A Study Of Production Function And Decision In A Fuzzy Environment

Production function is an important concept in economics theory, it describes the maximal output for limited input in perfect condition. There are many kinds of production function, among which Cobb-Douglas has been wildly accepted and applied in many fields, because of its good characteristics and exact economic signification. However, for real problem, it is always hard to collect enough information to estimate the parameter of production function or it is costly to get the exact figure, the parameter of the production function should be considered as a fuzzy varibale. Since it became hard to measure the output, this paper introduces the expection value of function of fuzzy variable to stand for the average output in perfect condition.Based on credibility theory, this thesis proposes an expression to calculate the expection value of function of fuzzy variable, which will be applied to evaluate the maximal output under the Cobb-Douglas production function theory. And then this thesis establishes models of the maximal expected value of income of short-term production and short term production, respectively, since ccording to the adjustability of the inputs, production functions were divided in to short-term and long-term production function. This thesis presents two examples and gets the solutions by PSO method.Finally, this thesis points out both the inside and outside management efficiencies, which charactered as fuzzy varibales since they were hard to describe as exact numbers, determine the realistic output of an organization, and evaluates the highest acceptable cost of inner or outside revolution in a fuzzy environment, which provides a direction for the organization revolution.