Multi-dimensional observers and relative entropy of dynamical systems
DOI:
https://doi.org/10.30495/jme.v14i0.912Keywords:
Multi-dimensional observer, Fuzzy information system, Relative entropy, Relative conditional entropy, dynamical systemAbstract
Abstract. In this paper the notion of relative probabilitymeasure of a set E is considered with respect to a multi-dimensional observer of a set X as a superset of E. Relative entropy of a multi-dimensional
observer for the partitions is defined and the properties of relative entropy is extended to multi-dimensional observers. It is shown that the observer of a set plays a role in uncertainty of a partition of it. Relative conditional entropy is also considered and its main properties are proved. Moreover, the relative entropy off a relative measure preserving map is studied as well.
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