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Linear optimization on Hamacher-fuzzy relational inequalities | ||
| Journal of Algorithms and Computation | ||
| مقاله 10، دوره 49، شماره 1، شهریور 2017، صفحه 115-150 اصل مقاله (351.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22059/jac.2017.7988 | ||
| نویسندگان | ||
| Amin Ghodousian* 1؛ Mohammadsadegh Nouri2 | ||
| 1Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran | ||
| 2Faculty of Engineering Science, College of Engineering, University of Tehran, P.O.Box 11365-4563, Tehran, Iran. | ||
| چکیده | ||
| In this paper, optimization of a linear objective function with fuzzy relational inequality constraints is investigated where the feasible region is formed as the intersection of two inequality fuzzy systems and Hamacher family of t-norms is considered as fuzzy composition. Hamacher family of t-norms is a parametric family of continuous strict t-norms, whose members are decreasing functions of the parameter. The resolution of the feasible region of the problem is firstly investigated when it is defined with max-Hamacher composition. Based on some theoretical results, a necessary and sufficient condition and three other necessary conditions are derived for determining the feasibility. Moreover, in order to simplify the problem, some procedures are presented. It is shown that a lower bound is always attainable for the optimal objective value. Also, it is proved that the optimal solution of the problem is always resulted from the unique maximum solution and a minimal solution of the feasible region. A method is proposed to generate random feasible max-Hamacher fuzzy relational inequalities and an algorithm is presented to solve the problem. Finally, an example is described to illustrate these algorithms. | ||
| کلیدواژه‌ها | ||
| Fuzzy relation؛ fuzzy relational inequality؛ linear optimization؛ fuzzy compositions and t-norms | ||
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آمار تعداد مشاهده مقاله: 410 تعداد دریافت فایل اصل مقاله: 329 |
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