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Probability Integral as a Linearization Cover

Probability Integral as a Linearization

Tatra Mountains Mathematical Publications
Volume 72 (2018): Issue 1 (December 2018)
By: Dušana Babicová  
Open Access
|Mar 2019

References

  1. [1] ADÁMEK, J.: Theory of Mathematical Structures, Reidel, Dordrecht, 1983.
    Search in Google ScholarBack to article
  2. [2] BARNETT, J. H.: Origins of Boolean algebra in the logic of classes: George Boole, John Venn, and C. S. Pierce, Convergence; Mathematical Association of America, www.maa.org/publications/periodicals/convergence.
    Search in Google ScholarBack to article
  3. [3] BERNOULLI, J.: Ars Conjectandi, Opus Posthumum. Accedit Tractatus de Seriebus Infinitis, et Epistola Gallicé Scripta de Ludo Pilae Reticularis. Basileae: Impensis Thurnisiorum, Fratrum, 1713.10.5479/sil.262971.39088000323931
    Search in Google ScholarBack to article
  4. [4] BUGAJSKI, S.: Statistical maps I. Basic properties, Math. Slovaca 51 (2001), 321–342.
    Search in Google ScholarBack to article
  5. [5] ______ Statistical maps II. Operational random variables, Math. Slovaca 51 (2001), 343–361.
    Search in Google ScholarBack to article
  6. [6] BUTNARIU, D.—KLEMENT, E. P.: Triangular Norm-Based Measures and Games with Fuzzy Coalitions, Kluwer Academic Publishers, Dordrecht, 1993.10.1007/978-94-017-3602-2
    Search in Google ScholarBack to article
  7. [7] CHOVANEC, F.—KÔPKA, F.: D-posets, in: Handbook of Quantum Logic and Quantum Structures: Quantum Structures (K. Engesser et al., eds.), Elsevier, Amsterdam, 2007, pp. 367–428.10.1016/B978-044452870-4/50031-5
    Search in Google ScholarBack to article
  8. [8] CHOVANEC, F.—FRIČ, R.: States as morphisms, Internat. J. Theoret. Phys. 49 (2010), 3050–3060.10.1007/s10773-009-0234-4
    Search in Google ScholarBack to article
  9. [9] DVUREČENSKIJ, A.—PULMANNOVÁ, S.: New Trends in Quantum Structures. Kluwer Academic Publ. and Ister Science, Dordrecht and Bratislava, 2000.10.1007/978-94-017-2422-7
    Search in Google ScholarBack to article
  10. [10] FOULIS, D. J.: Algebraic measure theory, Atti Semin. Mat. Fis. Univ.Modena 48, (2000), 435–461.
    Search in Google ScholarBack to article
  11. [11] FRIČ, R.: Łukasiewicz tribes are absolutely sequentially closed bold algebras, Czechoslovak Math. J. 52 (2002), 861–874.10.1023/B:CMAJ.0000027239.28381.31
    Search in Google ScholarBack to article
  12. [12] ______ Remarks on statistical maps and fuzzy (operational) random variables, TatraMt. Math. Publ. 30 (2005), 21–34.
    Search in Google ScholarBack to article
  13. [13] ______ Statistical maps: a categorical approach, Math. Slovaca 57 (2007), 41–57.10.2478/s12175-007-0013-8
    Search in Google ScholarBack to article
  14. [14] ______ Extension of domains of states, Soft Comput. 13 (2009), 63–70.10.1007/s00500-008-0293-0
    Search in Google ScholarBack to article
  15. [15] ______ On D-posets of fuzzy sets, Math. Slovaca 64 (2014), 545–554.10.2478/s12175-014-0224-8
    Search in Google ScholarBack to article
  16. [16] FRIČ, R.—PAPČO, M.: On probability domains, Internat. J. Theoret. Phys. 49 (2010), 3092–3100.10.1007/s10773-009-0162-3
    Search in Google ScholarBack to article
  17. [17] ______ A categorical approach to probability, Studia Logica 94 (2010), 215–230.10.1007/s11225-010-9232-z
    Search in Google ScholarBack to article
  18. [18] ______ Fuzzification of crisp domains, Kybernetika 46 (2010), 1009–1024.
    Search in Google ScholarBack to article
  19. [19] ______ On probability domains II. Internat. J. Theoret. Phys. 50 (2011), 3778–3786.10.1007/s10773-011-0855-2
    Search in Google ScholarBack to article
  20. [20] ______ On probability domains III. Internat. J. Theoret. Phys. 54 (2015), 4237–4246.10.1007/s10773-014-2471-4
    Search in Google ScholarBack to article
