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Register a new userInteractive Cutting-Plane Method for Multiobjective Programming with Fuzzy Parameters
طريقة المستوي القاطع التفاعلية للبرمجة المتعددة الأهداف بوسائط ضبابية
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تقدم في هذا البحث طريقة حل تفاعلية لمسائل البرمجة الرياضية المتعددة الأهداف مع وجود وسائط ضبابية في كل من دوال الهدف و في القيود، و تعالج تلك الوسائط كأعداد ضبابية. و من أجل هذه المسائل يقدم مفهوم أمثلية a-بارتو كتوسيع لأمثلية بارتو العادية و ذلك بالاعتماد على مجموعات a-مرتبة للأعداد الضبابية. و تعتمد طريقة الحل المقترحة على المستويات القاطعة التي تبنى على نسب مقايضة موضعية بين دوال الهدف موصوفة من قبل متخذ القرار و ذلك عند كل تكرار مولد بالطريقة. و تم تقديم مثال عددي لتوضيح هذه الطريقة.
This paper presents an interactive solution method for treating multi objective mathematical programming problems with fuzzy parameters in the objective functions and in the constraints. Theses fuzzy parameters are characterized by fuzzy numbers. For such problems, the concept of a-Pareto optimality introduced by extending the ordinary Pareto optimality based on the a-level sets of fuzzy numbers. The proposed solution method is based on cutting planes, which are based on local trade off ratios between the objective functions as prescribed by the decision maker at each iterate generated by the method. An illustrative numerical example is given to clarity this method.
References used
DUBOIS, D.; PRADE, H. Operations on fuzzy numbers. International Journal of Systems Science, 9, 1978, 613-626
DUBOIS, D.; PRADE, H. Fuzzy sets and systems: theory and application. Academic Press, New York, 1980, 393
DYER, J. S. A time sharing computer program for the solution of the multiple criteria problem. Management Science, 19, 1973, 1379-1383
GEOFFRION, A. M.; DYER, J. S.; FEINBERG, A. An interactive approach for multicriterion optimization with an application to the operation of an academic department. Management Science, 19, 1972, 357-368
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