راه حل همزمان مدل های فازی: کاربرد برای تجزیه و تحلیل تعادل اقتصادی

The fuzzy modeling technology, which uses a rule-based description of the relationship between variables, is discussed. We then turn to the problem of the simultaneous solution of relationships involving fuzzy models. We illustrate this problem by considering the equilibrium problem in economics. In this case we have two relationships, one between price and supply and the other between price and demand, and we desire to find the price for which the supply equals the demand. It is shown that if the fuzzy models have antecedent fuzzy sets which are of the trapezoidal–triangular type then a solution technique can be found.

Modern technology makes great use of the idea of relationships between variables. Once having obtained a relationship between two variables one can use this relationship to obtain the value of the dependent variable given knowledge of the independent variable. Thus, if we have a relationship V=F(U) given a value for U we can obtain the value for V. In some situations, rather than knowing the value of the independent variable, we may have another relationship between the variables,V=G(U),and we want tond a solution that simultaneously solves both equations.A prototypical example of this situation is the solution of two linear equations y=2x+3andy=6x−9.Here, we need to solve for both the values of x and y Fuzzy systems models[15]have shown themselves to be a very useful tool for the modeling of complex nonlinear relationships between variables. They have found particular use in modeling of intelligent control systems[9,10,19,20].Using this technology we model a complex relationship with the aid of a rule base in which each rule represents a part of the whole relationship.In this framework our relationship is a set of rules of the form if U is A i then V is B i where A i and B i are fuzzy subsets. As indicated above once having obtained a fuzzy model a typical usage of this model involves the determination of the output variable for a given value of theinput variable.This is accomplished by using the fuzzy inference algorithm. we consider an extension of the usage of the fuzzy systems modeling technology to the case in which, rather than knowing the value of the input variable,we have some other relationship between the variables, which may be another fuzzy model and desireto nd the simultaneous solution of these two models.Weillustrate this situation by considering the equilibrium problem in economics [8]. In this case we have two relationships, one between price and supply and the other between price and demand,and we desire to nd the price for which the supply equals the demand.

We have investigated the problem of the simultaneous solution of equations involving a fuzzy modeling of the relationships.We showed that if the antecedents fuzzy set sarepie cewise line arthen weareabletond an analytic solution to the problem.