This paper outlines two contributions to stability analysis of fuzzy systems: knowledge of the membership function shape (actually, constraints on the membership function values) and polynomial approaches. Both ideas reduce the conservativeness in the stability analysis of a nonlinear system when expressed as a fuzzy model by using membership shape information and by allowing a more general cla...

Fuzzy-Systeme sind im Allgemeinen statische Systeme. Des Weiteren lassen sich aber auch dynamische Systeme direkt durch Fuzzy-Funktionen und Regeln beschreiben. Ihre Dynamik ist dabei inhärent und wird nicht durch das Gewichten von dynamischen Modellen wie im Falle von Takagi–Sugeno–Kang-Systemen erreicht, sondern durch direkte Rückführung der Ausgangsgrößen eines Fuzzy-Systems. In diesem Beitr...

Fuzzy logic is a powerful tool to model knowledge uncertainty, measurements imprecision, and vagueness. However, there is another type of vagueness that arises when data have multiple forms of expression that fuzzy logic does not address quite well. This is the case for multiple instance learning problems (MIL). In MIL, an object is represented by a collection of instances, called a bag. A bag ...

The integration of neural networks and fuzzy inference systems could be formulated into three main categories: cooperative, concurrent and integrated neuro-fuzzy models. We present three different types of cooperative neuro-fuzzy models namely fuzzy associative memories, fuzzy rule extraction using self-organizing maps and systems capable of learning fuzzy set parameters. Different Mamdani and ...

This paper deals with the extension of the positive invariance approach to Takagi-Sugeno fuzzy systems. The saturations on the control are taken into account during the design phase. This attempt is firstly applied to a class of fuzzy systems. Sufficient conditions of asymptotic stability are given ensuring in the same time that the global control is always admissible inside a common polyhedral...

Stability analysis and optimality are important in any systems. In the paper, “Optimal Fuzzy Controller Design: Local Concept Approach,” optimal fuzzy controller is design for Takagi–Sugeno fuzzy model. Unfortunately, it seems that some errors are happen and no simple correction can be done. In this paper, we show that some errors exit in the aforementioned paper with simple and clear examples.

Recently, the Takagi-Sugeno fuzzy controllers [3] have been applied to nonlinear systems (see, for example, [3] and [4]). In these studies, a nonlinear plant was represented by a set of linear models interpolated by membership functions and then a model-based fuzzy controller was developed. This technique seems particularly suitable for the control of complex nonlinear systems since the dynamic...

The “fuzzy dot” (or fuzzy relation) representation of fuzzy rules in fuzzy rule based systems, in case of classical fuzzy reasoning methods (e.g. the Zadeh-MamdaniLarsen Compositional Rule of Inference (CRI) (Zadeh, 1973) (Mamdani, 1975) (Larsen, 1980) or the Takagi Sugeno fuzzy inference (Sugeno, 1985) (Takagi & Sugeno, 1985)), are assuming the completeness of the fuzzy rule base. If there are...

This paper concerns the use of fuzzy structures to model linear dynamic systems. A systematic method is proposed to generate the rules and also select the antecedent and consequent membership functions directly from the mathematical expression. The procedure is applied to the Takagi-Sugeno-Kang fuzzy structures and later adapted to the Mamdani fuzzy structures. It is shown that the Mamdani stru...

A novel adaptive control strategy is proposed herein to increase the efficiency of adaptive control by combining Takagi–Sugeno (T–S) fuzzy modeling and the Ge–Yao–Chen (GYC) partial region stability theory. This approach provides two major contributions: (1) increased synchronization efficiency, especially for parameters tracing and (2) a simpler controller design. Two simulated cases are prese...