Abstract
This paper proposes a methodology for the design of fuzzy inference systems based on Boolean relations. The approach using Boolean sets presents limited performance due to the abrupt transitions that occur during its functioning, therefore, fuzzy sets can be used aiming the improvement of the performance. In this approach, firstly, the design of a Boolean controller is performed, which is later extended into fuzzy under design guidelines proposed in this paper. The methodology uses Kleene algebra via truth tables for the fuzzy system design, allowing the simplification of the equations that implement the fuzzy system.
Highlights
Fuzzy Inference Systems (FIS) have wide applicability in control systems due to their flexibility for control strategy implementation when ambiguity or imprecisions occur in a plant model [1,2,3]
The design based on Boolean algebra allows to represent the knowledge of a system by means of specific cases established with Boolean-type variables; this way, an advantage of the control systems based on Boolean logic consists of a design methodology based on truth tables
A detail of these characteristics is shown in Figure 22, where an oscillatory behavior is observed for the Boolean controller while the BBR controller presents a continuous and smooth behavior
Summary
Fuzzy Inference Systems (FIS) have wide applicability in control systems due to their flexibility for control strategy implementation when ambiguity or imprecisions occur in a plant model [1,2,3]. More cases to considerer appear in the system operation when using fuzzy sets; to design process several properties of Boolean algebra are not met for fuzzy sets; these issues can be addressed using Kleene algebra, which is an aspect to consider in this work. In this regard, it should be kept in mind that Boolean algebra (named B )-based tools have been developed using sets whose values are {0, 1}, while Kleene algebra (denoted K) includes a third element u, having a structure of {0, u, 1} [7]
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