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Kybernetika 41(2):143-160, 2005.

Entropy on Effect Algebras with Riesz Decomposition Property I: Basic Properties.

Antonio Di Nola, M. Hycko, Corrado Manara and Anatolij Dvurečenskij


Abstract:

We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.


Keywords: effect algebra; Riesz decomposition property; MV-algebra; state; entropy;


AMS: 06D35; 03B50; 03G12 ;


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BIB TeX

@article{kyb:2005:2:143-160,

author = {Di Nola, Antonio and Hycko, M. and Manara, Corrado and Dvure\v{c}enskij, Anatolij},

title = {Entropy on Effect Algebras with Riesz Decomposition Property I: Basic Properties.},

journal = {Kybernetika},

volume = {41},

year = {2005},

number = {2},

pages = {143-160}

publisher = {{\'U}TIA, AV {\v C}R, Prague },

}


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