Simplified methods of reasoning in fuzzy models

An obvious reason for the success of the Mamdani method of reasoning was that this method was efficiently simplified. However, it is widely known that the Mamdani method has one major drawback-it cannot work when the partitioning of the input space is not complete, i.e. some gaps in the rule-base exist. This is the reason that one of the basic requirement in fuzzy modeling is the complete partitioning of the input space by the antecedent fuzzy sets. An alternative solution to this problem is simply to replace the Mamdani method by the so-called logical method; but it has one major drawback it requires more calculations and there is no analytical description of the input-output relationship presented by the fuzzy model. Consequently this method is not suitable for learning. In this paper we show that the logical method can be significantly simplified. The result is a new reasoning method that is characterized with an analytical input-output description; in addition, its computational complexity is comparable to this of the Mamdani method