## Abstract

Fuzzy rule-based systems are one of the most important areas of application of fuzzy sets and fuzzy logic. Constituting an extension of classical rule-based systems, these have been successfully applied to a wide range of problems in different domains for which uncertainty and vagueness emerge in multiple ways. In a broad sense, fuzzy rule-based systems are rule-based systems, where fuzzy sets and fuzzy logic are used as tools for representing different forms of knowledge about the problem at hand, as well as for modeling the interactions and relationships existing between its variables. The use of fuzzy statements as one of the main constituents of the rules allows capturing and handling the potential uncertainty of the represented knowledge. On the other hand, thanks to the use of fuzzy logic, inference methods have become more robust and flexible. This chapter will mainly analyze what is a fuzzy rule-based system (from both conceptual and structural points of view), how is it built, and how can be used. The analysis will start by considering the two main conceptual components of these systems, knowledge, and reasoning, and how they are represented. Then, a review of the main structural approaches to fuzzy rule-based systems will be considered. Hierarchical fuzzy systems will also be analyzed. Once defined the components, structure and approaches to those systems, the question of design will be considered. Finally, some conclusions will be presented.

## Keywords

Membership Function Fuzzy System Fuzzy Rule Linguistic Variable Linguistic Term- CG
center of gravity

- DNF
disjunctive normal form

- FLC
fuzzy logic controller

- FL
fuzzy logic

- FRBS
fuzzy rule-based system

- FS
fuzzy system

- KB
knowledge base

- MISO
multiple inputs-single output

- MOM
mean of maxima

- MV
maximum value

- RB
rule base

- TSK
Takagi–Sugeno–Kang

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