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

TLDR

The aggregation formulation is equivalent to the well‑known Gibbs free energy problem in chemical engineering. The study proposes an algorithm that aggregates antecedents into a single value for use in the detachment or implication operator of a forward‑chaining expert system. The algorithm sorts antecedent confidences (or applies Saaty’s paired‑comparison weighting when unsorted), then uses a novel fuzzy OWA operator and a two‑variable geometric program to compute weights for aggregation. The method achieves computational efficiency with an O(n log n) sort and O(n) inner product, making it well suited for real‑time expert systems and fuzzy multi‑objective decision tasks.

Abstract

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.