Cobb–Douglas Economy Model Optimum Production Control with Fuzzy Logic Principles

Abstract Production function evaluation plays a fundamental role in economic relations for optimal solutions. The Cobb–Douglas (C–D) production function is widely used to mathematically describe the nonlinear relationship between labor and capital. Various solution alternatives exist in the literature, including traditional regression analysis, artificial neural networks (ANNs), genetic algorithms (GAs), and mathematical optimization procedures. Each of these approaches relies on dense bivalent (two-valued) logical mathematical expressions and architectural structures that provide approximate precise solutions. This paper presents three algorithms for optimal C–D function evaluation, including interval, bivalent, and fuzzy logic parameter representations, and the comparative calculation of the final solutions between them. The proposed methodology encompasses two-valued logic labor estimation with membership degree 1 and multiple fuzzy logic estimations through fuzzy sets with a range of risk levels. In this study, triangular fuzzy membership degree functions are adopted as fuzzy sets. This same approach demonstrates how fuzzy logic approximation of fundamental economic variables produce not only the most probable solution but also a set with the desired membership degree. The appeal of fuzzy logic mathematics lies in the ability of numerical data as well as the ability to combine all kinds of rational-based expert language experience with intuitive inference. Furthermore, in fuzzy logic, depending on the membership degrees, the solution set is represented by a probability cumulative distribution function (CDF) that provides reliability and risk values at any given probability level.