Measurement uncertainty fuzzy logic

Semantic uncertainty is the type of uncertainty for which we shall need fuzzy logic. Expressed by phrases such as "acidic" or "much weaker," this is imprecision in the description of an event, state, or object rather than its measurement. Fuzzy logic offers a way to make credible deductions from uncertain statements. We shall illustrate this with a simple example. 

In many experimental cases, a certain degree of interference occurs among the measures, which gives rise to possible collections of results however, the situation is even more complex if the input data are subjected to uncertainty or imprecision (Kaufmann and Gupta, 1991). Fuzzy logic is the only mathematical application that can properly solve problems with imprecision in input data. 

These questions reduce to two fundamental points. Firstly how good is a theory Secondly how good is the matching between the way we can use the theory and the problem we are trying to solve In this section we will demonstrate that probability is not the correct measure to use to answer these questions. We will return to them more positively in Chapter 10 where a tentative general method, based upon approximate reasoning and fuzzy logic, is described, which will enable us to consider system uncertainty as well as human based uncertainty. 

Here the basic model used is one which is tested hi the laboratory and contains as much as is known about the influences of the X and Y parameters on the fatigue life. The known variabilities of the X and Y in the WOL are then used to calculate a fuzzy probability of failure which is the chance that the actual life will be less than the design life. A fuzzy logical hierarchy is then set up exactly as in the example of Section 10.5, to allow for the uncertainty associated with the application of the model in the laboratory. This new fuzzy probabUity is then again truth functionally modified to allow for the uncertainty of the matching with the WOL The procedure would then be exactly as for that example, so that a fuzzy truth restriction upon the statement, the structure is perfectly safe would result and this is the final measure of structural safety. 

It is very clear from the complexity of the situations described in the case studies of the last two chapters, that simple factors of safety, load factors, partial factors or even notional probabilities of failure can cover only a small part of a total description of the safety of a structure. In this chapter we will try to draw some general conclusions from the incidents described as well as others not discussed in any detail in this book. The conclusions will be based upon the general classification of types of failure presented in Section 7.2. Subjective assessments of the truth and importance of the checklist of parameter statements within that classification are analysed using a simple numerical scale and also using fuzzy set theory. This leads us on to a tentative method for the analysis of the safety of a structure yet to be built. The method,however, has several disadvantages which can be overcome by the use of a model based on fuzzy logic. At the end of the chapte(, the discussion of the various possible measures of uncertainty is completed. 

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