SET-NORM EXHAUSTIVE SET MULTIFUNCTIONS

Document Type: Research Paper

Authors

1 Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no 11, Iasi-700506, Romania

2 Faculty of Mathematics, "A.I. Cuza" University, Bd. Carol I, no 11, Iasi-700506, Romania

Abstract

In this paper we present some properties of set-norm exhaustive
set multifunctions and also of atoms and pseudo-atoms of set multifunctions
taking values in the family of non-empty subsets of a commutative semigroup
with unity.

Keywords


[1] S. Asahina, K. Uchino and T. Murofushi,Relationship among continuity conditions and nulladditivity ditions in non-additive measure theory, Fuzzy Sets and Systems, 157 (2006),691-698. 

[2] R. J. Aumann and L. S. Shapley,Values of non-atomic games, Princeton University Press,Princeton, New Jersey, 1974. 

[3] I. Chitescu,Finitely purely atomic measures: coincidence and rigidity properties, Rendiconti del Circolo Matematico di Palermo, Serie II, Tomo L, (2001), 455-476. 

[4] G. Choquet,Theory of capacities, Ann. Inst. Fourier (Grenoble), 5 (1953-1954), 131-292.

[5] A. Croitoru,Set-norm continuity of set multifunctions, ROMAI Journal, 6 (2010), 47-56.

[6] A. Croitoru, A. Gavrilut, N. E. Mastorakis and G. Gavrilut On dierent types of non-additiveset multifunctions,WSEAS Transactions on Mathematics, 8 (2009), 246-257.

[7] A. Daneshgar and A. Hashemi,Fuzzy sets from a meta-system-theoretic point of view, Iranian Journal of Fuzzy Systems,3(2) (2006), 1-20.

[8] A. P. Dempster,Upper and lower probabilities induced by a multivalued mapping, Ann. Mat.Statist.,38(1967), 325-339.

[9] D. Denneberg,Non-additive Measure and Integral, Kluwer Academic Publishers, Dorrecht/Boston/London, 1994.

[10] L. Drewnowski,Topological rings of sets, continuous set functions. Integration, I, II, III,Bull. Acad. Polon. Sci. Ser. Math. Astron. Phy, s20(1972), 269-286.

[11] D. Dubois and H. Prade, Fuzzy sets and systems. Theory and applications, Academic Press,New York, 1980. 

[12] T. Funiokova,LK-Interior systems of "almost open" L-sets, Iranian JournaL of Fuzzy Systems,4(2)(2007), 47{55.

[13] A. Gavrilut,Non-atomicity and the Darboux property for fuzzy and non-fuzzy Borel/Bairemultivalued set functions, Fuzzy Sets and Systems, 160 2009), 1308-1317.

[14] A. Gavrilut and A. Croitoruon-atomicity for fuzzy and non-fuzzy multivalued set functions,Fuzzy Sets and Systems,160(2009), 2106-2116.

[15] A. Gavrilut and A. Croitoru, Pseudo-atoms and Darboux property for set multifunction,Fuzzy Sets and Systems,(2010), 2897-2908.

[16] J. Li,On Egoro theorem on fuzzy measure spaces, Fuzzy Sets and Systems, 135 (2003),367-375. 

[17] F. Merghadi and A. Aliouche,A related xed point theorem in n fuzzy metric spaces, Iranian Journal of Fuzzy Systems,7(3) (2010), 73-86.

[18] E. Pap,Null-additive set functions, Kluwer Academic Publishers, Dordrecht, 1995.

[19] A. M. Precupanu,On the set valued additive and subadditive set functions, An. St. UniIa29(1984), 41-48.

[20] G. Shafer,A Mathematical theory of evidence, Princeton University Press, Princeton, N. J.,1976. 

[21] M. Sugeno,Theory of fuzzy integrals and its applications, PhD. Thesis, Tokyo Institute ofTechnology, 1974. 

[22] H. Suzuki,Atoms of fuzzy measures and fuzzy integrals, Fuzzy Sets and Systems, 41 (1991),329-342. 

[23] S. M. Vaezpour and F. Karini,t-Best approximation in fuzzy normed spaces, Iranian Journal of Fuzzy Systems,5(2) (2008), 93-99.

[24] G. F. Wen, F. G. Shi and H.Y. Li,Almost S-compactness in L-topological spaces, Iranian Journal of Fuzzy Systems,5(3) (2008), 31-44.

[25] C. Wu and S. Bo,Pseudo-atoms of fuzzy and non-fuzzy measures , Fuzzy Sets and Systems,1582007), 1258-1272.

[26] L. A. Zadeh,Fuzzy sets, Information and Control, 8 (1965), 338{353.