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Triangular structures and duality

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EN
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EN
We introduce and study the category AFD the objects of which are generalized convergence D-posets (with more than just one greatest element) of maps into a triangle object T and the morphisms of which are sequentially continuous D-homomorphisms. The category AFD can serve as a base category for antagonistic fuzzy probability theory. AFD-measurable maps can be considered as generalized random variables and ADF-morphisms, as their dual maps, can be considered as generalized observables.
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autor
  • Department of Mathematics, Pedagogical Faculty Catholic University in Ružomberok Námestie A. Hlinku. 56/1, 034 01 Ružomberok, Slovak Republic and Mathematical Institute, Slovwak Academy of Sciences Grešakova 6, 040 01 Košice, Slovak Republic
autor
  • Department of Mathematics, Pedagogical Faculty Catholic University in Ružomberok Námestie A. Hlinku. 56/1, 034 01 Ružomberok, Slovak Republic
Bibliografia
  • [1] J. Adámek. Theory of Mathematical Structures. Reidel, Dordrecht, 1983.
  • [2] K. Atanasov. Intuitionistic Fuzzy Sets: Theory and Applications. Physica Verlag, New York, 1999
  • [3] S. Bugajski. Statistical maps I. Basic properties. Math. Slovaca, 51, 321-342, 2001.
  • [4] S. Bugajski. Statistical maps II. Operational random variables. Math. Slovaca, 51,343-361, 2001
  • [5] F. Chovanec, F. Kôpka. Difference posets in the quantum structures background. Int. J. Theoret, Phys., 39, 571-583, 2000.
  • [6] A: Dvurečenskij, S. Pulmannová, New Trends in Quantum Structures. Kluwer Academic Publ., Ister Science, Dordrecht, Bratislava, 2000.
  • [7] D.J. Foulis, M.K. Bennett. Effect algebras and un sharp quantum logics. Found. Phys., 24, 1331-1352, 1994.
  • [8] R. Frič. A Stone-type duality and its applications to probability. Topology Proceedings, Vol.22, Summer 1997,pp. 125-137. Proceedings of the 12th Summer Conference on General Topology and its Applications, North Bay, August 1997.
  • [9] R. Frič. Convergence and duality, Appl. Categorical Structures., 10, 257- 266,2002.
  • [10] R. Frič. Duality for generalized events. Math. Slovaca, 54, 49-60, 2004.
  • [11] R. Frič. Remarks on statistical maps and fuzzy (operational) random variables. Tatra Mountains Math, Publ., 30, 21-34, 2005.
  • [12] R. Frič, Statistical maps: a categorical approach. Math: Slovaca, 57, 41-57, 2007.
  • [13] S. Gudder. Fuzzy probability theory. Demonstratio Math., 31, 235-254, 1998.
  • [14] H. Herrlieh G.E. Strcker. Category Theory, Heldermann Verlag, Berlin, second edition, HJ76.
  • [15] F. Kôpka. D-posets of fuzzy sets. Tatra Mountains Math: Publ., 1,83-87, 1992.
  • [16] F. Kôpka, F. Chovanec. D-posets. Math. Slovaca, 44, 21-34, 1994.
  • [17] R. Mesiar. Fuzzy sets and probability theory. Tatra Mountains Math. Publ., 1,105-123, 1992.
  • [18] M. Papčo. On measurable spaces and measurable maps. Tatra Mountains Math. Publ., 28, 1215-140, 2004.
  • [19] M. Papčo. On fuzzy random variables: examples and generalizations. Tatra Mountains Math. Publ., 30, 175-185, 2005
  • [20] B. Riečan, D. Mundici. Probability on MV-algebras. In: Handbook of Measure Theory, Vol. II (Editor: E. Pap), pp. 869-910, North-Holland, Amsterdam, 2002.
  • [21] B. Riečan. On a problem of Radko Mesiar: general form of intuitionistic fuzzy probabilities. Fuzzy Sets and Systems, 152, 1485-1490, 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-06005378-1168-4b09-996e-a94425453258
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