Properties of Fuzzy Systems

The paper presents a short review of some main properties of the most general fuzzy systems used in a large class of practical applications. The fuzzy systems, implemented using different rule bases, fuzzy values, membership functions, fuzzyfication and defuzzification methods, may be classified based on these fuzzy methods used in their development. This paper proposes a unitary theory for describing Mamdani fuzzy controllers based on their characteristics. Fuzzy rules bases may be seen as fuzzy applications between fuzzy sets. These rule bases have algebraic properties as: commutative law, neutral element and symmetric elements. The fuzzy systems may be analytical described with MISO, SISO and gain transfer characteristics, which may be calculated using computer programs. The fuzzy systems have algebraic properties as: commutative law and symmetric elements. These algebraic properties may be noticed on their transfer characteristics. The fuzzy systems have a variable gain with their inputs. Some gain characteristics values are presented. The rule bases and the fuzzy systems have the sector property. The paper emphasizes, based on the transfer characteristics, planar and spatial sector properties useful in stability analysis with Lyapunov techniques. The transfer characteristics, system linear characteristic around the origin and the gain in origin are usefull in the design of fuzzy PID controllers. Based on transient characteristics of fuzzy control systems some quality criteria are presented. The fuzzy systems used in control assure better control quality criteria and a greater robustness at disturbances effects and at the error at the identification of controlled processes parameters. Key-Words: Fuzzy systems, fuzzy logic, nonlinear systems, algebraic properties, absolute global internal stability, fuzzy controllers, empirical control quality criteria, system robustness, circle criterion, fuzzy PID controllers.