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Calculating the entropy for complex systems is a significant problem in science and engineering problems. However, this calculation is usually computationally expensive when the entropy is computed directly. This paper introduces three classes of information sources that for all members of each class, the entropy value is the same. These classes are characterized according to special dynamics created by three kinds of self-mappings on Ω, and A, where Ω is a probability space and A is a finite set. An approximation of rank variables of the product of information sources is made, and it is proved that the topological entropy of the product of two information sources is equal to the summation of their topological entropies. [ABSTRACT FROM AUTHOR]

Studying the evolution of a system and dealing with its complexity are key issues in analyzing and predicting its future behavior. In this respect, the uncertainty problem for a wide variety of mathematical structures such as hyper MV–algebras and stochastic processes (information sources) that provide models for varied systems has been studied. This paper presents the algebraic and Shannon entropies for hypergroupoids and commutative hypergroups, respectively, and studies their fundamental properties. These notions are established in a way that they are technically feasible to be adapted to other algebraic hyperstructures. Moreover, it is investigated that how these two types of entropies are connected for the case of commutative hypergroups. In addition, conditions under which the algebraic entropy is connected with the information and permutation entropies are detected. In the end, the algebraic entropy is calculated for some hypergroupoids and chemical algebras. [ABSTRACT FROM AUTHOR]