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Using necessarily weak efficient solutions for solving a biobjective transportation problem with fuzzy objective functions coefficients | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 17، شماره 3، مرداد و شهریور 2020، صفحه 85-102 اصل مقاله (434.28 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2020.5351 | ||
| نویسندگان | ||
| A. Zamzamzadeh* 1؛ M. A. Yaghoobi2 | ||
| 1Department of Applied Mathematics, Faculty of Sciences and Modern Technologies, Graduate University of Advanced Technology, Kerman, Iran | ||
| 2Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| چکیده | ||
| This paper considers a biobjective transportation problem with various fuzzy objective functions coefficients. Fuzzy coefficients can be of different types such as triangular, trapezoidal, (semi) $L-R$, or flat (semi) $L-R$ fuzzy numbers. First, we convert the problem to a parametric interval biobjective transportation problem using $\gamma$-cuts of fuzzy coefficients. Then, we consider a fix $\gamma$-cut and obtain a necessarily weak efficient solution to the yielded interval biobjective program by a new algorithm. It uses basic feasible solutions and the parametric simplex algorithm. Furthermore, we suggest another algorithm for finding a reasonable solution, called $\gamma^*$-necessarily weak efficient, to the main biobjective transportation problem. To illustrate the validity and performance of the proposed algorithms, we present some numerical examples. | ||
| کلیدواژهها | ||
| Biobjective transportation problem؛ inerval biobjective linear programming problem؛ necessarily week efficient solution؛ fuzzy membership function؛ $gamma$-cut | ||
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