Extensions of the Shannon entropy and the chaos game algorithm to hyperbolic numbers plane. (English) Zbl 1493.60006
Summary: In this paper, we provide extensions to hyperbolic numbers plane of the classical Chaos game algorithm and the Shannon entropy. Both notions connected with that of probability with values in hyperbolic number, introduced by D. Alpay et al. [Adv. Appl. Clifford Algebr. 27, No. 2, 913–929 (2017; Zbl 1388.60011)]. Within this context, particular attention has been paid to the interpretation of the hyperbolic valued probabilities and the hyperbolic extension of entropy as well.
MSC:
| 60A05 | Axioms; other general questions in probability |
| 60A10 | Probabilistic measure theory |
| 62B10 | Statistical aspects of information-theoretic topics |
| 94A17 | Measures of information, entropy |
Citations:
Zbl 1388.60011References:
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