Tsallis Entropy of Product MV-Algebra Dynamical Systems

This paper is concerned with the mathematical modelling of Tsallis entropy in product MV-algebra dynamical systems. We define the Tsallis entropy of order [Formula: see text] where [Formula: see text] 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 [Formula: see text] where [Formula: see text] has the property of sub-additivity. This property allows us to define, for [Formula: see text] 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.