TAILIEUCHUNG - Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 74

Handbook of Reliability, Availability, Maintainability and Safety in Engineering Design - Part 74 studies the combination of various methods of designing for reliability, availability, maintainability and safety, as well as the latest techniques in probability and possibility modelling, mathematical algorithmic modelling, evolutionary algorithmic modelling, symbolic logic modelling, artificial intelligence modelling, and object-oriented computer modelling, in a logically structured approach to determining the integrity of engineering design. . | 714 5 Safety and Risk in Engineering Design The problem is that the fuzzy sets F and H are both defined by their membership functions J with domainR the set of real numbers the input vectors of the training set having infinite elements. Obviously it is impossible to have infinitely large neural networks so the membership functions are transformed so that they are discrete by taking samples at equal intervals . Furthermore the range of the membership functions are contained to the interval 0 1 . If the range is - the transform T is then D - D 0 1 . This is termed a loss-less transformation. To graphically present this transformation as illustrated in Fig. draw a semicircle in the region defined by 0 x 1 0 y with the centre and draw lines to all points on the x-axis. T x0 is the x coordinate of the intersection of the line crossing the x-axis at x0 with the semicircle. With k samples of the membership function at x and i 0. k x i k i the training set of the fuzzy neural network is JF x0L jFi x1 . . jFi xk jHi x0L jHi xi . . jHi xk i 0 .n The training set consists of pairs of sampled membership functions. The pairs correspond to the rules of the fuzzy rule-based neural network considered. As indicated previously the advantage of fuzzy rule-based neural networks is the fact that the designer does not have to program the system and the fuzzy neural network makes the membership functions. With the example above the membership functions were already known. In actual use of fuzzy ANN models the membership functions would be extracted from the training pairs using the ANN. Fuzzy artificial perceptrons FAP Fuzzy T-norm functions have the following properties T 0 1 x 0 1 0 1 T x y T y x T 0 x 0 T 1 x x T T x y z T x T y z x a Oy b T x y T a b From the definition of intersection of fuzzy sets the notation JFnG x y min jf x jg y is a T-norm where x y . Fig. Graph of membership function transformation of a fuzzy ANN Analytic Development of Safety and .

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