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Granular entropy and granulation procee

Rybalov A.

Archives of Control Sciences

2002

Vol. 12, no. 4

457-467

People use granulation to represent original data as a set of entities that are better suited for managing resulting subtasks. Concept that are introduced in this paper are based on two features of granulation: the revelance of all the points in a granule and relative number of points in every granule. Based on these features several concepts are introduced that include granular relevance, defined as sum of relevancies of all the points in the granule and granular entropy, that is similar to information entropy and reflects the dispersion of relevant points across granules. Using these concepts granulation process is represented as solution of optimization problem where objective function is granular entropy. To this end the theorem, that shows how the change in relevance of points in a granule affects granular entropy, was proved. The last two sections of the paper show how leverage over the granulation process can be achieved by using t-norm and uni-norm operators.