Structural developments of fuzzy systems with the aid of information granulation

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Abstract

We introduce a design procedure for fuzzy systems using the concept of information granulation and genetic optimization. Information granulation and resulting information granules themselves become an important design aspect of fuzzy models. By accommodating the formalism of fuzzy sets, the model is geared towards capturing relationship between information granules (fuzzy sets) rather than concentrating on plain numeric data. Information granulation realized with the use of the standard C-Means clustering helps determine the initial values of the parameters of the fuzzy models. This in particular concerns such essential components of the rules as the initial apexes of the membership functions standing in the premise part of the fuzzy rules and the initial values of the polynomial functions standing in the consequence part. The initial parameters are afterwards tuned with the aid of the genetic algorithms (GAs) and the least square method (LSM). The overall design methodology arises as a hybrid development process involving structural and parametric optimization. Especially, genetic algorithms and C-Means are used to generate the structurally as well as parametrically optimized fuzzy model. To identify the structure and estimate parameters of the fuzzy model we exploit the methodologies such as joint and successive method realized by means of genetic algorithms. The proposed model is evaluated using experimental data and its performance is contrasted with the behavior of the fuzzy models available in the literature.

Section snippets

Introductory notes

Over the recent years, there has been a great deal of developments in fuzzy modeling [1]. Let us highlight some of the pursuits. Linguistic modeling [2], [3] and fuzzy relation equation-based approach [4], [5] were proposed as primordial identification methods for fuzzy models. In the linguistic approach, Tong identified a gas furnace process by means of a logical examination of data [6]. Xu reported interesting results obtained through the use of the modified Tong’s method [7] and proposed an

Fuzzy inference systems based on fuzzy set with the aid of information granules (IG-FIS)

The identification procedure for fuzzy models is usually split into the identification activities dealing with the premise and consequence parts of the rules. The identification completed at the premise level consists of two main steps. First, we select the input variables x1, x2, …, xk of the rules. Second, we form fuzzy partitions (by specifying fuzzy sets with well-defined semantics such as e.g., Small, Large) in the spaces over which these individual variables are defined. In essence, this

Optimization of the IG-based FIS

The need to solve optimization problems arises in many fields and is especially dominant in the engineering environment. There are several analytic and numerical optimization techniques yet one can easily encounter problems that are not well handled by them. The standard gradient-based optimization techniques might not be effective in the context of rule-based systems given their nonlinear character (in particular the form of the membership functions) and modularity of the systems. This forces

Experimental studies

In this section, we discuss three numerical examples in order to evaluate the advantages and the effectiveness of the proposed approach.

The first one concerns the nonlinear static system [19]. The second one deals with the time series dataset of gas furnace process [12], [26], [27], [28]. The third is the chaotic Mackey–Glass time series data [29].

Prior to the experiments, we summarize the essential features of the optimization environment. For the genetic optimization of the fuzzy model, the

Conclusions

We have introduced and investigated a certain class of fuzzy models along with their comprehensive design strategy. The main idea treats the fuzzy model based on information granules with the aid of C-Means clustering in the separate fuzzy space and a structural and parametric optimization of the fuzzy model by exploiting of genetic algorithms. We constructed some initial membership functions and the polynomial functions of the conclusion parts of the rules with the aid of information

Acknowledgements

This work has been supported by KESRI (R-2007-2-044), which is funded by MOCIE (Ministry of commerce, industry and energy). Support from the Natural Sciences and Engineering Council of Canada (NSERC) and the Canada Research Chair (CRC) Program (W. Pedrycz) is gratefully acknowledged.

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