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Mathematical Morphology is a powerful non-linear image analysis techniques based on lattice theory. The definitions of morphological operators need an ordered lattice algebraic structure. In order to apply these operators to the colour images it is required, on one hand the choice of a suitable colour space representation and on the other hand, to establish an order in the colour space providing an ordered lattice algebraic structure. The HSI space represents the colour in terms of physical attributes that separate the achromatic component from the chromatic one and it yields a more intuitive description of the colour properties than the RGB space. The suggested order weighs the hue and the intensity according to the saturation level: it has a lexicographical order in which the intensity has priority if the saturation is high, and the hue has priority if the saturation is low.