On Takagi Sugeno approximations of Mamdani fuzzy systems

Abstract

In the present paper we propose, and investigate different constructive approaches to approximate Mamdani fuzzy systems, using Takagi-Sugeno systems. The Takagi- Sugeno fuzzy systems that we construct will be based on a piecewise linear approximation, an interpolation polynomial, and an approach based on cubic splines. Since using a Mamdani system with Center of Gravity defuzzification is computationally expensive, a Takagi-Sugeno system is a natural idea to reduce computation and keep high quality on the performance side. We extend these approaches to fuzzy rule bases with multiple antecedents. As application we construct a computing with words system using the proposed approach, and also we use the proposed approach in a video game.