Abstract
In this paper, we present the concept of the logical entropy of order m, logical mutual information, and the logical entropy for information sources. We found upper and lower bounds for the logical entropy of a random variable by using convex functions. We show that the logical entropy of the joint distributions and is always less than the sum of the logical entropy of the variables and . We define the logical Shannon entropy and logical metric permutation entropy to an information system and examine the properties of this kind of entropy. Finally, we examine the amount of the logical metric entropy and permutation logical entropy for maps.
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