Takagi-Sugeno model

As a result authors propose take under consideration to use in future projects Takagi-Sugeno models or neutral network. 

Takagi-Sugeno models are particularly suited to model dynamic systems (de Bruin and Rof-fel, 1996). The most common structure is the NARX (Non-linear autoregressive with exogenous input) model, which can represent a large class of discrete time nonlinear systems. 

The algorithms summarized in the previous two sections can easily be applied to identify the consequence part of a fuzzy Takagi-Sugeno model. 

Dragan K (2002) Design of adaptive takagi-sugeno-kang fuzzy models. Appl Soft Comput 2(2) 89-103... 

Let us assume that we like to approximate the function z = shown in Fig. 28.3, in the regions = [-2, 2] by a Takagi-Sugeno fuzzy model. 

The most classical inference engine models used in FLC systems are the Mamdani and Takagi-Sugeno (TS) models. Equation 16-33 shows the form of each rule for the Mamdani type inference model. 

The rules in the Takagi-Sugeno type inference model have the form shown in Eq. 16-34. 

Tavanai et al (2005) developed a fuzzy system to model the color yield k/s) of polyester (PET) yarns as a function of time, temperature, and dispersed dye concentration. A typical rule for the color yield was if (temperature is low) and (time is low) and (concentration is low), then (color yield is very low). Only a small number of rules were necessary to create a viable model. In a later paper, Nasiri et al (2011) developed this model by further offering a compromise between the accuracy of classic Takagi-Sugeno systems and the interpretability of Mamdani models by applying genetic algorithms to improve the fuzzy rules. 

The output of the model of the Takagi-Sugeno inference is therefore a linear combination of input values with coefficients non-linearly dependent on these values. In a simple manner, this extends the model to nonlinear ARX, where nonlinearity is determined by the membership function of the fuzzy inputs. A similar approach may be used with neural MLP instead of linear ARX local models (Fig. 3.8). 

In this model, Takagi-Sugeno inference is a strictly static process, not containing any dynamics. Dynamics can be taken into account by adding into each of the rules of inference a differential equation describing the local dynamics of the object. 

Takagi, T. and SuGENO, M., 1985, Fuzzy identification of systems and its apvplications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, SMC-15,... 

Takagi and Sugeno (1985) proposed models where the consequent part of the rule is described by a linear regression model. These models are easier to identify because each rale describes a fuzzy region in which the output depends on the inputs in a linear maimer. An example of such a model is shown in Eqn. (28.3) ... 

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