Abstract
This document presents some considerations and procedures to design a compact fuzzy system based on Boolean relations. In the design process, a Boolean codification of two elements is extended to a Kleene’s of three elements to perform simplifications for obtaining a compact fuzzy system. The design methodology employed a set of considerations producing equivalent expressions when using Boole and Kleene algebras establishing cases where simplification can be carried out, thus obtaining compact forms. In addition, the development of two compact fuzzy systems based on Boolean relations is shown, presenting its application for the identification of a nonlinear plant and the control of a hydraulic system where it can be seen that compact structures describes satisfactory performance for both identification and control when using algorithms for optimizing the parameters of the compact fuzzy systems. Finally, the applications where compact fuzzy systems are based on Boolean relationships are discussed allowing the observation of other scenarios where these structures can be used.
Highlights
Modeling, controlling, and performing any system is an essential task for the designer/user to apply the necessary corrections to make it more effective
Two schemes of compact fuzzy systems based on Boolean relationships were formalized, which can be used in identification and control; other architectures can be established, such as when an activation is used with partial dependence on the input sets or ad hoc structures for dynamic systems
This work reviewed the methodology for designing fuzzy inference systems applied to specific cases to have compact fuzzy inference systems based on Boolean relations
Summary
Modeling, controlling, and performing any system is an essential task for the designer/user to apply the necessary corrections to make it more effective. Evaluating a system is done under fuzzy rules, for instance, by employing qualitative instead of numeric marks or incomplete numeric functions, etc. Fuzzy systems theory is built on concrete and practical formation for many relevant applications, especially in decision-making processes [2,3]. Various real-life problems are problematic since they involve human beings, mechanical elements, and other issues. Cases like these or even simpler ones may include diverse uncertainty conditions of high relevance when achieving satisfactory outcomes. Uncertainty may include randomness, fuzziness, indistinguishability, and incompleteness [4,5]. The theory on fuzzy sets and fuzzy logic permits manipulating incomplete and imprecise information of objects belonging to a concept [6]
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