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

Aliya Fahmi; Saleem Abdullah; Fazli Amin; Asad Ali; Khaista Rahman

doi:doi:10.11648/j.engmath.20180201.11

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

Aliya Fahmi, Saleem Abdullah, Fazli Amin, Asad Ali, Khaista Rahman

Published in Engineering Mathematics (Volume 2, Issue 1)

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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[2]	A. Fahmi, S. Abdullah, F. Amin, N. Siddiqui and A. Ali. Aggregation operators on triangular cubic fuzzy numbers and its application to multi-criteria decision making problems. Journal of Intelligent & Fuzzy Systems, 33,(2017), 3323-3337.
[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).
[4]	A. Fahmi, S. Abdullah, F. Amin & A. Ali, A. Weighted Average Rating (War) Method for Solving Group Decision Making Problem Using Triangular Cubic Fuzzy Hybrid Aggregation (Tcfha). Punjab University Journal of Mathematics, 50(1), (2018), 23-34.
[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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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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TY  - JOUR
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

Aliya Fahmi

Department of Mathematics, Hazara University, Mansehra, Pakistan
Saleem Abdullah

Department of Mathematics, Abdul Wali Khan University, Mardan, Pakistan
Fazli Amin

Department of Mathematics, Hazara University, Mansehra, Pakistan
Asad Ali

Department of Mathematics, Hazara University, Mansehra, Pakistan
Khaista Rahman

Department of Mathematics, Hazara University, Mansehra, Pakistan

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Plain Text BibTeX RIS

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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  -

Copy | Download