规划问题的一种新提法

用数学工具去解决实际问题的一个前提条件是需要建立一个恰当的数学模型。随着问题研究的深入,往往需要人们寻求一些新的数学工具去建立更加符合客观实际的数学模型。传统的单目标最优化问题(规划问题)的数学模型(?)f(x),R={x|g_i(x)≥0,i=1,2,…,m}是有局限的。主要反映在下面两方面:1.实际问题中的约束条件常常发生在一种不分明的环境中,按分明情况处理有时会丢失更为恰当的解。2.多目标最优化问题与单目标最优化问题,目标函数与约束条件之间往往没有不可逾越的鸿沟。有的问题本来是多目标最优化问题,但为了处理上的方便人为地把有些目

A NEW MODEL OF PROGRAMMING PROBLEMS

In this paper,the limitations of the classical model of programming problems areindicated and a more general model is given in terms of fuzzy subset theory.This mo-del may contain more realistic cases which cannot be included in the classical mathemati-cal model.The concept of fuzzy value set of a function is defined and other important conceptsinvolved with the model of optimization are established on the basis of the fuzzy valueset.The effectiveness of the solution in this model is proved.Therefore the theoreticalsuitability of this soltion is ensured.Meanwhile,the concept of fuzzy convex functionis introduced.The fuzzy convex function will reserve the convexity of the original fun-ction under general conditions.