采场模糊渗流定解问题的可表示性

Expressible problem of definite solution of fuzzy permeating flow in stope

采空区气体模糊渗流问题由模糊偏微分方程所描述。模糊微分方程是未知函数及其导数与已知模糊函数或者模糊常数的条件等式,方程解的模糊性是由已知模糊函数或模糊常数所引起的。当已知函数或常数为区间值函数或区间数时,相应的方程为区间微分方程。由于模糊函数或模糊数的截集为区间值函数或区间数,通常,模糊微分方程的解是利用模糊函数或模糊数截集所对应的区间微分方程解通过表现定理给出。由于模糊微分方程的解必须是模糊函数,如果通过表现定理给出的模糊微分方程的解是模糊函数,则称方程的解是可表示的。本文在给出模糊微分方程解的可表示定义同时给出了解的可表示判定条件,并且证明了采空区气体模糊渗流定解问题的可表示性。

The problem of the fuzzy gas permeating flow in stop may be described by a fuzzy differential equation. The fuzzy differential equations are a kind of condition equation containing the unknown function it's differential and the known fuzzy function or fuzzy constant. The exist existing fuzzy function in the differential equation brings about un-definiteness of the solution of fuzzy differential equations. When a certain unknown function is the interval-value function, corresponding equation is called the interval differential equation. If cut-set of fuzzy function is the interval-value function, therefore the solution of the fuzzy differential equation is expressed as union of a family interval-value functions by using the representation theorem, and these interval-value functions are the definite solutions of the interval differential equations corresponding with every cut-set of the fuzzy differential equation. The solution of fuzzy differential equation must be described as a fuzzy function. If the solution of the fuzzy differential equation expressed by using the representation theorem is a fuzzy function, then we call this solution is expressible. In this paper, we not only define for deciding the concept for deciding that the solution of fuzzy equations is expressible but also present a criterion condition which solution is expressible. In the meantime we prove that definite solution of fuzzy permeating flow problem on stop is expressible.