Fuzzy Rule Based Method

The aim of this method is to develop a method that does not require a utility function to define the probability of occurrence (5/), severity (5) and detectability Sfi considered for the analysis and to avoid the use of the traditional RPN. This is achieved by using information gathered from experts and integrating them in a formal way to reflect a subjective method of ranking risk. 

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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. 

A traditional FMEA using the RPN ranking system is carried out in the first instance. This analysis is summarised in Table 7.9. In Table 7.9,5/represents the probability of occurrence, S the severity, and Sj the detectability. The values for Sf, S and Sd are obtained by using the values detailed in Tables 7.1, 7.2 and 7.3, respectively. The same pool of experts that carried out the analysis for the fuzzy rule based method and grey theory method is used for the traditional FMEA analysis. This ensures the consistency in the opinion of each expert. 

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... 

The traditional FMEA, the fuzzy rule based method and the grey theory approach may complement each other to produce a risk ranking with confidence. 

Fuzzy-Rule Based Approach Fuzzy Weighted Unsharp Masking Based Lanczos-3 Interpolation Technique (Proposed Method-2)... 

The marine industry is recognising the need for powerful techniques that can be used to perform risk analysis of marine systems. One technique that has been applied in both national and international marine regulations and operations is Failure Mode and Effects Analysis (FMEA). This risk analysis tool assumes that a failure mode occurs in a system/component through some failure mechanism. The effect of this failure is then evaluated. A risk ranking is produced in order to prioritise the attention for each of the failure modes identified. The traditional method utilises the Risk Priority Number (RPN) ranking system. This method determines the RPN by finding the multiplication of factor scores. The three factors considered are probability of failure, severity and detectability. Traditional FMEA has been criticised to have several weaknesses. These weaknesses are addressed in this Chapter. A new approach, which utilises the fuzzy rules base and grey relation theory, is presented. 

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. 

This method of rule reduction assumes that the probability of occurrence, severity and detectability have the same importance. Using this method to reduce the number of mles in the fuzzy rule base, a final set of rules is generated as shown in Table 7.11. 

Using the fuzzy rule base generated in Table 7.11, Rule 7 will apply to the first event. This rule is interpreted to read as, if the probability of occurrence is Remote, severity is High and detectability is High, then priority for attention is 0.58 Low, 0.68 Fairly low . The conclusion 0.58 Low, 0.68 Fairly low can be defuzzified using the WMoM method to produce a crisp number as shown here ... 

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 ... 

To apply this method onto the situation instances, it was necessary to convert the data items into a vector space. For each situation, the distance to all others could be calculated, based on the signal-wise distance between the recognized patterns. This allowed to apply the FastMap method [664], to create a lower dimensional space that approximately represented the situations distance matrix. Unfortunately, this preprocessing disallowed to apply the fuzzy-ID3-based rule generation mechanism of MIDAS ]969], as no conclusions about the process parameters could be drawn from rules about the generated vector space. 

A rule based approach to process control has for many years provided an alternative to traditional methods in the form of fuzzy logic control (8,9). Since the advent of expert systems, rulebases have been used for fault diagnosis [10], to advise operators (11) 9 to aid control engineers when installing PID controllers (12), to provide expert on-line tuning for PID controllers (13), and to control processes without the use of fuzzy logic (14,15). 

The described inference method, due to Mamdani (1974), is the most popular other inference methods for fuzzy systems based on linguistic rules are Sugeno models and Tsukamoto models (Mamdani 1974 Sugeno 1985). 

The rule base contains all the information required to relate the inputs and outputs. In this case, the independent variables of the membership functions of input and output are different, so the result will be two dimensional. Hence the minimum of the input and the output membership function is performed as per the fuzzy if-then rules. Subsequently, the inference engine operates with the min-max operator to generate the output responses. The output responses are then de-fuzzifled to produce a crisp output using the center of gravity method. Now the minimum of the two membership function is given by ... 

By making fuzzy evaluations, with zero at the bottom of the scale and 1.0 at the top, one can have an analysis rule basis for the fuzzy logic method, and s/he can accomplish analysis or control project. The results seem to turn out well for complex systems or systems where human experience is the only base from which to proceed, certainly better than doing nothing at all, which is where one would be if unwilling to proceed with fuzzy rules. 

Traditional control systems are in general based on mathematical models that describe the control system using one or more differential equations that define the system response to its inputs. In many cases, the mathematical model of the control process may not exist or may be too expensive in terms of computer processing power and memory. In these cases a system based on empirical rules may be more effective. In many cases, fuzzy control can be used to improve existing controller systems by adding an extra layer of intelligence to the current control method. 

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