基于效应的随机灰规划模型和应用

为了解决同时含有随机因素和灰色因素的不确定规划问题,通过结合区间灰数所属区间两个端点的随机性,给出随机区间灰数和随机区间灰函数的定义,提出了随机灰规划模型。通过综合效应函数理论用随机变量期望值和方差综合量化表示灰数所属区间的两个端点值。应用该理论对综合量化后的两个端点值继续进行综合量化,从而将随机灰规划转化为确定型规划问题。应用遗传算法进行求解。通过综合效应函数的理念,综合随机变量的期望和方差,同时综合区间灰数的区间因素,将随机灰规划数学模型转化为确定型规划模型即基于效应的随机灰规划模型。通过选取不同的综合效应函数,得到了关于不同决策意识下的随机灰规划的最优解。这个方法可为决策者进行不确定决策提供参考。

Stochastic gray programming model and application based on effect

n order to solve the problem of uncertain planning with both random and gray factors, the stochastic gray programming model is proposed by combining the randomness of the two endpoints of the interval gray number, and the definition of the random gray number and the random gray function of the interval are given. Through the theory of synthetic effect function, the expected value and variance of random variables are quantized to represent the two endpoints of the interval of the gray number. Then the comprehensive effect function theory is applied to the comprehensive quantization of the two endpoint values after the comprehensive quantification, so that the stochastic gray programming is transformed into a deterministic programming problem. Genetic algorithm is applied to solve the problem. Through the idea of comprehensive effect function, the expectation and variance of random variables are combined, and the interval factors of interval ash number are combined, and the stochastic gray programming mathematical model is converted into a definite programming model, namely, an effect-based random gray programming model. The optimal solution of random gray programming under different decision consciousness is obtained by selecting different synthetic effect functions. This method has certain reference value for different decision makers when making uncertain decisions.