhsh Nilashi & Romualdas Bausys, 2017. "Managing Information Uncertainty and Complexity in Decision-Making," Complexity, Hindawi, vol. 2017, pages 1-3, November.
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    Cited by:

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    2. Saleem Abdullah & Alaa O. Almagrabi & Ihsan Ullah, 2023. "A New Approach to Artificial Intelligent Based Three-Way Decision Making and Analyzing S-Box Image Encryption Using TOPSIS Method," Mathematics, MDPI, vol. 11(6), pages 1-19, March.

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