Fuzzy Set Theoretical Approach to the Tone Triangular System

The present study considers a fuzzy color system in which three input fuzzy sets are constructed on the tone triangle. This system can process a fuzzy input to a tone triangular system and output to a color on the RGB triangular system. Three input fuzzy sets (not black, white, and light) are applied to the tone triangle relationship. By treating three attributes 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 inputs and inference outputs are described, and the relationship between inference outputs for crisp inputs and for fuzzy inputs on the RGB triangular system are shown by the input-output characteristics between chromaticness, whiteness, and blackness as the inputs and redness (as one of the outputs).