Reducing Computational Overhead by Improving the CRI and IRI Implication Step

In conventional SISO fuzzy expert systems (n-element input, m-element output), the implication step requires the O(n×m) operations using compositional rule-based inference (CRI) and individual rule-based inference (IRI). However, this introduces excessive complexity. This paper proposes two methods, sort compositional rule-based inference (SCRI) and sort individual rule-based inference (SIRI) aiming at reducing both temporal and spatial complexity by changing the operation of the implication step to O((n+m)log2(n+m)). We also propose a divide-and-conquer technique, called Quicksort, to verify the accuracy of SCRI and SIRI algorithms deployment to easily outperform the CRI and IRI methods.