模糊线性分式规划的标准型及其最优值区间

The Standard Form of Fuzzy Linear Fractional Programming and Its Optimal Objective Value Interval

针对一类目标函数和约束条件均含有模糊系数的线性分式规划问题,利用模糊数的最佳逼近区间设计了一种新的求解模糊线性分式规划的解法.首先,提出了模糊线性分式规划的标准型及其最优值区间的定义,将模糊线性分式规划问题转化为基于模糊数最佳逼近区间的区间线性分式规划问题.其次,将区间线性分式规划问题的最优值求解转化为求解4个确定型的线性分式规划问题,进而利用Gilmore-Gomory算法求解.最后给出的数值算例,验证了该方法的有效性与可行性.

Aiming at a class of linear fractional programming problems that both objective function and constraint conditions had fuzzy coefficients,a new method to solve fuzzy linear fractional programming was proposed by using the optimal approximation interval of fuzzy numbers.Firstly,the standard form and optimal objective value interval of fuzzy linear fractional programming were defined,and the problem of fuzzy linear fractional programming was transformed into the linear fractional programming of interval based on the optimal approximation interval of fuzzy numbers.Secondly,the linear fractional programming model with interval coefficients was converted into four deterministic models.Then,the Gilmore-Gomory algorithm was used to solve these four deterministic models.Finally,a numerical example in practical application was given to verify the validity and feasibility of the proposed method.