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Tsallis Entropy of Product MV-Algebra Dynamical Systems
Dagmar Markechová1, Beloslav Riečan2,3
1Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01 Nitra, Slovakia.
Abstract:
This paper is concerned with the mathematical modelling of Tsallis entropy in product MV-algebra dynamical systems. We define the Tsallis entropy of order α , where α ∈ ( 0 , 1 ) ∪ ( 1 , ∞ ) , of a partition in a product MV-algebra and its conditional version and we examine their properties. Among other, it is shown that the Tsallis entropy of order α , where α > 1 , has the property of sub-additivity. This property allows us to define, for α > 1 , the Tsallis entropy of a product MV-algebra dynamical system. It is proven that the proposed entropy measure is invariant under isomorphism of product MV-algebra dynamical systems.
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