Multi dimensional second order defuzzification algorithm (M-SODA)

Multi dimensional second order defuzzification algorithm (SODA) minimizes the hardware requirement and ensures easier implementation of a fuzzy controller as compared to the LUT and the triangular membership approach when extended to multiple dimensions. In this paper we have put forward the extension of the SODA to multiple dimensions. Fuzzy controllers can handle multiple inputs and outputs however size of the fuzzy table grows exponentially with each input added. In this paper we put forward the extension of SODA into 4 dimension using three six bits input, (8 × 8 × 8) and (4 × 4 × 4) fuzzy look up tables (LUT) were used each having 512 and 64 values respectively. The system uses three inputs, the upper three bits of each input are used for addressing the exact position of the nearest data point in the look up table, and the rest of the input is the information about the membership function. The advantage of this method over other defuzzification methods like the LUT and the triangular membership function approach is its extensibility to multiple dimensions with the efficient usage of a relatively smaller look up table, which minimizes the hardware requirement and ensures easier implementation. In this paper we also demonstrate the extension of the method to more than 4 dimensions.