Fuzzy measure on p-adic balls defined on a finite number set

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The article explores an approach to constructing a fuzzy measure on p-adic balls that does not require the direct specification of the measure density. The relationships necessary for determining this measure for an arbitrary subset of a bounded numerical set, represented as a set of p-adic balls, are proven. Uniform and non-uniform fuzzy measures are considered. An algorithm for determining the fuzzy measure on p-adic balls is proposed. Examples of calculating this measure are provided.

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Sobre autores

V. Bocharnikov

INEKS-FT Consulting Group

Autor responsável pela correspondência
Email: bocharnikovvp@gmail.com
ORCID ID: 0000-0003-4398-5551
Ucrânia, ul. Desyatinnaya 13а, Kiev, 03011

S. Sveshnikov

INEKS-FT Consulting Group

Email: bocharnikovvp@gmail.com
ORCID ID: 0000-0001-8924-4535
Ucrânia, ul. Desyatinnaya 13а, Kiev, 03011

Bibliografia

  1. Becker O.M., Karplus M. The topology of multidimensional protein energy surfaces: theory and application to peptide structure and kinetics // Journal of Chemical Physics. 1997. V. 106. P. 1495–1517.
  2. Grabisch M., Murofushi T., Sugeno M. Fuzzy Measures and Integrals: Theory and Applications. Berlin, Germany, Physica-Verlag GmbH & Co, 2000, 477 p., ISBN10 3790812587
  3. Wekker L.M. Psyche and reality: a unified theory of mental processes. — M.: Smysl, 1998. — 685 p. — Access mode: https://vshp.pro/wp-content/uploads/2020/03/Vekker-L.M.-Psihika-i-realnost.-Edinaya-teoriya-psihicheskih-protsessov.pdf
  4. Philosophical encyclopedic dictionary. / Chief editor: L. F. Ilyichev, P. N. Fedoseev, S. M. Kovalev, V. G. Panov. — M.: Soviet Encyclopedia, 1983. — 840 p.
  5. Aliev R. A. Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions. Studies in Fuzziness and Soft Computing. Springer, 2013, 324 p. ISBN 3642348955
  6. Keller J. M., Derong L., Fogel D. B. Fundamentals of Computational Intelligence: Neural Networks, Fuzzy Systems, and Evolutionary Computation. IEEE Press Series on Computational Intelligence. John Wiley & Sons, 2016, 378 p. ISBN 1119214343
  7. Vladimirov V. S, Volovich I. V, Zelenov E. I. P-adic Analysis and Mathematical Physics. Series on Soviet and East European Mathematics (Vol 1). World Scientific, 1994, 340 p. ISBN 9814505765
  8. Yager R.R., Liping L. Classic Works of the Dempster-Shafer Theory of Belief Functions. Studies in Fuzziness and Soft Computing (Vol 219). Springer, 2008, 806 p. ISBN 354044792X
  9. Torra V., Narukawa Y., Sugeno M. Non-Additive Measures: Theory and Applications. Studies in Fuzziness and Soft Computing (Vol 310). Springer, 2013, 201 p. ISBN 3319031554
  10. Bocharnikov V. P., Sveshnikov S. V. p-Adic Representation of Subsets of a Bounded Number Set. Programming and Computer Software, 2021, Vol. 47, No. 4, pp. 225–234.
  11. Koblitz N. p-adic Numbers, p-adic Analysis, and Zeta-Functions. Springer, Science & Business Media, 2012, 153 p. ISBN 1461211123
  12. Katok S. p-adic Analysis Compared with Real. Student mathematical library (Vol 37), American Mathematical Society. American Mathematical Soc., 2007, 152 p. ISBN 9780821842201
  13. Volovich I. V., Kozyrev S. V. p-Adic mathematical physics: basic constructions, applications to complex and nanoscopic systems, Mathematical physics and its applications. Introductory courses. Issue 1, Samara State. University, Samara, 2009. http://www.mi.ras.ru/noc/irreversibility/p-adicMF1.pdf
  14. Khrennikov A. Yu. Modeling of thinking processes in p-adic coordinate systems. — M.: FIZMATLIT, 2004. — 296 p. ISBN 5-9221-0501-9
  15. Kozyrev S. V. Wavelet theory as p-adic spectral analysis. Izv. RAN. Ser. Mat., 2002, Vol. 66, No. 2, pp. 149–158
  16. Кононюк А. Е. Обобщённая теория моделирования: Книга 2: Числа: количественные оценки параметров модели. Киев: «Освіта України», 2012. — 548 с. ISBN 9789667599508
  17. Deza M-M, Deza E. Encyclopedia of distances. Berlin, Springer, 2008. 412 p. (Russ. ed.: Deza M-M, Deza E. Entsiklopedicheskii slovar’ rasstoyanii. Moscow, Nauka Publ., 444 p)
  18. Borevich Z.I., Shafarevich I.R. Teoriya chisel [Number theory]. Moscow, Science. The main edition of the physical and mathematical literature, 3rd ed., 1985. 504 p.
  19. Bocharnikov V., Bocharnikov I., Sveshnikov S. Fundamentals of the systemic organization’s management. Theory and Practice. Berlin, LAP LAMBERT Academic Publishing, 2012, 296 p. ISBN 9783659223327

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