求解模糊排队性状指标隶属函数的通用方法

General method for solving membership function of characters index for fuzzy queueing

针对顾客到达率和系统服务率等参数均为模糊数的排队模型,应用模糊结构元理论研究系统模糊指标的解析表达式.在模糊分析的基础上,将模糊排队模型中主要指标求解转化成了模糊多元函数的运算.通过模糊结构元表示方法,将模糊多元函数转化成了模糊一元函数,根据模糊一元函数可得到性状指标的隶属函数,避免了只利用α-截集的定义和Zadeh的扩展原理方法带来的运算困难,也给模糊多元函数的求解提供了途径.实例分析了多重休假策略成批到达排队问题,其中,顾客的平均到达率、系统的平均服务率和服务员的平均休假率均用模糊结构元表示,求解出了顾客平均逗留时间及隶属函数,说明了方法的有效性.

According to the arrival rate and service rate are both fuzzy numbers in queueing model, the method of fuzzy structuring element is applied to study membership function of characters index which is waiting time, queuing captain. The mutual conversion method is given between membership function and monotonic transformation function for the same fuzzy nmnber. By making use of fuzzy structured element methods and fuzzy expansion principle, bivariate fuzzy number flmction transforms fuzzy number function with one variable. At the same time, monotonic transformation function of fuzzy number function with one variable is obtained. In generally, the characters index of queuing system index and arrival rate （service rate） are direct proportion （inverse proportion）. So characters index which contains the arrival rate and service rate are both fuzzy numbers is described by bivariate fuzzy number function. In addition, monotonic transformation function of characters index may be obtained. Through the use of mutual conversion relationship between membership function and monotonic transformation function, membership function of characters index is produced. This paper＇s method is more simple and general by example comparison.