A Study on the Equivalence of FATI and FITA in Multifold Approximate Reasoning with Normally Partitioned Fuzzy Rules

Abstract

An approximate reasoning on multiple fuzzy rules has two main methods. One is FATI (First Aggregation Then Inference) and the other is FITA (First Inference Then Aggregation), It is generally known that FATI shows a more specific inference result, in other words, a less vague inference result than FITA. However, FITA is better than FATI from the viewpoint of easiness and the efficiency of computing because FITA makes parallel computing possible. In this paper, we set up the approximate reasoning environment that has sup-t-norm composition, Godel implication, min aggregation, and multiple fuzzy rules with normally partitioned L-R type fuzzy numbers, and then we study the conditions of equivalence of FATI and FITA. Under these conditions, the approximate reasoning method based on FITA can give a less vague inference result.