Upper and Lower ?-Continuity of Soft Multifunctions

Authors

  • Metin Akdağ
  • Fethullah Erol Cumhuriyet University

Keywords:

Soft sets, soft multifunction, soft continuity, soft topological spaces.

Abstract

In this paper, we introduced the upper and lower ?-continuous soft multifunctions. Also we obtain some characterizations and several properties concerning upper and lower ?-continuous soft multifunctions.

 

References

[1] O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970.
[2] A.S.Mashour, I.A. Hasanein, S.N. El-deeb, ?-continuous and ?-open mappings, Acta. Math. Hung., 41 (1983), 213-218.
[3] C. Berge, Topological Spaces, Macmillian, New York, 1963. English translation by E. M. Patterson of Espaces Topologiques, Fonctions Multivoques, Dunod, Paris, 1959.
[4] N. S. Papageorgiou, Fuzzy topol. and fuzzy multifunctions, J. Math. Anal. Appl., 109 (1985) 397-425.
[5] J. Albrycht, M. Maltoka, On fuzzy multivalued functions, Fuzzy Sets and Systems, 12 (1984) 61-69.
[6] I. Beg, Fixed points of fuzzy multivalued mappings with values in fuzzy ordered sets, J. Fuzzy Math., 6 (1) (1998) 127-131.
[7] S. Heilpern, Fuzzy mappings and fixed points theorem, J. Math. Anal. Appl., 83 (1981) 566-569.
[8] D. Batnairu, Fixed points for fuzzy mappings, Fuzzy Sets and Systems, 7 (1982) 191-207.
[9] D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37 (4/5) (1999), 19-31.
[10] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), 555-562.
[11] P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in desicion making problem, Comput. Math. Appl. 44 (2002), 1077-1083.
[12] H. Akta?, N. Ça?man, Soft sets and soft groups, Inform. Sci., 177(13)(2007), 2726-2735.
[13] C. L. Chang, Fuzzy topological spaces, Journal of Math. Anal. and Appl., 24 (1968), 182-190.
[14] E. F. Lashin, A. M. Kozae, A. A. Abo Khadra and T. Medhat, Rough set for topological spaces, Int. J. of Approximate Reasoning, 40 (2005), 35-43.
[15] M. Shabir and M. Naz, On Soft Topological Spaces, Comput. Math. Appl. 61 (2011), 1786-1799.
[16] ?. Zorlutuna, M. Akda?, W. K. Min and S. Atmaca, On Soft Topological Spaces, Annals of Fuzzy Mathematics and Informatics, Vol. 3, No: 2, 171-185 (2012).
[17] A. Aygüno?lu and H. Aygün, Some notes on soft topological spaces, Neural Computing and Applications, DOI: 10.1007/s00521-011-0722-3, (2011).
[18] A. Kharal and B. Ahmad, Mappings On Soft Classes, New Math. and Natural Compt., Vol:7 No:3 (2011), 471-481.
[19] M.Akdag and A. Ozkan, Soft ?-open Sets and Soft ?-continuous Functions, Hindawi Publ. Corp. Abst. and Apll. Anal. (2014).
[20] M. Akda? and F. Erol, Upper and Lower Continuity of Soft Multifunctions, Appl. Math. Inf. Sci.,7, 1-8 (2014).
[21] W. J. Lipski, On databases with incomplete information, Journal of the ACM 28 (1981) 41-70.
[22] Z. Pawlak, Information systems - theoretical foundations, Information Systems 6(1981) 205-218.
[23] Z. Pawlak, Rough sets, Int. J. Computer and Information Sciences 11(1982) 341-356.
[24] Y Y. Yao, Constructive and algebraic methods of the theory of rough sets, Information Sciences 109(1998) 2147.
[25] Y Y Yao and N. Zhong, Granular computing using information tables, in: T. Y Lin, et al. (eds.), Data Mining, Rough Sets and Granular Computing, Physica-Verlag, pp. 102-124, 2002.
[26] D. Pei and D. Miao, From soft sets to information systems, in Proceedings of the IEEE International Conference on Granular Computing, 2 (2005), 617--621.
[27] M. Irfan Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553.

Downloads

Published

2014-06-21

How to Cite

Akdağ, M., & Erol, F. (2014). Upper and Lower ?-Continuity of Soft Multifunctions. American Scientific Research Journal for Engineering, Technology, and Sciences, 8(1), 96–107. Retrieved from https://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/756