Aggregating Template Or Rule Antecedents In Real-time Expert Systems With Fuzzy Set Logic

An algorithm based on fuzzy set logic and nonlinear program- ming optimization is proposed for aggregating antecedents within a template or rule into a single valued entity for use in a detachment or implication operator for forward chaining in an expert system. The method assumes that confidences of the observed antecedents can be sorted, otherwise a paired comparison weighting developed by Saaty [1] must be employed to equalize the relative importances of the arguments before sorting is performed. The method is based on a new type of fuzzy Ordered Weighted Average (OWA) operator proposed by Yager [2,3]. An offline nonlinear program (geometric program) involving only two optimization variables is used to develop the weights using a formulation by O’Hagan [4]. This formulation is equivalent to the well-known Gibbs free energy problem of chemical engineering [5,6]. The proposed aggregation method is computationally efficient involving only an 0(n – In(n)) sort and an 0(n) inner product when aggregating n antecedents and is ideally suited for real-time expert system or fuzzy multi- objective decision applications.