Fuzzy rules, application

All the three techniques mentioned above may make use of fuzzy sets and fuzzy logic (for fuzzy classification, fuzzy rules or fuzzy matching) but this does not effect the discussion of the applicability to NDT problems in the next section. 

Chen et al. [24] provide a good review of Al techniques used for modeling environmental systems. Pongracz et al. [25] presents the application of a fuzzy-rule based modeling technique to predict regional drought. Artificial neural networks model have been applied for mountainous water-resources management in Cyprus [26] and to forecast raw-water quality parameters for the North Saskatchewan River [27]. 

Pongracz R, Bogardi I, Duckstein L (1999) Application of fuzzy rule-based modelling technique to regional drought. J Hydrol 224 100-114... 

Fuzzy Logic Control The application of fuzzy logic to process control requires the concepts of fuzzy rules and fuzzy inference. A fuzzy rule, also known as a fuzzy IF-THEN statement, has the form... 

After input data are fuzzified and their membership values obtained, the next step involves application of them to the antecedents of fuzzy rules. If a given fuzzy rule has multiple antecedents, a fuzzy operator (AND or OR) is used to obtain a single number that represents the result of antecedent evaluation. This number is then applied to a consequent membership function. 

This book chapter critically compares the capabilities and limitations of crisp-mle and fuzzy-rule based up-sampling techniques and their relevance in view of robustness, adaptability to varying constraints, complexities, quality enhancement and their effectiveness in real time applications. 

Generally, in a terrestrial communication system, a transmitter possesses more processing ability than the receiver. Therefore, the major computational burden is easily taken up by the transmitter and less computational burden is left for the receiver. Since the proposed method is based on a preprocessing approach, it imparts more computational burden on the transmitting side than the receiving end and thus makes the receiver computationally less complex, fast and suitable for various real time applications. In addition, since this method is a spatial domain approach, it is computationally less complex than transform domain techniques such as DCT and wavelet. The proposed fuzzy-rule based method is a low complex, highly flexible and efficient technique that works fine with all types of video data. 

The data from the FMEA in Tables 7.9 and 7.12 is used here to demonstrate the application of the grey theory method. The same data is used for all three methods (traditional I lEA, fuzzy rule base and grey theory), to enable comparisons of the results. The comparative series is generated based on the linguistic terms assigned to each event for the three variables considered and is represented in a matrix linguistically and then converted by defuzzification to express it numerically as seen in the matrix below ... 

The advantages of the described fuzzy rule based method and grey theory method for application to FMEA of ships can be summarised as follows (Pillay (2001), Pillay and Wang... 

Interpolation serves an important purpose it greatly reduces the number of rules that are needed to describe a dependency. Thus, in many of the applications of fuzzy logic in control, the number of rules is of the order of 20 and rarely exceeds 90. By contrast, when crisp if-then rules are used, their number may be in the hundreds. 

In many of the early applications of fuzzy logic, the s and B s in the if-then rules had to be calibrated by cut-and-trial to achieve a desired level of performance. During the past few years, however, the techniques related to the induction of rules from observations have been developed to a point where the calibration of rules—by induction from input-output pairs—can be automated in a wide variety of cases. Particularly effective in this regard are techniques centered on the use of neural network methods and genetic computing for purposes of system identification and optimization. Many of the so-called neuro-fuzzy and fuzzy-genetic systems are of this type. 

In practice, SMB processes are controlled using similar manual schemes (Kiisters et al., 1995, Juza, 1999 and Miller et al., 2003). Antia (2003) suggested that these heuristic rules are included in a fuzzy controller to achieve full automatic control of SM B processes, but no applications have been described so far. Cox et al. (2003) recently reported a successful control and monitoring system for the separation of an enantiomer mixture based on the concentration profiles in the recycle loop. 

Data of different units and uncertainties can be combined using IF... THEN... rules, based on expert knowledge. Recently, the application of the traceability concept on ecotoxicological studies has been described (Ahlf and Heise, 2007). A suggestion for an ecotoxicological classification system for sediments based on fuzzy sets and fuzzy expert systems is under development (see Chapter 6.2). 

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