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Expected Values of Aggregation Operators on Cubic Triangular Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems

Received: 26 December 2017     Accepted: 16 March 2018     Published: 31 May 2018
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Abstract

In this paper, we define triangular cubic fuzzy numbers and their operational laws. Originated on these operational laws, approximately aggregation operators, with triangular cubic fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are suggested. Expected values, score function and accuracy function of triangular cubic fuzzy numbers are defined. Founded on these, an amicable of triangular cubic fuzzy multi-criteria decision making method is proposed. By these aggregation operators, criteria values are aggregated and integrated triangular cubic fuzzy numbers of alternatives are conquered. By relating score function and accuracy function values of integrated fuzzy numbers, a positioning of the entire option set can be accomplished. An example is given to appear the achievability and convenience of the process.

Published in Engineering Mathematics (Volume 2, Issue 1)
DOI 10.11648/j.engmath.20180201.11
Page(s) 1-11
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Triangular Cubic Fuzzy Numbers, Aggregation Operators, Multi-Criteria Decision Making

References
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[5] A. Fahmi, S. Abdullah, F. Amin, A. Ali and W.A. Khan. Some geometric operators with Triangular Cubic Linguistic Hesitant Fuzzy number and Their Application in Group Decision-Making, Journal of Intelligent and Fuzzy System, accept (2018).
[6] A. Fahmi, S. Abdullah and F. Amin. TRAPEZOIDAL LINGUISTIC CUBIC HESITANT FUZZY TOPSIS METHOD AND APPLICATION TO GROUP DECISION MAKING PROGRAM. 19, (2017), 27-47.
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[8] A. Fahmi, S. Abdullah, F. Amin and M. S. A. Khan. Trapezoidal cubic fuzzy number Einstein hybrid weighted averaging operators and its application to decision making, soft computing, (2018) DOI: 10.1007/s00500-018-3242-6.
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Cite This Article
  • APA Style

    Aliya Fahmi, Saleem Abdullah, Fazli Amin, Asad Ali, Khaista Rahman. (2018). Expected Values of Aggregation Operators on Cubic Triangular Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems. Engineering Mathematics, 2(1), 1-11. https://doi.org/10.11648/j.engmath.20180201.11

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    ACS Style

    Aliya Fahmi; Saleem Abdullah; Fazli Amin; Asad Ali; Khaista Rahman. Expected Values of Aggregation Operators on Cubic Triangular Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems. Eng. Math. 2018, 2(1), 1-11. doi: 10.11648/j.engmath.20180201.11

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    AMA Style

    Aliya Fahmi, Saleem Abdullah, Fazli Amin, Asad Ali, Khaista Rahman. Expected Values of Aggregation Operators on Cubic Triangular Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems. Eng Math. 2018;2(1):1-11. doi: 10.11648/j.engmath.20180201.11

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  • @article{10.11648/j.engmath.20180201.11,
      author = {Aliya Fahmi and Saleem Abdullah and Fazli Amin and Asad Ali and Khaista Rahman},
      title = {Expected Values of Aggregation Operators on Cubic Triangular Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems},
      journal = {Engineering Mathematics},
      volume = {2},
      number = {1},
      pages = {1-11},
      doi = {10.11648/j.engmath.20180201.11},
      url = {https://doi.org/10.11648/j.engmath.20180201.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.engmath.20180201.11},
      abstract = {In this paper, we define triangular cubic fuzzy numbers and their operational laws. Originated on these operational laws, approximately aggregation operators, with triangular cubic fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are suggested. Expected values, score function and accuracy function of triangular cubic fuzzy numbers are defined. Founded on these, an amicable of triangular cubic fuzzy multi-criteria decision making method is proposed. By these aggregation operators, criteria values are aggregated and integrated triangular cubic fuzzy numbers of alternatives are conquered. By relating score function and accuracy function values of integrated fuzzy numbers, a positioning of the entire option set can be accomplished. An example is given to appear the achievability and convenience of the process.},
     year = {2018}
    }
    

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    T1  - Expected Values of Aggregation Operators on Cubic Triangular Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems
    AU  - Aliya Fahmi
    AU  - Saleem Abdullah
    AU  - Fazli Amin
    AU  - Asad Ali
    AU  - Khaista Rahman
    Y1  - 2018/05/31
    PY  - 2018
    N1  - https://doi.org/10.11648/j.engmath.20180201.11
    DO  - 10.11648/j.engmath.20180201.11
    T2  - Engineering Mathematics
    JF  - Engineering Mathematics
    JO  - Engineering Mathematics
    SP  - 1
    EP  - 11
    PB  - Science Publishing Group
    SN  - 2640-088X
    UR  - https://doi.org/10.11648/j.engmath.20180201.11
    AB  - In this paper, we define triangular cubic fuzzy numbers and their operational laws. Originated on these operational laws, approximately aggregation operators, with triangular cubic fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are suggested. Expected values, score function and accuracy function of triangular cubic fuzzy numbers are defined. Founded on these, an amicable of triangular cubic fuzzy multi-criteria decision making method is proposed. By these aggregation operators, criteria values are aggregated and integrated triangular cubic fuzzy numbers of alternatives are conquered. By relating score function and accuracy function values of integrated fuzzy numbers, a positioning of the entire option set can be accomplished. An example is given to appear the achievability and convenience of the process.
    VL  - 2
    IS  - 1
    ER  - 

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Author Information
  • Department of Mathematics, Hazara University, Mansehra, Pakistan

  • Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan

  • Department of Mathematics, Hazara University, Mansehra, Pakistan

  • Department of Mathematics, Hazara University, Mansehra, Pakistan

  • Department of Mathematics, Hazara University, Mansehra, Pakistan

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