Using special structured fuzzy measure to represent interaction among IF-THEN rules

When fuzzy IF-THEN rules are used to approximate reasoning, interaction exists among rules. Handling the interaction based on a non-integral can lead to an improvement of reasoning accuracy but the determination of non-linear integral usually needs to solve a linear programming problem with too many parameters when the rules are a little many. That is, the number of parameters increases exponentially with the number of rules. This paper proposes a new approach to denoting the interaction by a 2-additive fuzzy measure which replaces the general set function of the old non-linear integral approach. The number of parameters determined in the new approach is greatly less than the number of parameters in the old approach. Compared with the old approach, the new one has a little loss of accuracy but the new approach reduces the number of parameters from an exponential to polynomial quantity.