A large class of nonlinear systems can be represented or well approximated by Takagi- Sugeno (TS) fuzzy models, which in theory can approximate a general nonlinear system to an arbitrary degree of accuracy. The TS fuzzy model consists of a fuzzy rule base. The rule antecedents partition a given subspace of the model variables into fuzzy regions, while the consequent of each rule is usually a linear or affine model, valid locally in the corresponding region. In this paper, the observer design problem for a T-S fuzzy system subject to Lypschitz perturbation is investigated. First, an observer of Kalman type is designed to estimate the unknown system states. Then, the class of one-sided Lipschitz for a TS fuzzy system subject to a sufficient condition on the bound is studied. The challenges are discussed and some analysis oriented tools are provided. An example is given to show the applicability of the main result.

In this paper, the observer design problem for a T-S fuzzy bilinear control system is investigated. First, an observer of Kalman type is designed to estimate the system states for the linear case. Then, some new sufficient conditions are derived to show the exponential convergence of the solutions of the error equation for fuzzy bilinear systems. Furthermore, we consider some uncertainties of the system that are bounded and satisfy a certain condition where an observer is designed. Moreover, an application to Van de Vusse system is given.

Abstract. In this paper we present a new class of neuro-fuzzy systems designed for system modelling and pattern classi.cation. Our approach is characterized by automatic determination of fuzzy inference in the process of learning. Moreover, we introduce several .exibility concepts in the design of neuro-fuzzy systems. The method presented in the paper is characterized by high accuracy which outperforms previous techniques applied for system modelling and pattern classi.cation.

The paper focuses on the problem of robust fault detection using analytical methods and soft computing. Taking into account the model-based approach to Fault Detection and Isolation (FDI), possible applications of analytical models, and first of all observers with unknown inputs, are considered. The main objective is to show how to employ the bounded-error approach to determine the uncertainty of soft computing models (neural networks and neuro-fuzzy networks). It is shown that based on soft computing models uncertainty defined as a confidence range for the model output, adaptive thresholds can be described. The paper contains a numerical example that illustrates the effectiveness of the proposed approach for increasing the reliability of fault detection. A comprehensive simulation study regarding the DAMADICS benchmark problem is performed in the final part.

The article includes presentation of fuzzy numbers application in projects prioritizing at

manufacturing and service providing enterprises. The following criteria have been applied

as a basis for projects prioritizing analysis in enterprise: NPV index, linked with the enterprise strategic aims, project execution cost, project time, project scope and risk. As the

criteria selected were of measurable and non-measurable character in projects prioritizing

evaluation, the fuzzy decision making system has been developed, in which a linguistic value

has been defined for each criterion of projects prioritizing. Knowledge base has been developed afterwards, presenting cause-effect dependencies in projects prioritizing. Knowledge

base consisted of conditional rules. Fuzzy system of decision making in project prioritizing

has been developed in MATLAB application.

The decision making fuzzy system established, constitutes an efficient tool for projects prioritizing, on the basis of criteria given and concluding system developed. The obtained analysis

results provide basis for the decision making parties to set the projects execution sequences.