Fuzzy Metagraph and Its Combination with the Indexing Approach in Rule-Based Systems

Abstract—This paper presents a graph-theoretic construct called a fuzzy metagraph (FM) with the capability of describing the relationships between sets of fuzzy elements instead of only single fuzzy elements. The algebraic structure of FM and its properties are extensively investigated. Subsequently, the FM construct is applied to rule-based systems. First, we propose FM-based knowledge representation in both graphic and algebraic format. The representation is capable of identifying dependencies across compound propositions in the rules. In the algebraic representation, the FM closure matrix is considered a precompiled rule base enabling efficient query processing. An iterative approach is presented to facilitate the construction and expansion of the FM closure matrix, which is a key for real-world applications. Next, we introduce the concept of indexing, which was originally developed for information retrieval (IR), to enable an immediate extraction of relevant entries from the FM closure matrix. The indexing approach is applied in combination with the FM closure matrix. Based on the combination, corresponding inference mechanisms are introduced to achieve instant acquisition of relevant rules over a large collection of rules. The application in rule-based systems indicates that the combination of FM and IR techniques offers advantages for the mathematical analysis of systems. Index Terms—Fuzzy graphs, knowledge representation, fuzzy reasoning, information retrieval, rule-based systems