Possibility linear programming with trapezoidal fuzzy numbers |
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Institution: | 1. College of Information Technology, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China;2. Jiangxi Key Laboratory of Data and Knowledge Engineering, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China;3. College of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China |
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Abstract: | Fuzzy linear programming with trapezoidal fuzzy numbers (TrFNs) is considered and a new method is developed to solve it. In this method, TrFNs are used to capture imprecise or uncertain information for the imprecise objective coefficients and/or the imprecise technological coefficients and/or available resources. The auxiliary multi-objective programming is constructed to solve the corresponding possibility linear programming with TrFNs. The auxiliary multi-objective programming involves four objectives: minimizing the left spread, maximizing the right spread, maximizing the left endpoint of the mode and maximizing the middle point of the mode. Three approaches are proposed to solve the constructed auxiliary multi-objective programming, including optimistic approach, pessimistic approach and linear sum approach based on membership function. An investment example and a transportation problem are presented to demonstrate the implementation process of this method. The comparison analysis shows that the fuzzy linear programming with TrFNs developed in this paper generalizes the possibility linear programming with triangular fuzzy numbers. |
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Keywords: | Fuzzy linear programming Trapezoidal fuzzy number Triangular fuzzy number Multi-objective linear programming |
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