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Expected Values of Aggregation Operators on Cubic Triangular Fuzzy Number and Its Application to Multi-Criteria Decision Making Problems
Engineering Mathematics
Volume 2, Issue 1, June 2018, Pages: 1-11
Received: Dec. 26, 2017; Accepted: Mar. 16, 2018; Published: May 31, 2018
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Authors
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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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.
Keywords
Triangular Cubic Fuzzy Numbers, Aggregation Operators, Multi-Criteria Decision Making
To cite this article
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, Engineering Mathematics. Vol. 2, No. 1, 2018, pp. 1-11. doi: 10.11648/j.engmath.20180201.11
Copyright
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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