Rule Base Structure and Influence of Existing Rules: An Initial Investigation

Fuzzy rule interpolation (FRI) provides an interpretable decision while mak-ing inference with a sparse rule base. The common FRI theories postulate that more existing rules involved can derive better reasoning outcomes. However, certain empirical results show that a large number of rules in-volved may adversely lead to worsening outcomes. The objective of this work is to establish a mathematical mapping of the structural pattern of a given fuzzy rule base for use in FRI, such that the original rule base can be effectively described and analysed. The resulting mathematically mapped pattern helps to produce a theorem which determines the upper limit of the number of rules required to perform FRI. The experimental investigations carried out so far demonstrate that the number of required rules, which can result in the best interpolative outcomes, obeys the theorem proposed by this work.