Kolmogorov - Sinaj entropy on MV-algebras
نویسنده
چکیده
There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličký modification of the Kolmogorov Sinaj entropy for fuzzy sets ([6], [14], [15]).
منابع مشابه
Entropy on effect algebras with Riesz decomposition property II: MV-algebras
We continue the study of entropy. In Part I, we have introduced basic properties of entropy. Here we concentrate mainly on the state space which allows us to understand the entropy better, Section 8, and we introduce also quotient effect algebras. Section 9 studies shortly the problem of a so-called entropy generator theorem for effect algebras or MV-algebras. The main results of the present pa...
متن کاملNew Results on Ideals in $MV$-algebras
In the present paper, by considering the notion of ideals in $MV$-algebras, we study some kinds of ideals in $MV$-algebras and obtain some results on them. For example, we present definition of ultra ideal in $MV$-algebras, and we get some results on it. In fact, by definition of ultra ideals, we present new conditions to have prime ideals, positive implicative ideals and maximal ideals in $MV$...
متن کاملLogical Divergence, Logical Entropy, and Logical Mutual Information in Product MV-Algebras
In the paper we propose, using the logical entropy function, a new kind of entropy in product MV-algebras, namely the logical entropy and its conditional version. Fundamental characteristics of these quantities have been shown and subsequently, the results regarding the logical entropy have been used to define the logical mutual information of experiments in the studied case. In addition, we de...
متن کاملEntropy of Intuitionistic Fuzzy-Dynamical Systems on MV -algebras
In this paper, intuitionistic fuzzy-dynamical systems (IF-dynamical systems) on an MV -algebra are introduced. Also the entropy of IF-dynamical systems is introduced and studied. Several related results are proved.
متن کاملA new approach to characterization of MV-algebras
By considering the notion of MV-algebras, we recall some results on enumeration of MV-algebras and wecarry out a study on characterization of MV-algebras of orders $2$, $3$, $4$, $5$, $6$ and $7$. We obtain that there is one non-isomorphic MV-algebra of orders $2$, $3$, $5$ and $7$ and two non-isomorphic MV-algebras of orders $4$ and $6$.
متن کامل