| A branch and bound technique for finding the minimal solutions of the linear optimization problems subjected to Lukasiewicz |
| کد مقاله : 1006-CSANS2022 |
| نویسندگان: |
|
Amin Ghodousian *1، zahra boreiri2، faeze habibi2 1Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran. 2College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran. |
| چکیده مقاله: |
| In this paper, an optimization model with a linear objective function subjected to a system of fuzzy relation equations (FRE) is studied where the feasible region is defined by the Lukasiewicz t-norm. Since the feasible solutions set of the problem is a non-convex set, the feasible region is completely determined by one maximum solution and a finite number of minimal solutions and the finding of all minimal solutions is an NP-hard problem, designing an efficient solution procedure for solving such problems is not a trivial job. Firstly, the feasible domain is characterized. It is shown that the feasible region can be always obtained in terms of a finite closed convex cells. Some mathematical and basic structural properties are investigated. Then the problem is solved with a modified branch-and-bound solution technique based on a new solution set that includes the minimal solutions. After presenting our solution procedure, a concrete example is included for illustration purpose. |
| کلیدواژه ها: |
| Fuzzy relational equations; formatting; linear optimization; strict t-norm; Lukasiewicz t-norm |
| وضعیت : مقاله برای ارائه به صورت پوستر پذیرفته شده است |
