Boolean algebra as algebra is value indifferent. Although it is very important, the classical two-valued realization of the Boolean algebra is only a special case. The real valued realization of the Boolean algebra is a frame for the Boolean consistent fuzzy logic in wider sense, such as the two valued realization is a frame for the classical case. This paper presents the brief review of the real-valued realization of the finite (atomic) Boolean algebra and its application. The real-valued implication is a Boolean consistent generalization of the classical binary implication. The real-valued implication plays important roles in the real-valued set theory as a generalization of the classical set theory, as well as, in many applications such as morphology in image processing, association rules in data mining and decision making generally.
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