On order-continuous set multifunctions in Hausdorff topology

A.Croitoru; A.C.Gavriluc{t}

In this paper we present some properties of order-continuous (shortly, o-continuous) set multifunctions with respect to the Hausdorff topology and establish some results related to atoms and pseudo-atoms of o-continuous multisubmeasures.

1. G.~Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953-1954), 131--292.

2. A.P.~Dempster, Upper and lower probabilties induced by a multivalued mapping, Ann. Math. Statist. 38 (1967), 325--339.

3. N.~Dinculeanu, Vector Measures, Veb Deutscher Verlag Der Wissenschaften, Berlin, 1966.

4. L.~Drewnowski, Topological rings of sets, continuous set functions, Integration. I, II, III, Bull. Acad. Polon. Sci., 20 (1972), 269--287.

5. A.~Gavrilut, Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions, Fuzzy Sets and Systems (to appear).

6. A.~Gavrilut, A.~Croitoru, Non-atomicity for fuzzy and non-fuzzy multivalued set functions, Fuzzy Sets and Systems (to appear).

7. C.~Godet-Thobie, Multimesures et multimesures de transition, Th\`ese de Doctorat, Univ. des Sci. et Techn. du Languedoc, Montpellier, 1975.

8. S.~Hu, N.S.~Papageorgiou, Handbook of Multivalued Analysis, Vol. I, Kluwer Acad. Publ., Dordrecht, 1997.

9. D.~Liginlal, T.T.~Ow, Modelling attitude to risk in human decision process: An application of fuzzy measures, Fuzzy Sets and Systems 157 (2006), 3040-3054.

10. E.~Pap, Null-Additive Set Functions, Kluwer Academic Publishers, Dordrecht, 1995.

11. T.D.~Pham, M.~Brandl, N.D.~Nguyen, T.V.~Nguyen, Fuzzy measure of multiple risk factors in the prediction of osteoporotic fractures, Proceedings of the 9th WSEAS International Conference on Fuzzy Systems [FS'08], Sofia, Bulgaria, May 2-4, 2008, 171--177.

12. A.M.~Precupanu, On the set valued additive and subadditive set functions, An. St. Univ. Iasi 29 (1984), 41--48.

13. G.~Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, N.J., 1976.

14. M.~Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974.

15. C.~Wu, C.~Wu, A note on the range of null-additive fuzzy and non-fuzzy measure, Fuzzy Sets and Systems 110 (2000), 145--148.

	On order-continuous set multifunctions in Hausdorff topology
Author	A.Croitoru, A.C.Gavriluț croitoru@uaic.ro, gavrilut@uaic.ro Faculty of Mathematics,Al. I. Cuza University, 700506-Ia\csi, Romania
Abstract	In this paper we present some properties of order-continuous (shortly, o-continuous) set multifunctions with respect to the Hausdorff topology and establish some results related to atoms and pseudo-atoms of o-continuous multisubmeasures.
Keywords	order-continuous set multifunction, Hausdorff topology, atom, pseudo-atom, multisubmeasure
DOI	doi:10.30970/ms.31.2.149-156
Reference	1. G.~Choquet, Theory of capacities, Ann. Inst. Fourier (Grenoble) 5 (1953-1954), 131--292. 2. A.P.~Dempster, Upper and lower probabilties induced by a multivalued mapping, Ann. Math. Statist. 38 (1967), 325--339. 3. N.~Dinculeanu, Vector Measures, Veb Deutscher Verlag Der Wissenschaften, Berlin, 1966. 4. L.~Drewnowski, Topological rings of sets, continuous set functions, Integration. I, II, III, Bull. Acad. Polon. Sci., 20 (1972), 269--287. 5. A.~Gavrilut, Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Baire multivalued set functions, Fuzzy Sets and Systems (to appear). 6. A.~Gavrilut, A.~Croitoru, Non-atomicity for fuzzy and non-fuzzy multivalued set functions, Fuzzy Sets and Systems (to appear). 7. C.~Godet-Thobie, Multimesures et multimesures de transition, Th\`ese de Doctorat, Univ. des Sci. et Techn. du Languedoc, Montpellier, 1975. 8. S.~Hu, N.S.~Papageorgiou, Handbook of Multivalued Analysis, Vol. I, Kluwer Acad. Publ., Dordrecht, 1997. 9. D.~Liginlal, T.T.~Ow, Modelling attitude to risk in human decision process: An application of fuzzy measures, Fuzzy Sets and Systems 157 (2006), 3040-3054. 10. E.~Pap, Null-Additive Set Functions, Kluwer Academic Publishers, Dordrecht, 1995. 11. T.D.~Pham, M.~Brandl, N.D.~Nguyen, T.V.~Nguyen, Fuzzy measure of multiple risk factors in the prediction of osteoporotic fractures, Proceedings of the 9th WSEAS International Conference on Fuzzy Systems [FS'08], Sofia, Bulgaria, May 2-4, 2008, 171--177. 12. A.M.~Precupanu, On the set valued additive and subadditive set functions, An. St. Univ. Iasi 29 (1984), 41--48. 13. G.~Shafer, A Mathematical Theory of Evidence, Princeton University Press, Princeton, N.J., 1976. 14. M.~Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology, 1974. 15. C.~Wu, C.~Wu, A note on the range of null-additive fuzzy and non-fuzzy measure, Fuzzy Sets and Systems 110 (2000), 145--148.
Pages	149-156
Volume	31
Issue	2
Year	2009
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html