Relevance of computer based learning and testing of students are discussed. Construction of mixed diagnostic tests that are a compromise between unconditional and conditional components is used in order to develop blended education and training. It is proposed for control, monitoring students' knowledge, professional and personal skills and abilities, and designing learning trajectory of courses for every student. We suggest a technique for construction of optimal mixed diagnostic tests that is based only on the experts' knowledge about problem area. KEY WORDS Intelligent pattern recognition, tree of mixed diagnostic tests, learning trajectory, blended education and training.

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Theoretical foundation of n-simplex construction which is used for decision-making in intelligent system and its substantiation based on test methods of the logicalcombinatorial pattern recognition are given. The used way for data and knowledge representation in intelligent systems, concept of regularities in the data and knowledge, the main revealing regularities are proposed. The idea of decision-making of a membership object under study to one or another pattern on each diagnostic test shortly is described. Mathematical foundations of mapping object under study in n-simplex are given. Decision-making and its substantiation based on 3simplex is described in detail. Illustrative example of visualization of data and knowledge and regularities is offered. Application expediency of the visualization method based on 3-simplex for different problem fields is considered. KEY WORDS Cognitive graphics, intelligent systems, decision-making and its substantiation, matrix model of data and knowledge representation, regularities in data and knowledge, n-simplex, 3-simplex.