A New Approach to Inference Under Uncertainty for Knowledge Based Systems

Uncertainties Expert systems for diagnosis, decision support systems, robot and real time control, engineering design etc. must necessarily use incomplete, contaminated and imprecise knowledge. A database of diseases with associated symptoms may not register presence or absence of a given symptom for a given disease. We can say that the symptom may or may not be present. We may be able to express this incompleteness in terms of probabilities. This is a form of incomplete information and is common in real application areas. Incompleteness can arise because of complete absence of knowledge or through only knowing approximately the answer. In the latter case this might be expressed in words with imprecise meaning such as "tail", "strong", "probable" etc. This imprecision can be taken into account by expressing it by means of fuzzy sets, ZADEH 1965, 75, 83. These fuzzy sets impose a possibility distribution over the set of possible values a variable can take, ZADEH 1978. This in turn imposes a family of possible probability distributions for the value of the variable. Contaminated knowledge arises from noise present in the system, perhaps through the unreliability of a communication channel or the unreliability of a measuring device etc. This form of uncertainty can be represented in probabilistic terms, perhaps as a family of conditional probability distributions, but may also require the use of fuzzy sets to express imprecision once again. Imprecise knowledge is fuzzy. Most everyday concepts cannot be precisely defined by means of necessary and sufficient conditions. The meaning of concepts which are acquired through examples of their usage and their applicability to new situations which do not perfectly match with those used previously cannot be deduced with certainty.