模糊网络最大流算法研究

Study on Fuzzy Network Maximum Flow Algorithm

将模糊数差值B^-A~视为模糊方程X^+A~=B~的解,进而探讨了模糊方程的求解问题,并基于目的规划理论,给出了模糊方程的广义解定义.运用目的规划的单纯型方法,得到了模糊方程广义解的计算公式及模糊方程广义解的若干性质.由模糊方程的广义解引申出了模糊数差值的定义.运用该定义将传统的网络最大流算法推广到模糊环境.结果表明,模糊数差值定义,克服了基于扩展原理意义下的模糊运算所产生的各种问题,解决了这些传统理论方法的拓展问题.

This paper takes fuzzy number difference B^^- A^~ as the solution of the fuzzy equation, therefore discusses the problem of finding the solution of fuzzy equation, and based on theory of goal programming, gives the generalized solution of fuzzy equation. By use of the simplex method of the goal programming, we obtains the calculation formula and some properties of the generalized solution of fuzzy equation. Therefore based on the generalized solution of fuzzy equation, we presents the concept for the difference of two fuzzy numbers. By use of it, we widened classical Maximum Flow Algorithm. the results shows that the concept for the difference of two fuzzy numbers mentioned on this paper over cames the problems caused by fuzzy operations based on the extension principal, and solves the generalized problem of these classical theories.