Multi-dimensional observers and relative entropy of dynamical systems

Mohammadhosein Asadian, Mohammadreza Molaei

Abstract


Abstract.  ‎In this paper the notion of relative probability‎

‎measure 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.



Keywords


Multi-dimensional observer; Fuzzy information system; Relative entropy; Relative conditional entropy; dynamical system

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