Monotonic Systems and Their Properties

E. I. Kuznecov, I,B. Muchnik, L.V. Shvartzer

(translated from Russian by D. Fradkin)

July 21, 2003

Abstract

This paper presents, for the first time, a systematic description of a new method of
structural analysis of data, based on so-called monotonic systems. It is aimed at
constructing a systematic description of the data. In this theory, the structure of the
data is described as a sequence of mathematical objects - quasi-kernels, which gives this
approach a certain resemblance to a classical agglomerative methods (however here the
starting point of the sequence - the kernel - is determined by the theory). The paper
mainly concerns itself with presenting the mathematical basis for the suggested methods.
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