E-1-3 Fuzzy Set Theoretical Approach to the Tone Triangular System

Abstract

The present study considers a fuzzy color system in which three input fuzzy sets are constructed on the tone triangle. This system process a fuzzy input and outputs a color on the color triangle system. Two fuzzy sets (not black and white) are applied to the tone triangle relationship. By treating the attributes of chromaticness, whiteness, and blackness on the tone triangle, a target color can be easily obtained as the center of gravity of the resulting fuzzy set. The output of the system is a tone triangle, which includes a compound vector with three weights (scalars) in color space. The differences between a fuzzy input and the resulting inference output is shown by the input-output characteristics (linear shape and right triangle shape) between the chromaticness, the whiteness, and the blackness of the input and the chromaticness of the output.