The Geometric Mean as a Generator of Truth-Value in Heuristic Expert Systems: An Improvement over the Fuzzy Weighted Arithmetic Mean

Many earlier expert systems that were modeled after MYCIN, the first expert system, employed truth-value factors for their rule antecedents (premises) and consequents (conclusions). These crisp truth-value factors were usually called certainty factors and attempted to provide a measure of confidence and computational capability to the analysis of rule uncertainty (Shortliffe, 1977; Kandel, 1994). However, in the literature criticism has been often expressed concerning the lack of precision a crisp truth/certainty factor value conveys (Zadeh, 1983; Turban, 1993). Zadeh (1973) and Xingui (1988) utilized the weighted fuzzy average algorithm to improve the precision of truth/certainty factor values. Kandel (1994) further extended the fuzzy weighted mean concept introducing rule confidence, priority, and conclusion weighting factors. Later, Chen (1996) further modified the fuzzy weighted mean algorithm through the factoring of independent rule premise and consequent weights, truth-values and certainty factors. All of these progressive variants of the fuzzy weighted mean enhanced perceived rule antecedent and consequent truth-value. This research investigated a modification of the fuzzy weighted algorithms of Chen and Kandel utilized in assessing heuristic expert system rule truth-value. Their algorithms were modified to demonstrate that a more statistically precise rule truth-value can be achieved by utilizing the geometric mean to aggregate rule truth-value components