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In the present paper we have derived some properties of the pseudo-metric introduced by Riećanova on a lattice effect algebra E corresponding to a valuation u on E, which turns out to be a metric if u happens to be faithful. Using these properties we have been able to prove that this metric is complete. Also it is observed that the resulting metric space is convex if and only if w is non-atomic if and only if E is atomless.
Wydawca
Czasopismo
Rocznik
Tom
Strony
249--258
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
autor
- Department of Mathematics University of Allahabad, Allahabad 211 001, India, dr.mkhare@gmail.com.
Bibliografia
- [1] A. Avallone and A. Basile, On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286 (2003), 378-390.
- [2] A. Avallone, A. De Simone and P. Vitolo, Effect algebra and extension of measure, Bollentino U.M.I. (8) (9-B), (2006), 423-444.
- [3] M. K. Bennett and D. J. Foulis, Effect algebras and unsharp quantum logics, Found. Phys. 10 (1994), 1331-1352.
- [4] M. K. Bennett and D. J. Foulis, Phi-symmetric effect algebras, Found. Phys. 25 (1995), 1699-1722.
- [5] A. Dvurečenskij and S. Pulmannová, New Trends in Quantum Structure, Kluwer Acad. Pub., Dordrecht, 2000.
- [6] P. Hajek, Mathematics of Puzzy Logic, Kluwer Acad. Pub., Dordrecht, 1998.
- [7] P. R. Halmos, Measures Theory, Van Nostrand, Princeton, NJ, 1950.
- [8] U. Höhle and E. P. Klement (eds.), Non-classical Logics and their Application to Fuzzy Subsets, Kluwer Acad. Pub., Dordrecht, 1995.
- [9] M. Khare, Fuzzy σ-algebras and conditional entropy, Fuzzy Sets and Systems 102 (1999), 287-292.
- [10] M. Khare, The dynamics of F-quantum spaces, Math. Slovaca 52 (4), (2002), 425-432.
- [11] F. Kôpka, D-posets of fuzzy sets, Tatra Mount. Math. Publ. 1 (1992), 83-87.
- [12] Z. Riečanova, Proper effect algebras admitting no states, Internat. J, Theor. Phys. 40 (2001), 1683-1691.
- [13] Z. Riečanova, Lattice effect algebras with o-continuous faithful valuations, Fuzzy Sets and Systems 124 (2001), 321-327.
- [14] Z, Riečanova, State uniformities and metrices on lattice effect algebra, Internat. J. Uncertain., Fuzziness Knowledge-Based Systems 10 (2002), 125-134.
- [15] P. Srivastava and M. Khare, Conditional entropy and Rokhlin metric, Math. Slovaca 49 (4), (1999), 433-441.
- [16] P. Srivastava, M. Khare and Y. K. Srivastava, A fuzzy measure algebra as a metric space, Fuzzy Sets and Systems 79 (1996), 395-400.
- [17] P. Srivastava, M. Khare and Y. K. Srivastava, m-equivalence, entropy and F-dynamical systems, Fuzzy Sets and Systems 121 (2001), 275-283.
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Bibliografia
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bwmeta1.element.baztech-article-PWA3-0048-0001