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The motivation for the present research is to develop an interactive visualization of concept lattices. We introduce bi-concept lattices to deal with large data sets or to re visualize data given by different information sources, allowing the knowledge to be constructed more reasonable and more logically.Our objective of this work has different streams. First we introduce and study new classes of bi-lattices with extra unary operations to represent the data given by different information sources. We define bi-concept lattices, bi-concept algebras and bi-weakly dicomplemented lattices and investigate the mathematical theory of that new classes. Second we start applications of such classes in data analysis and knowledge representation. We discuss association rules mining according to the information arising from two data sources. An algorithm also be described to compute the confidence and the support of the newly defined bases.
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