Fuzzy Set Theoretical Approach to Achromatic Relevant Color on the Natural Color System

The present study considers a fuzzy natural color system (NCS) in which triangular pyramid membership functions are constructed on the NCS color triangle. This system can process a fuzzy input to an NCS and output a center of gravity of three weights associated with respective grades. Triangular membership functions are applied to the hue angle, and triangular pyramid membership functions are applied to the NCS color triangle relationship. By treating three membership functions of blackness, whiteness, and chromaticness on the NCS color triangle, a target color can be easily obtained as the center of gravity of the output fuzzy set. In the present paper, the differences among crisp achromatic colors, fuzzy achromatic colors, and fuzzy modified achromatic colors (e.g., reddish achromatic colors) are described, and crisp modified achromatic colors are shown to be a result of achromatic colors that have appropriate vagueness.