Fuzzy Rule Base Application

The fuzzy rule base is developed in such a way so as to enable comparison with the traditional FMEA method. Hence, in fuzzy terms, the linguistic variables are determined to be the probability of occurrence, severity and detectability. Each of these variables can be described in linguistic terms as Remote, Low, Moderate, High and Very High. The interpretations of these linguistic terms have already been given in Table 7.4. 

Rule 1 if probability of occurrence is Moderate, severity is Low and detectability is Low then priority for attention is 0.66 Moderate, 0.94 Fairly High. 

The degrees of belief 0.66 and 0.94, depend heavily upon the opinion of the experts involved in the study, as such, it can be assumed that these figures only represent the average values for all the opinions of the experts. 

---

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... 

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... 

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). 

The application of fuzzy sets theory in this case is reasonable because expert s knowledge can be used to build a suitable rule base (Bukowski Feliks 2005). Expert knowledge on the impact of the various parameters on result is expressed in the form of if... then rules. The knowledge encoded in a rule base is derived from human experience and intuition as well as on the basis of theoretical and practical understanding of the properties of the studied object. The main task of this dedue-tion system is to calculate the approximate value of the output variable based on the share of each rule from the rule base with an appropriate factor determining the validity of the rule. Fuzzy logic based systems are a kind of expert system built on a knowledge base that contains inference... 

Besides the deteraiinatioii of the timely dynamics fector has to be considered to derive an adjustment between the periods t=l and t=2. The intensity and the speed of competition are supposed to be = 80 and the = 65, In application of the rule base shown in Table 5-2 and the rule of inference depicted in Eq. (5-5), the fuzzy output for the determination of the timely adjustment of is obtained. The aggregated output is shown in Figure 5-9. Using the MoM an alteration of 0.75% between the periods t=l and t=2 is calculated. 

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. 

The meaning of the application of fuzzy models in risk analysis is to provide mathematical formulations that could characterize the uncertain parameters involved in complex safety evaluation me ods. Fuzzy logic is a decisional system based on linguistic rules once the membership functions have been defined for all the fuzzy variable sets, each set has to be connect by... 

ABSTRACT Smart structures usually incorporate some control schemes that allow them to react against disturbances. In mechanics we have in mind suppression of mechanical vibrations with possible applications on noise and vibration isolation. A model problem of a smart beam with embedded piezoelectric sensors and actuators is used in this paper. Vibration suppression is realized by using active control. Classical mathematical control usually gives good results for linear feedback laws under given assumptions. The design of nonlinear controllers based on fuzzy inference rules is proposed and tested in this chapter. 

Fuzzy inference rules systematize existing experience, available in terms of linguistic rules, and can be used for the realization of nonlinear controllers. The feedback is based on fuzzy inference and may be nonlinear and complicated. Knowledge or experience on the controlled system is required for the application of this technique. Since the linguistic rules are difficult to be explained and formulated for multi-input, multi-output systems, most applications are based on multi-input, single-output controllers. 

---