#### Publication Date

9-1-2022

#### Abstract

In practice, there is often a need to describe the relation y = f(x) between two quantities in algorithmic form: e.g., we want to describe the control value y corresponding to the given input x, or we want to predict the future value y based on the current value x. In many such cases, we have expert knowledge about the desired dependence, but experts can only describe their knowledge by using imprecise ("fuzzy") words from a natural language. Methodologies for transforming such knowledge into an algorithm y = f(x) are known as fuzzy methodologies. There exist several fuzzy methodologies, a natural question is: which of them is the most adequate? In this paper, we formulate the natural notion of adequacy: that if the expert rules are formulated based on some function y = f(x), then the methodology should reconstruct this function as accurately as possible. We show that none of the existing fuzzy methodologies is the most adequate in this sense, and we describe a new fuzzy methodology that is the most adequate.

*Original file*

## Comments

Technical Report: UTEP-CS-22-102a

To appear in: Chiranjibe Jana, Madhumangal Pal, G. Muhiuddin, and Peide Liu (eds.),

Fuzzy Optimization, Decision-making and Operations Research -- Theory and Applications, Springer