Algebra of Clusterizable Relations

Relations are usually represented in a space of attributes whose values differ only in names similar to algebra of sets. The order of the values or any other preference measures are not significant for such attributes. The paper proposes a mathematical model based on n-tuple algebra (NTA), for relations in which the values of attributes are ordered. For this case, a mathematical tool has been developed that can be used to perform not only the previously discussed methods and means of logical-semantic analysis on the basis of NTA, including analysis of defeasible reasoning and logic-probabilistic analysis, but also to analyze the order and connectivity of structures and implement clustering methods. The concept of granules is introduced, the power of connectivity between the granules is defined, and methods to calculate distances between the disconnected granules are proposed. The obtained dependencies make it possible to extend the scope of classification techniques.