模糊随机多目标规划性质的研究

Study of the Properties of Fuzzy Random Multi-objective Programming

在模糊随机环境下,针对于多目标规划问题的性质,给出了一系列的重要结论。首先,基于模糊随机理论,提出了模糊随机多目标规划问题的期望值模型,实现了对实际问题的不确定性到确定性的转化,并为解决实际问题提供了理论模型。规划问题的凸性在优化理论中占有非常重要的地位,因此,对于所提出模型的凸性,利用模糊随机变量的期望值的特殊性质,给出了严格的证明。定义了模糊随机多目标规划的期望值绝对最优解、期望值有效解及期望值弱有效解的概念,并研究了它们的性质。根据生活中的实际问题所建立的模糊随机规划模型的求解,所得结果为其算法的研究及最优决策的执行提供了重要的理论依据。

Under the fuzzy random environment and aimed at the properties of multi-objective programming,this paper gains many important conclusions.Based on the fuzzy random theory,the expected value model of fuzzy random multi-objective programming is presented which transforms the uncertainties of practical problems into the certainties and provides the theoretical foundation for solving the real-life world problem.As we known,the convexity of programming problem plays an important part in optimization theory,this paper strictly proves the convexity of the model presented above by the properties of expectation of fuzzy random variable.Furthermore,this paper defines the concepts of expected-value non-inferior i.e.the expected-value absolutely optimal solution,the expected-value efficient solution and the expected-value wake efficient solution,and also investigates their properties.To solve the model of fuzzy random programming established by the real problem in practice,the conclusions obtained in this paper provide a theoretical foundation for designing algorithms and making the optimal decisions.