Relations between various continuity concepts in effect algebras

• Autorzy: Khare M. , Gupta S.
• Języki publikacji: EN

Abstrakty

EN

The aim of the present paper is to establish relations between continuity concepts for a nonnegative extended real-valued function [...] defined on an effect algebra. Examples and counterexamples are given to illustrate various situations arising in this study.

Słowa kluczowe

EN

effect algebra; nonadditive function; order continuity

PL

algebra; funkcje nieaddytywne; porządek ciągłości

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 3
• Strony: 507--518
• Opis fizyczny: Bibliogr. 33 poz.

Twórcy

autor

Khare M.

autor

Gupta S.

• Department of Mathematics University of Allahabad Allahabad - 211 002, India,

Bibliografia

• [1] A. Avallone, Cafiero and Nikodym boundedness theorems in effect algebras, Ital. J. Pure Appl. Math. 20 (2006), 203-214.
• [2] A. Avallone, A. Basile, On a Marinacci uniqueness theorem for measures, J. Math. Anal. Appl. 286 (2) (2003), 378-390.
• [3] A. Avallone, A. De Simone, P. Vitolo, Effect algebras and extensions of measures, Bollettino U.M.I. 9-B (8) (2006), 423-444.
• [4] M. K. Bennet, D. J. Foulis, Effect algebras and unsharp quantum logics, Found. Phys. 24 (10) (1994), 1331-1352.
• [5] M. K. Bennet, D. J. Foulis, Phi-symmetric effect algebras, Found. Phys. 25 (1995), 1699-1722.
• [6] M. K. Bennet, D. J. Foulis, R. J. Greechie, Sums and products of interval algebras, Inter. J. Theoret. Phys. 33 (1994), 2114-2136.
• [7] E. G. Beltrametti, G. Cassinelli, The Logic of Quantum Mechanics, Addison-Wesley Publishing Co., Reading, Mass, 1981.
• [8] D. Butnriu, E. P. Klement, Triangular Norm-based Measures and Games with Fuzzy Coalitions, Kluwer, Acad. Pub., 1993.
• [9] G. Choquet, Theory of capacities, Ann. Inst. Fourier (Genoble) 5 (1953-1954), 421-427.
• [10] D. Dennenberg, Nonadditive Measure and Integral, Kluwer, Dordrecht, 1994.
• [11] I. Dobrakov, On submeasures I, Dissertationes Math. 112 (1974), 5-35.
• [12] I. Dobrakov, J. Farkova, On submeasures II, Math. Slovaca 30 (1980), 65-81.
• [13] L. Drewnowski, On the continuity of certain nonadditive set functions, Coll. Math. 38 (1978), 243-253.
• [14] A. Dvurečenskij, S. Pulmannov ́a, New Trends in Quantum Structures, Kluwer Acad. Pub., 2000.
• [15] L. G. Epstein, J. Zhang, Subjective probabilities on subjectively unambiguous eve nts, Econometrica 69 (2) (2001), 265-306.
• [16] P. Ghirardato, M. Marinacci, Ambiguity made precise : a comparative foundation, J. Econom. Theory 102 (2002), 251-289.
• [17] P. R. Halmos, Measure Theory, Van Nostrand, Princeton, NJ, 1950.
• [18] Q. Jiang, H. Suzuki, Z. Wang, G. J. Klir, Exhaustivity and absolute continuity of fuzzy measures, Fuzzy Sets and Systems 96 (1998), 231-238.
• [19] G. Kalmbach, Orthomodular Lattices, Academic Press, London, 1983.
• [20] M. Khare, Fuzzy σ-algebras and conditional entropy, Fuzzy Sets and Systems 102 (1999), 287-292.
• [21] M. Khare, The dynamics of F-quantum spaces, Math. Slovaca 52(4) (2002), 425-432.
• [22] M. Khare, B. Singh, Weakly tight functions and their decomposition, Int. J. Math. and Math. Sci. 18 (2005), 2991-2998.
• [23] F. Kôpka, F. Chovanec, D-posets of fuzzy sets, Tatra Mount. Math. Publ. 1(1992), 83-87.
• [24] E. Pap, On nonadditive set functions, Atti. Sem. Mat. Fis. Univ. Modena 39 (1991), 345-360.
• [25] E. Pap, Null-additive Set Functions, Kluwer, Dordrecht, Ister Science, Bratislava, 1995.
• [26] P. Srivastava, M. Khare, Y. K. Srivastava, A fuzzy measure algebra as a metric space, Fuzzy Sets and Systems 79 (1996), 395-400.
• [27] P. Srivastava, M. Khare, Y. K. Srivastava, Fuzzy dynamical systems: inverse and direct spectra, Fuzzy Sets and Systems 113 (2000), 439-445.
• [28] P. Srivastava, M. Khare, Y. K. Srivastava, m-equivalance, entropy and F-dynamical systems, Fuzzy Sets and Systems 121 (2001), 275-283.
• [29] M. Sugeno, Theory of fuzzy integrals and its applications, Ph. D. Thesis, TokyoInstitute of Technology, 1974.
• [30] K. Uchino, S. Asahina, T. Murofushi, Relationship among continuity conditions and null-additivity conditions in nonadditive measure the ory, Fuzzy Sets and Systems 157 (2006), 691-698.
• [31] Z. Wang, The autocontinuity of set function and the fuzzy integral, J. Math. Anal. Appl. 99 (1984), 195-218.
• [32] Z. Wang, G. J. Klir, Fuzzy Measure Theory, Plennum Press, New York and Lodon, 1992.
• [33] A. Zadeh, Probability measures of fuzzy events, J. Math. Anal. Appl. 23 (1968), 421-427.