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An interactive algorithm for linear assignment problem on fuzzy graphs | ||
| Iranian Journal of Fuzzy Systems | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 25 مهر 1405 اصل مقاله (1.53 M) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2026.54652.9680 | ||
| نویسندگان | ||
| J. Tayyebi* 1؛ E. Hosseinzade2؛ M. Niksirat3 | ||
| 1Department of Industrial Engineering, Birjand University of Technology, Birjand, Iran. | ||
| 2Department of Mathematics, Kowsar University, Bojnord, Iran | ||
| 3Department of Computer Science, Faculty of Industrial and Computer Engineering, Birjand University of Technology, Birjand, Iran. | ||
| چکیده | ||
| The assignment problem is a foundational combinatorial optimization problem that requires a decision maker to allocate agents to tasks in order to minimize the total cost incurred. From a graph-theoretic perspective, this problem can be framed as a matching problem on a bipartite graph. This paper presents a natural extension of the traditional assignment problem by considering fuzzy graphs as the underlying framework. This extension proves significant in practical situations where expert opinions contribute to assessing the relative significance level of agents (or tasks) and the satisfaction levels associated with different assignments. The main goal for the decision maker is not just to minimize costs but also to consider expert opinions. This paper addresses this problem by first formulating it as a tri-objective optimization problem. Subsequently, the ϵ-constraint method is applied to propose an interactive algorithm designed to identify satisfactory solutions. Finally, a practical example of assigning teachers to schools is provided to demonstrate the algorithm in a real-world application. | ||
| کلیدواژه‌ها | ||
| Assignment problem, combinatorial optimization؛ fuzzy graph؛ significance level؛ satisfaction level؛ ϵ-constraint method؛ Interactive algorithm | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 6 تعداد دریافت فایل اصل مقاله: 2 |
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