Simple computation for the defuzzifications of center of sum and center of gravity

In most inference engines, the output of a fuzzy rule base before defuzzifying is the union of some trapezoidal or/and triangular fuzzy sets and it is always of irregular shape. The defuzzification by using the "center of sum" (COS) method or the "center of gravity" (COG) method for the irregular fuzzy set is then a troublesome computation because of some integrations. This paper proposes two formulas to compute the center of gravity of triangular and trapezoidal fuzzy sets respectively. Based on the proposed two formulas, the computation of COS defuzzification for an irregular fuzzy set can be simplified to a weighted average of the gravities of the trapezoidal or/and triangular fuzzy sets. An example is illustrated to show that the computation time of the pre-defuzzification method with the proposed formula is much less than that of the commonly used COS and COG defuzzification method.