Communications to the Pseudo-Additive Probability Measure and the Induced Probability Measure Realized by <img src=image/13492447_01.gif>

doi:10.13189/ms.2024.120104

Journals Information

Mathematics and Statistics Vol. 12(1), pp. 24 - 30
DOI: 10.13189/ms.2024.120104
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Communications to the Pseudo-Additive Probability Measure and the Induced Probability Measure Realized by

Dhurata Valera ¹^,*, Bederiana Shyti ¹, Silvana Paralloj ²
¹ Department of Mathematics, Faculty of Natural Sciences, University of Elbasan “Aleksandër Xhuvani”, Elbasan, 3001, Albania
² Faculty of Mathematics and Informatics, University St. Kliment Ohridski, Sofia, Bulgaria

ABSTRACT

The Theory of Pseudo-Additive Measures has been studied by analyzing and evaluating significant results. The system of pseudo-arithmetic operations (SPAO) as a system generated by the generator is shown directly by taking results of Rybárik and Pap, but is a further development of . Using the meaning of entropy as a logarithmic measure in information theory. Through examples we present the relation between the and the entropy, realized by the , i.e. a . The paper studies the construction of relationships between entropy and supported by and the connection with Shannon Entropy. For the pseudo-additive probabilistic measure , using as well as in the system generated by , the problem of modification of this measure by is addressed. The modifications of the Pseudo-Additive Probability Measure and the Induced Probability Measure supported by are presented, showing the relationships between the two modifications of the Pseudo-Additive Probability Measure (PAPM) and the Induced Probability Measure (IPM). Further, the Bi-Pseudo-Integral for and the Lebesgue Integral are represented in a relationship.

KEYWORDS
Pseudo-Arithmetic Operations, Modified Function, Pseudo-Additive Measure, , ,

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Dhurata Valera , Bederiana Shyti , Silvana Paralloj , "Communications to the Pseudo-Additive Probability Measure and the Induced Probability Measure Realized by ," Mathematics and Statistics, Vol. 12, No. 1, pp. 24 - 30, 2024. DOI: 10.13189/ms.2024.120104.

(b). APA Format:
Dhurata Valera , Bederiana Shyti , Silvana Paralloj (2024). Communications to the Pseudo-Additive Probability Measure and the Induced Probability Measure Realized by . Mathematics and Statistics, 12(1), 24 - 30. DOI: 10.13189/ms.2024.120104.