A new approach to determine the true domain of fuzzy inference sentence

Fuzzy rules are the base of the designing of fuzzy controller. How to give the true domain according to the fuzzy rules is the key step in the designing process. One important approach is to solving a system of fuzzy relation equations corresponding to the fuzzy inference sentence. We have given a new method to construct the system in an earlier paper where we gave the method to determine the solution of the system when the system is consistent. In this paper, we will give a new approach for solving the system. In this new approach, both the forward inference and the reverse inference are considered to change a series fuzzy inference sentences into a system of fuzzy relation equations. We also present the conditions to judge the consistency of the system of fuzzy relation equations from two different angles and the corresponding maximum solutions. Examples show the rationale of the new approach.