Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions

Year 2019, Issue: 26, 1 - 12, 01.01.2019

İsmail Ibedou , Salah Abbas

Abstract

In this paper, we introduce the concepts of upper and lower (\alpha, \beta, \theta, \delta, \ell)-continuous fuzzy multifunctions. It is in order to unify several characterizations and properties of some kinds of modifications of fuzzy upper and fuzzy lower semi-continuous fuzzy multifunctions, and to deduce a generalized form of these concepts, namely upper and lower \eta \eta^{*}-continuous fuzzy multifunctions.

Keywords

General topology , fuzzy topology , multifunction , fuzzy multifunction

References

• [1] N. S. Papageoriou, Fuzzy topology and fuzzy multifunctions, J. of Math. Anal. Appl. Vol. 109 (1985), 397 - 425.
• [2] M. N. Mukherjee and S. Malakar, On almost continuous and weakly continuous fuzzy multifunctions, Fuzzy Sets and Systems Vol. 41 (1991), 113 - 125.
• [3] E. Tsiporkova, B. D. Baets and E. Kerre, A fuzzy inclusion based approach to upper inverse images under fuzzy multivalued mappings, Fuzzy Sets and Systems Vol. 85 (1997), 93 - 108.
• [4] E. Tsiporkova, B. D. Baets and E. Kerre, Continuity of fuzzy multivalued mappings, Fuzzy Sets and Systems Vol. 94 (1998), 335 - 348.
• [5] R. A. Mahmoud, An application of continuous fuzzy multifunctions, Chaos, Solitons and Fractals, Vol. 17(2003), 833 - 841.
• [6] M. A. Mohammady, E. Ekici, Jafari and M. Roohi, On fuzzy upper and lower contra continuous multifunctions, Iranian J. of Fuzzy Systems Vol. 8(3) (2011), 149 - 158.
• [7] C. H. Chang, Fuzzy topological spaces, J. of Math. Anal. Appl. 24 (1968) 182 - 190.
• [8] A. P. · Sostak, On a fuzzy topological structure, Suppl Rend. Circ. Math. Palermo Ser.II 11 (1985) 89 - 103.
• [9] K. Kuratowski, Topology, Academic Press, New York (1966).
• [10] A. A. Ramadan, S. E. Abbas and Y. C. Kim, Fuzzy irresolute mappings in smooth fuzzy topological spaces, J. Fuzzy Mathematics Vol. 9(4) (2001), 865 - 877.
• [11] Y. C. Kim, A. A. Ramadan and S. E. Abbas, Weaker forms of continuity in · Sostak's fuzzy topology, Indian J. of Pure and Appl. Math. Vol. 34(2) (2003), 311 - 333.
• [12] O. Njastad, On some classes of nearly open sets, Paci¯c J. of Math. Vol. 15 (1965), 961 - 970.
• [13] A. A. Ramadan and A. Abd El-Latif, Fuzzy pairwise multifunctions, Asian J. of Math. and comp. Res. Vol. 2(4) (2015), 219 - 234.
• [14] J. Vielma, E. Rosas, (®; ¯; µ; ±; I)-continuous mappings and their decomposition, Divulgaciones Matematicas Vol. 12(1) (2004), 53 - 64.
• [15] A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar. Vol. 96 (2002), 351 - 357.
• [16] H. Maki, J. Umehara and T. Noiri, Every topological space is pre-T1 2, Mem. Fac. Sci. Kochi Univ. Ser. A Math. Vol. 17 (1996), 33 - 42.
• [17] Y. H. Yoo, N. K. Min and J. I. Kim, Fuzzy r-minimal structures and fuzzy r-minimal spaces, Far East J. Math. Sci. Vol. 33(2) (2009), 193 - 205.
• [18] C. Carpintero, E. Rosas and M. Salas, Minimal structures and separation properties, Int. J. of pure and Appl. Math., Vol. 34(3) (2007), 473 - 488.