Engineering Mathematics

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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.

DOI 10.11648/j.engmath.20180201.11
Published in Engineering Mathematics (Volume 2, Issue 1, June 2018)
Page(s) 1-11
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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), 2024. Published by Science Publishing Group

Keywords

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

References
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[3] A. Fahmi, S. Abdullah, F. Amin & A. Ali (2017). Precursor Selection for Sol--Gel Synthesis of Titanium Carbide Nanopowders by a New Cubic Fuzzy Multi-Attribute Group Decision-Making Model. Journal of Intelligent Systems (2017).
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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).
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[17] M. H. Shu, Cheng C H, Chang J R. Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectronics Reliability, 2006(46): 2139-2148.
[18] J, Q. Wang, Programming method of fuzzy group multiple criteria decision making with incomplete information. Systems Engineering and Electronics, 2004, 26(11): 1604-1608.
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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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  • 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://download.sciencepg.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
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    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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