  21. [21] ______ On probability domains IV, Internat. J. Theoret. Phys. (to appear).
    Search in Google ScholarBack to article
  22. [22] ______ Upgrading probability via fractions of events, Commun. Math. 24 (2016), 29–41.10.1515/cm-2016-0004
    Search in Google ScholarBack to article
  23. [23] ______ Probability: from classical to fuzzy, Fuzzy Sets Syst. 326 (2017), 106–114.10.1016/j.fss.2017.06.003
    Search in Google ScholarBack to article
  24. [24] GUDDER, S.: Fuzzy probability theory, Demonstratio Math. 31 (1998), 235–254.10.1515/dema-1998-0128
    Search in Google ScholarBack to article
  25. [25] KOLMOGOROV, A. N.: Grundbegriffe der wahrscheinlichkeitsrechnung. Springer-Verlag, Berlin, 1933.10.1007/978-3-642-49888-6
    Search in Google ScholarBack to article
  26. [26] KÔPKA, F.—CHOVANEC, F.: D-posets, Math. Slovaca 44 (1994), 21–34.
    Search in Google ScholarBack to article
  27. [27] MESIAR, R.: Fuzzy sets and probability theory, Tatra Mt. Math. Publ. 1 (1992), 105–123.
    Search in Google ScholarBack to article
  28. [28] MUNDICI, D.: A geometric approach to MV-algebras, in: On Logical, Algebraic and Probabilistic Aspects of Fuzzy Set Theory, Dedicated to E. P. Klement (R. Mesiar et al., eds.), Springer, Berlin, 2016, pp. 57–70.10.1007/978-3-319-28808-6_4
    Search in Google ScholarBack to article
  29. [29] NAVARA, M.: Probability theory of fuzzy events, in: 4th Conference of the European Society for Fuzzy Logic and Technology and 11 Rencontres Francophones sur la Logique Floue et ses Applications (E. Montseny and P. Sobrevilla, eds.), Barcelona, Spain, 2005, Universitat Polit’ecnica de Catalunya, Barcelona, Spain, 2005, pp. 325–329.
    Search in Google ScholarBack to article
  30. [30] PAPČO, M.: On measurable spaces and measurable maps, Tatra Mt. Math. Publ. 28 (2004), 125–140.
    Search in Google ScholarBack to article
  31. [31] ______ On fuzzy random variables: examples and generalizations, Tatra Mt. Math. Publ. 30 (2005), 175–185.
    Search in Google ScholarBack to article
  32. [32] ______ On effect algebras, Soft Comput. 12 (2008), 373–379.10.1007/s00500-007-0171-1
    Search in Google ScholarBack to article
  33. [33] ______ Fuzzification of probabilistic objects, in: 8th Conf. of the European Society for Fuzzy Logic and Technology—EUSFLAT ‘13 (G. Pasi et al., eds.), Milano, Italy, 2013, Atlantis Press, Amsterdam, 2013, pp. 67–71.
    Search in Google ScholarBack to article
  34. [34] RIEČAN, B.—MUNDICI, D.: Probability on MV-algebras, in: Handbook of Measure Theory, Vol. II (E. Pap, ed.), North-Holland, Amsterdam, 2002, pp. 869–910.10.1016/B978-044450263-6/50022-1
    Search in Google ScholarBack to article
  35. [35] RIEČAN, B.—NEUBRUNN, T.: Integral, Measure, and Ordering. Kluwer Acad. Publ., Dordrecht, 1997.10.1007/978-94-015-8919-2
    Search in Google ScholarBack to article
  36. [36] SKŘIVÁNEK, V.—FRIČ, R.: Generalized random events, Internat. J. Theoret. Phys. 54 (2015), 4386–4396.10.1007/s10773-015-2594-2
    Search in Google ScholarBack to article
  37. [37] ZADEH, L. A.: Probability measures of fuzzy events, J. Math. Anal. Appl. 23 (1968), 421–27.10.1016/0022-247X(68)90078-4
    Open DOISearch in Google ScholarBack to article
DOI: https://doi.org/10.2478/tmmp-2018-0017 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
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Language: English
Page range: 1 - 15
Submitted on: Oct 20, 2017
Published on: Mar 12, 2019
Published by: Slovak Academy of Sciences, Mathematical Institute
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year
Keywords:
generalized probability,
measurable function,
fuzzy random event,
D-poset,
effect algebra,
A-poset,
IA-poset,
Łukasiewicz tribe,
epireflection,
probability integral,
linearization
Related subjects:
Mathematics,
General mathematics

© 2019 Dušana Babicová, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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