Fuzzy set theoretical approach to the RGB tone triangular system

The present study considers a fuzzy color system in which two membership functions are constructed on the tone triangle. This system can process a fuzzy input to a tone triangular system and output to an RGB triangular system. Two membership functions (anti-blackness and whiteness) are applied to the tone triangle relationship. By treating the input parameters of chromaticness, whiteness, and blackness on the tone triangle, a target color can be easily obtained as the center of gravity of the output fuzzy set. In the present paper, the differences between fuzzy input and inference output are described, and the relationship between inference outputs for crisp inputs and inference outputs for fuzzy inputs on the RGB triangular system are shown by the characteristics between chromaticness, whiteness, and blackness as the inputs and redness as one of outputs.