**5. Fuzzy classifier**

250 Fuzzy Inference System – Theory and Applications

With the previous operation all features that are processed by sensors have been fixed. Through feature extraction and selection the initial data can be reduced in order to diminish the computational complexity of the system. Moreover a reduction of features number simplifies both the pattern representation and the classifier structure; finally a reduction of features number solve the problem of "curse of dimensionality" (Roudys & Jain, 1991). The so-called curse of dimensionality problem consists in the fact that the number of instances for feature exponentially increases with the number of features itself; also in order to reduce the complexity of the computational intelligence modules under training, it is fundamental to limit the number of features to consider. Both feature extraction and feature selection are used for the reduction of the feature space. The main difference between the two approaches is that the feature extraction approach generates new features based on transformation or combination of the original features while feature selection approach selects the best subset of the original feature set (Dalton,

This operation combines the available features in order to obtain more significant information concerning the quality of the industrial process under consideration. A widely used technique is the so called *sensor fusion*, which combines information of different type coming from several sensors. A lot of papers, concerning the use of intelligent techniques have been proposed, such as (Bloch, 1996; Filippidi et al., 2000; Xia et al., 2002; Benediktsson et al., 1997). Data fusion systems can be composed by several elements such as sensors, data-fusion nodes, data-fusion databases and expert knowledge

Once the features are fixed, they are led in input to a classifier which outputs a value associated to the classification of the quality (integer value) or a quality index (real value).

The classification can be divided into two approaches: conventional classification and computational intelligence-based classification. The computational intelligence-based approach includes statistical approach (Fukunaga, 1972), neural networks (Haykin, 1999)

Modules belonging to the quality control system contain parameters which need to be fixed in order to improve final accuracy, computational complexity, maximum possible throughput and memory exploitation. These parameters include, for instance, thresholds,

In order to build a satisfactory quality control system it is important to integrate all the above cited activities. In order to obtain more accurate, adaptive and performing systems

and fuzzy systems (Bezdek, 1992). This last issue will be treated in the next section.

filter coefficients and number of hidden neurons in the case of use of neural network.

the use of computational intelligence techniques are recommended.

**4.3 Features extraction and selection** 

1996).

**4.4 Data fusion** 

databases.

**4.5 Classification** 

**4.6 System optimization** 

Fuzzy Logic has been introduced by Zadeh (Zadeh, 1965) and it is based on the concept of "partial truth", i.e. truth values between "absolutely true" and "absolutely false". Fuzzy Logic provides a structure to model uncertainty, the human way of reasoning and the perception process. Fuzzy Logic is based on natural language and through a set of rules an inference system is built which is the basis of the fuzzy computation. Fuzzy logic has many advantages, firstly it is essential and applicable to many systems, moreover it is easy to understand and mostly flexible; finally it is able to model non linear functions of arbitrary complexity. The Fuzzy Inference System (FIS) is one of the main concepts of fuzzy logic and the general scheme is shown in Fig.3.

Fig. 3. FIS scheme

A FIS is a way of mapping input data to output data by exploiting the fuzzy logic concepts.

Fuzzification is used to convert the system inputs, which is represented by crisp numbers into fuzzy set through a fuzzification function. The fuzzy rule base is characterized in the form of *if-then* rules and the set of these fuzzy rules provide the rule base for the fuzzy logic system. Moreover the inference engine simulates the human reasoning process: through a suitable composition procedure, all the fuzzy subsets corresponding to each output variable, are combined together in order to obtain a single fuzzy for each output variable. Finally the defuzzification operation is used to convert the fuzzy set coming from the inference engine into a crisp value (Abraham, 2005).

Fuzzy classification is an application of fuzzy theory. In fuzzy classification an instance can belong to different classes with different membership degrees; conventionally the sum of the membership values of each single instance must be unitary. The main advantage of fuzzy classification based method includes its applicability for very complex processes.
