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