# Fuzzy Set Theoretical Analysis of Human Membership Values on the Color Triangle

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## 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.

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