https://doi.org/10.1140/epjp/i2018-12107-x
Regular Article
Logical entropy on effect algebras with the Riesz decomposition property
1
Department of Mathematics, Sirjan Branch, Islamic Azad University, Sirjan, Iran
2
Young Researchers and Elite Club, Zahedan Branch, Islamic Azad University, Zahedan, Iran
3
Department of Mathematics, Faculty of Natural Sciences, Constantine the Philosopher University in Nitra, A. Hlinku 1, SK-949 01, Nitra, Slovakia
* e-mail: z.eslami@iausirjan.ac.ir
Received:
30
December
2017
Accepted:
16
June
2018
Published online:
30
July
2018
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018
