Algebraic and Shannon entropies of commutative hypergroups and their connection with information and permutation entropies and with calculation of entropy for chemical algebras
| Autor: | Adel Mehrpooya, Yamin Sayyari, Mohammadreza Molaei |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics Stochastic process 02 engineering and technology Key issues Theoretical Computer Science 020901 industrial engineering & automation 0202 electrical engineering electronic engineering information engineering Entropy (information theory) 020201 artificial intelligence & image processing Geometry and Topology Mathematical structure Algebraic number Commutative property Software Mathematics |
| Zdroj: | Soft Computing. 23:13035-13053 |
| ISSN: | 1433-7479 1432-7643 |
| DOI: | 10.1007/s00500-019-04314-7 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink