Fuzzy associative matrix

About: Fuzzy associative matrix is a research topic. Over the lifetime, 8027 publications have been published within this topic receiving 194790 citations.

Exact Output Regulation for Nonlinear Systems Described by Takagi–Sugeno Fuzzy Models

Abstract: The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T-S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.

Designing a hierarchical fuzzy logic controller using the differential evolution approach

Abstract: In conventional fuzzy logic controllers, the computational complexity increases with the dimensions of the system variables; the number of rules increases exponentially as the number of system variables increases. Hierarchical fuzzy logic controllers (HFLC) have been introduced to reduce the number of rules to a linear function of system variables. However, the use of hierarchical fuzzy logic controllers raises new issues in the automatic design of controllers, namely the coordination of outputs of sub-controllers at lower levels of the hierarchy. In this paper, a method is described for the automatic design of an HFLC using an evolutionary algorithm called differential evolution (DE). The aim in this paper is to develop a sufficiently versatile method that can be applied to the design of any HFLC architecture. The feasibility of the method is demonstrated by developing a two-stage HFLC for controlling a cart-pole with four state variables. The merits of the method are automatic generation of the HFLC and simplicity as the number of parameters used for encoding the problem are greatly reduced as compared to conventional methods.

Fuzzy description of topological relations I: a unified fuzzy 9-intersection model

Abstract: First, the impacts of uncertainty of position and attribute on topological relations and the disadvantages of qualitative methods in processing the uncertainty of topological relations are concluded. Second, based on the above point, the fuzzy membership functions for dividing topology space of spatial object and for describing uncertainty of topological relations are proposed. Finally, the fuzzy interior, exterior and boundary are defined according to those fuzzy membership functions, and then a fuzzy 9-intersection model that can describe the uncertainty is constructed. Since fuzzy 9-intersection model is based on fuzzy set, not two-value logic, the fuzzy 9-intersection model can describe the impacts of position and attribute of spatial data on topological relations, and the uncertainty of topological relations between fuzzy objects, relations between crisp objects and fuzzy objects, and relations between crisp objects in a united model.

Fuzzy classifications using fuzzy inference networks

Abstract: In this paper, fuzzy inference models for pattern classifications have been developed and fuzzy inference networks based on these models are proposed. Most of the existing fuzzy rule-based systems have difficulties in deriving inference rules and membership functions directly from training data. Rules and membership functions are obtained from experts. Some approaches use backpropagation (BP) type learning algorithms to learn the parameters of membership functions from training data. However, BP algorithms take a long time to converge and they require an advanced setting of the number of inference rules. The work to determine the number of inference rules demands lots of experiences from the designer. In this paper, self-organizing learning algorithms are proposed for the fuzzy inference networks. In the proposed learning algorithms, the number of inference rules and the membership functions in the inference rules will be automatically determined during the training procedure. The learning speed is fast. The proposed fuzzy inference network (FIN) classifiers possess both the structure and the learning ability of neural networks, and the fuzzy classification ability of fuzzy algorithms. Simulation results on fuzzy classification of two-dimensional data are presented and compared with those of the fuzzy ARTMAP. The proposed fuzzy inference networks perform better than the fuzzy ARTMAP and need less training samples.