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Logical entropy on effect algebras with the Riesz decomposition property

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Abstract.

In this study, the notion of logical entropy is generalized for the case when the considered probability space is an effect algebra with the Riesz decomposition property. We define the logical entropy and conditional logical entropy of finite partitions in an effect algebra with the Riesz decomposition property and prove the basic properties of these measures. Furthermore, we introduce the concepts of logical cross entropy and logical divergence and discuss their desirable properties.

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Authors and Affiliations

  1. Department of Mathematics, Sirjan Branch, Islamic Azad University, Sirjan, Iran

    Zahra Eslami Giski

  2. Young Researchers and Elite Club, Zahedan Branch, Islamic Azad University, Zahedan, Iran

    Abolfazl Ebrahimzadeh

  3. Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01, Nitra, Slovakia

    Dagmar Markechová

Authors
  1. Zahra Eslami Giski
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  2. Abolfazl Ebrahimzadeh
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  3. Dagmar Markechová
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Correspondence to Zahra Eslami Giski.

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Eslami Giski, Z., Ebrahimzadeh, A. & Markechová, D. Logical entropy on effect algebras with the Riesz decomposition property. Eur. Phys. J. Plus 133, 286 (2018). https://doi.org/10.1140/epjp/i2018-12107-x

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