CMOS Fuzzification Circuits for Linear Membership Functions

The subject of the study was hardware implementations of fuzzy controllers as CMOS analog devices on the base of implementation of fuzzy inference rules as multi-valued logic functions using summing amplifiers as building blocks. Earlier a functional completeness of summing amplifier with saturation in an arbitrary-valued logic was proven that gave a theoretical background for analog implementation of fuzzy controllers. In previous works it was suggested to put into accordance to input and output linguistic variables of a controller description logical values of some multi-valued variables and instead of fuzzification and defuzzification procedures to apply piecewise-linear approximation between variable logical levels. In the case when derived logical levels were not evenly distributed in the range of an analog signal change it was suggested to increase the number of logical levels to reach even distribution. Such approach leaded to decreasing controller accuracy. This paper suggested instead of increasing logical levels to use special devices transforming analog input variables into multi-valued variables with even distribution of logical levels and output multi-valued variables into analog view. For these devices the names fuzzifier and defuzzifier were kept. The paper illustrated a design example for real industrial fuzzy controller and provided SPICE simulation results of its functioning. Key-Words: Fuzzy Logic, Fuzzy Controller, Multi-Valued Logic Functions, Summing Amplifier with Saturation, Fuzzy Inference, Fuzzification, Defuzzification.