Fuzzy Set Theoretical Analysis of Human Membership Values on the Tone Triangle

Abstract

The present study considers a fuzzy color system in which three input fuzzy sets are constructed on the tone triangle. For a given fuzzy input, this system outputs the center of gravity of the three weights that are associated with respective grades. Two fuzzy sets (not black and white) are applied to the tone triangle relationship. By evaluating the attributes of chromaticness, whiteness, and blackness, 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. Vagueness relates the number of elements (e.g., red-relevant colors selected by subjects) of fuzzy set linearly. Also possibility relates the height of fuzzy set linearly.