By J M Bruce; Profile Publications Ltd
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How can we determine AND and OR operations? Since our goal is to describe the expert knowledge, we must elicit these operations from the experts. This can be done in the following manner: • We form several pairs of statements (Ak' B k), k = 1,2, ... &(t(Ak), t(Bk)) ~ t(Ak&Bk). Similar procedures enable us to determine OR and NOT operations. Historical comment. Empirical evidence shows that in different fields, people use different AND and OR operations. &(a, b) = a· b). , in geology), we cannot measure as many parameters as in medicine, so, we have to rely more on expertise, and hence, experts must take risks.
1980) Fuzzy sets and Systems: Theory and Application Academic Press. , Grabisch, M. and Prade, H. (1994) Gradual rules and the approximation of control laws. T. Nguyen, M. Sugeno, R. 147182. , Prade, H. (1996) What are fuzzy rules and how to use them. Fuzzy Sets and Systems, 84, 169-185. W. S. (1974) The kth optimal policy algorithm for decision-making in a fuzzy environment. In Identification and System Parameter Estimation (P. ), North-Holland, Amsterdam, pp. 10521059. [13] Geyer-Schulz, A. (1996) Fuzzy Rule-Based Expert Systems and Genetic Machine Learning, Physica-Verlag, Heidelberg.
First elicitation method: selecting on a scale. If we cannot elicit a real number from an expert, maybe we can elicit some number from him, and then convert the result into a real number from the interval [0,1]. , on a scale from 0 to 5, or on a scale from 0 to 10. So, we can ask an expert to mark his grade of truth in a given statement P(x) on a given scale 0 to S (0 to 5, 0 to 10, etc). On this scale: • 0 corresponds to "P(x) is absolutely false"; • S corresponds to "P(x) is absolutely true"; • intermediate marks represent different grades of truth.