JOURNAL OF COMPUTERS (JCP)

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

Full Text: PDF (786 KB)

**Abstract**

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

ISSN : 1796-203X

Volume : 4 Issue : 7 Date : July 2009

Page(s): 593-600

Full Text: PDF (786 KB)

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.

vague color, membership value, center of gravity