ISSN : 1796-203X
Volume : 4    Issue : 7    Date : July 2009

Fuzzy Set Theoretical Analysis of Human Membership Values on the Color Triangle
Naotoshi Sugano, Shou Komatsuzaki, Hiroyuki Ono, and Yuko Chiba
Page(s): 593-600
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The present study considers a fuzzy color system in which three membership functions are
constructed on the RGB color triangle. This system can process a fuzzy input (as the membership
values of subjects) to an RGB system and output the center of gravity of three weights associated
with respective grades. Three membership functions are applied to the RGB color triangle
relationship. By treating three membership functions of redness, greenness, and blueness on the
RGB color triangle, an average color value can be easily obtained as the center of gravity of the fuzzy
output. The differences between fuzzy input and inference output are described, and the relationship
between the centers of gravity of fuzzy inputs and inference outputs for fuzzy inputs are shown in the
present paper. A technique for obtaining expressions of the RGB color triangle using the fuzzy set
theoretical method has been reported [5] and improved [6]. In the previous study, the relationship
between input fuzzy sets with a plateau on the RGB triangle and fuzzy inputs of conical membership
functions was examined. The RGB color triangle (plane) represents the hue and saturation of a
color [8]. The six fundamental colors and white can be represented on the same color triangle (See  
Fig. 1). Vague colors on the RGB color triangle were clarified. In the present study, the membership
value on the RGB triangular system are examined to determine the average color value as the
center of gravity of the attribute information of vague colors. This fuzzy set theoretical approach is
useful for vague color information processing, color-naming systems, and similar applications.

Index Terms
fuzzy set theory, three additive primary colors, membership function, RGB system, color triangle,
vague color, membership value, center of gravity