Two-level tree search in fuzzy expert systems

Issues of rule search in fuzzy expert systems are investigated. Computation of overall similarity measure (OSM) is studied between a system observation and the left hand side of a rule for a class of T-similarity measure (SM) models. It is shown that for an n-antecedent system, if the connective AND in both the left hand side of a rule and a system observation is taken to be a t-norm operator which is the same t-norm operator used in the T-similarity measure model, then the OSM can be obtained by: 1) computing the SM between the linguistic term of an antecedent variable in the rule and the observation of the corresponding antecedent variable separately for each of the antecedent variables in the rule, and 2) combining all of these SMs using the t-norm operator. Thus, one avoids the computation of the OSM via the n-dimensional matrix operations. Based on an analysis of the relationship between the OSM and SMs for an n-antecedent system, a search scheme, called two-level tree search, is proposed as opposed to an exhaustive search to save search cost associated with the computation of the OSM. Computational complexity is analyzed for both the exhaustive and the two-level tree search schemes