This paper is devoted to introduce and study Rényi and Tsallis entropy, conditional Tsallis entropy and Tsallis mutual information of D-posets on a state s. Several relations between the conditional entropies are derived. Finally we define Tsallis entropy of dynamical system on D-posets and a new version of Kolmogorove-Sinai Theorem has been proved.
KolmogorovA., New metric invariant of transitive dynamical systems and auto-morphisms of lebesgue spaces, Dokl Russ Acad Sci119 (1958), 861–864.
11.
LandsbergP.T., Fragmentations, mergings and order: Aspects of entropy, Physica A305 (2002), 32.
12.
MaX., LiuQ., ZhanJ., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47 (2017), 507–530.
13.
RasteginA.E., Generalized Conditional entropies of partitions on quantum logic, 58 (2012), 819–822.
14.
RényiA., On measures of entropy and information, Proc 4th Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley, CA, 1961, p. 547.
15.
ShannonC., A mathematical theory of communication, Bell Syst Tech Journal27 (1948), 379–423.
16.
SinaiY., On the notion of entropy of a dynamical system Dokl, Russ Acad Sci124 (1959), 768–771.
17.
StanleyR., Two poset polytopes, Discrete and Computational Geometry1 (1986), 9–23.
18.
TsallisC., Possible generalization of Boltzmann-Gibbs statistics, J Stat Phys52 (1988), 479–487.
19.
WaltersP., An Introduction to Ergodic Theory, Springer Verlag, 1982.
20.
YanagiK., KuriyamaK., FuruichiS., Generalized Shannon inequalities based on Tsallis relative operator entropy, Linear Algebra Appl349 (2005), 109–118.
21.
ZhanJ., Irfan AliM., MehmoodN., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing56 (2017), 446–457.
22.
ZhanJ., LiuQ., HerawanT., A novel soft rough set: Soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
23.
ZhanJ., ZhuK., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing21 (2017), 1923–1936.
