Economic Applications of Fuzzy Subset Theory and Fuzzy Logic: A Brief Survey

Abstract

Traditional mathematics is the language of precision. Statements are either true or false. But, in reality there are few things that are truly simply true or false. Life is full of shades of grey. Capturing these shades of grey has been problematic using traditional mathematics. Mathematics can model the uncertainty itself but rarely incorporates it into the model. However, an emerging area of mathematical inquiry known as the mathematics of uncertainty seeks to overcome some of these problems by integrating the uncertainly, the shades of grey, directly into the model. Fuzzy theory is one of those emerging ideas. This paper is simply an overview of some of the basic mechanics of fuzzy theory and recent economic applications in both micro and macro-economics.

Comparison of the Evaluation of Performance Preconditions in Tennis with the Use of Equal and Expertly Judged Criteria Weights

“…The theory of fuzzy sets was created by Zadeh (1965) as an alternative to classical (binary) logic and pointed to the fact that the use of sharp boundaries may be unsuitable in certain cases in which binary logic fails. Since its inception, fuzzy logic has gradually been applied in many fields of human activity, such as geography (Božić-Štulić, Kruzic, Gotovac, & Papić, 2018), medicine (Das, Chowdhury, & Saha, 2012), economics (Shin, & Wang, 2010) and digital technology (Sagar, & Babu, 2012), while it is also widely used in domestic appliances such as washing machines and microwave ovens, in transport in the operation of traffic lights, and in banking.…”

Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem

“…It is primarily based on the fact that "all things happening in real world are unstable and unpredictable." This idea was put forward and successfully applied to many fields of research-such as medicine, computer science, engineering, and economicsowing to its remarkable effectiveness at solving problems that could not be solved by traditional logic; see [1][2][3] and references therein. In particular, fuzzy logic has long been applied to dynamic systems expressed in differential equations; see [4][5][6][7][8][9][10][11][12][13][14][15] and references therein.…”