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Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems

Author

Listed:
  • Saifullah Khan

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan)

  • Saleem Abdullah

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan)

  • Lazim Abdullah

    (School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, Kuala Nerus 21030, Malaysia)

  • Shahzaib Ashraf

    (Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan)

Abstract

The objective of this study was to create a logarithmic decision-making approach to deal with uncertainty in the form of a picture fuzzy set. Firstly, we define the logarithmic picture fuzzy number and define the basic operations. As a generalization of the sets, the picture fuzzy set provides a more profitable method to express the uncertainties in the data to deal with decision making problems. Picture fuzzy aggregation operators have a vital role in fuzzy decision-making problems. In this study, we propose a series of logarithmic aggregation operators: logarithmic picture fuzzy weighted averaging/geometric and logarithmic picture fuzzy ordered weighted averaging/geometric aggregation operators and characterized their desirable properties. Finally, a novel algorithm technique was developed to solve multi-attribute decision making (MADM) problems with picture fuzzy information. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable.

Suggested Citation

  • Saifullah Khan & Saleem Abdullah & Lazim Abdullah & Shahzaib Ashraf, 2019. "Logarithmic Aggregation Operators of Picture Fuzzy Numbers for Multi-Attribute Decision Making Problems," Mathematics, MDPI, vol. 7(7), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:608-:d:246615
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    References listed on IDEAS

    as
    1. 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.
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