Author
Abolfazl Ebrahimzadeh
Bio: Abolfazl Ebrahimzadeh is an academic researcher from Islamic Azad University. The author has contributed to research in topics: Dynamical systems theory & Conditional entropy. The author has an hindex of 6, co-authored 15 publications receiving 82 citations.
Papers
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TL;DR: The version of Kolmogorov-Sinai theorem is proved and the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic are introduced.
Abstract: Abstract This paper introduces the concepts of logical entropy and conditional logical entropy of hnite partitions on a quantum logic. Some of their ergodic properties are presented. Also logical entropy of a quantum dynamical system is dehned and ergodic properties of dynamical systems on a quantum logic are investigated. Finally, the version of Kolmogorov-Sinai theorem is proved.
18 citations
06 Jan 2017
TL;DR: Using the suggested concept of entropy of partitions, the logical entropy of a dynamical system is defined and it is proved that it is the same for two dynamical systems that are isomorphic.
Abstract: In the paper by Riecan and Markechova (Fuzzy Sets Syst. 96, 1998), some fuzzy modifications of Shannon’s and Kolmogorov-Sinai’s entropy were studied and the general scheme involving the presented models was introduced. Our aim in this contribution is to provide analogies of these results for the case of the logical entropy. We define the logical entropy and logical mutual information of finite partitions on the appropriate algebraic structure and prove basic properties of these measures. It is shown that, as a special case, we obtain the logical entropy of fuzzy partitions studied by Markechova and Riecan (Entropy 18, 2016). Finally, using the suggested concept of entropy of partitions we define the logical entropy of a dynamical system and prove that it is the same for two dynamical systems that are isomorphic.
14 citations
TL;DR: It was proved that this logical entropy on dynamical systems that their state spaces were sequential effect algebra is an invariant object under isomorphism relation.
13 citations
TL;DR: It is shown that by replacing the Shannon entropy function by the logical entropy function the authors obtain the results analogous to the case of classical Kolmogorov–Sinai entropy theory of dynamical systems.
Abstract: The main purpose of the paper is to extend the results of Ellerman (Int. J. Semant. Comput. 7:121–145, 2013) to the case of dynamical systems. We define the logical entropy and conditional logical entropy of finite measurable partitions and derive the basic properties of these measures. Subsequently, the suggested concept of logical entropy of finite measurable partitions is used to define the logical entropy of a dynamical system. It is proved that two metrically isomorphic dynamical systems have the same logical entropy. Finally, we provide a logical version of the Kolmogorov–Sinai theorem on generators. So it is shown that by replacing the Shannon entropy function by the logical entropy function we obtain the results analogous to the case of classical Kolmogorov–Sinai entropy theory of dynamical systems.
12 citations
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TL;DR: A novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy and the experimental results show that the properties of generalizedrelative entropy are better than relative entropy.
Abstract: Information entropy and its extension, which are important generalization of entropy, have been applied in many research domains today. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We presented the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy is presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric.
39 citations
TL;DR: In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy, which is proved to have a finite range and is a finite distance metric, and the experimental results show that the properties of the provided relative entropy are better than relative entropy.
Abstract: Information entropy and its extension, which are important generalizations of entropy, are currently applied to many research domains. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We present the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy are presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric. Finally, we predict nucleosome positioning of fly and yeast based on generalized relative entropy and relative entropy respectively. The experimental results show that the properties of generalized relative entropy are better than relative entropy.
39 citations
TL;DR: It can be concluded that Karci entropy is superior to Shannon entropy because Shannon entropy can be regarded as an element of this set of entropies as well as being compared to traditional centrality measures.
Abstract: In order to measure the amount of different information in a system, entropy concept can be used. Graph entropy measures nodes’ contribution to the entropy of the graph. By this way, the influential actors can be identified. Due to this case, a new entropy-based method was proposed to identify the influential actors. Karci entropy was applied to the social networks first time. The alpha parameter allowed us to combine many different conditions together when measuring in the network. The other important contribution of this paper is to predict the value of alpha parameter of Karci entropy by using fuzzy logic. After that Karci and Shannon entropies were compared based on experimental results. Moreover, Karci entropy was compared to traditional centrality measures. If Karci entropy definition is considered as a set of entropies, Shannon entropy can be regarded as an element of this set. Accordingly, it can be concluded that Karci entropy is superior to Shannon entropy.
22 citations
06 Jan 2017
TL;DR: Using the suggested concept of entropy of partitions, the logical entropy of a dynamical system is defined and it is proved that it is the same for two dynamical systems that are isomorphic.
Abstract: In the paper by Riecan and Markechova (Fuzzy Sets Syst. 96, 1998), some fuzzy modifications of Shannon’s and Kolmogorov-Sinai’s entropy were studied and the general scheme involving the presented models was introduced. Our aim in this contribution is to provide analogies of these results for the case of the logical entropy. We define the logical entropy and logical mutual information of finite partitions on the appropriate algebraic structure and prove basic properties of these measures. It is shown that, as a special case, we obtain the logical entropy of fuzzy partitions studied by Markechova and Riecan (Entropy 18, 2016). Finally, using the suggested concept of entropy of partitions we define the logical entropy of a dynamical system and prove that it is the same for two dynamical systems that are isomorphic.
14 citations
TL;DR: The concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case are introduced, and an analogy of the Kolmogorov-Sinai theorem on generators for IF-dynamical systems is proved.
Abstract: In this contribution, we introduce the concepts of logical entropy and logical mutual information of experiments in the intuitionistic fuzzy case, and study the basic properties of the suggested measures. Subsequently, by means of the suggested notion of logical entropy of an IF-partition, we define the logical entropy of an IF-dynamical system. It is shown that the logical entropy of IF-dynamical systems is invariant under isomorphism. Finally, an analogy of the Kolmogorov–Sinai theorem on generators for IF-dynamical systems is proved.
13 citations