ON FUZZY UPPER AND LOWER CONTRA-CONTINUOUS MULTIFUNCTIONS

[1] J. Albrycht and M. Maltoka, On fuzzy multivalued function, Fuzzy Sets and Systems, 12
(1984), 61-69.
[2] M. Alimohammady and M. Roohi, On fuzzy ' -continuous multifunction, J. Appl. Math.
Stoch. Anal., (2006), 1-7.
[3] J. P. Aubin and H. Frankowska, Set-valued analysis, Birkhauser, Boston, 1990.
[4] I. Beg, Continuity of fuzzy multifunction, J. Appl. Math. Stochastic Anal., 12(1) (1999),
17-22.
[5] I. Beg, Fuzzy closed graph fuzzy multifunctions, Fuzzy Sets and Systems, 115 (2000), 451-454.
[6] I. Beg, Fuzzy multivalued functions, Bull. Allahabad Math. Soc., 21 (2006), 41-104.
[7] I. Beg, Fixed points of fuzzy multivalued mappings with values in fuzzy ordered sets, J. Fuzzy
Math., 6(1) (1998), 127-131.

[8] K. R. Bhutani, J. Mordeson and A. Rosenfeld, On degrees of end nodes and cut nodes in
fuzzy graphs, Iranian Journal of Fuzzy Systems, 1(1) (2004), 57-64.
[9] J. M. Cadenas and J. L. Verdegay, A primer on fuzzy optimization models and methods,
Iranian Journal of Fuzzy Systems, 3(1) (2006), 1-21.
[10] M. Caldas, E. Ekici, S. Jafari and T. Noiri, On the class of contra -continuous functions,
Annales Univ. Sci. Budapest Sec. Math., 49 (2006), 75-86.
[11] C. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 191-201.
[12] J. Dontchev, Contra-continuous functions and strongly S-closed spaces, Internat. J. Math.
Math. Sci., 19(2) (1996), 303-310.
[13] E. Ekici, On some types of continuous fuzzy functions, Appl. Math. E-Not., 4 (2004), 21-25.
[14] E. Ekici and E. E. Kerre, On fuzzy contra-continuities, Advances in Fuzzy Mathematics, 1(1)
(2006), 35-44.
[15] E. Ekici, S. Jafari and T. Noiri, On upper and lower contra-continuous multifunctions,
Analele Stii. Univ. Cuza Iasi Mat., LIV, 1 (2008), 75-85.
[16] E. Ekici, New forms of contra-continuity, Carpathian J. Math., 24(1) (2008), 37-45.
[17] E. Ekici, On (LC,s)-continuous functions, Chaos, Solitons and Fractals, 38(2) (2008), 430-
438.
[18] H. Hassanpour, H. R. Maleki and M. A. Yaghoobi, Fuzzy linear regression model with crisp
coefficients: a goal programming approach, Iranian Journal of Fuzzy Systems, 7(2) (2010),
19-39.
[19] J. E. Joseph and M. H. Kwack, On S-closed spaces, Proc. Amer. Math. Soc., 80 (1980),
341-348.
[20] S. B. Mordukhovich and Y. Shao, Fuzzy calculus for coderivatives of multifunctions, Nonlinear
Anal., 29(6) (1997), 605-626.
[21] M. N. Mukherjee and S. Malakar, On almost continuous and weakly continuous fuzzy multifunctions,
Fuzzy Sets and Systems, 41 (1991), 113-125.
[22] T. Noiri and S. Jafari, Properties of (, s)-continuous functions, Topology and its Appl., 123
(2002), 167-179.
[23] D. Noll, Baire spaces and graphtheorems, Proc. amer. Math. Soc., 96 (1986), 141-151.
[24] A. A. Nouh and M. E. El-Shafei, Cluster sets of functions and multifunctions in fuzzy topological
spaces, J. Fuzzy Math., 15(4) (2007), 759-768.
[25] P. Pao-Ming and L. Ying-Ming, Fuzzy topology I. neighborhood structure of a fuzzy point and
Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.
[26] P. Pao-Ming and L. Ying-Ming, Fuzzy topology II. product and quotient spaces, J. Math.
Anal. Appl., 77 (1980), 20-37.
[27] N. S. Papageorgiou, Fuzzy topology and fuzzy multifunctions, J. Math. Anal. Appl., 109
(1985), 397-425.
[28] V. I. Ponomarev, Properties of topological spaces preserved under multivalued continuous
mappings on compacta, Amer. Math. Soc. Translations, 38(2) (1964), 119-140.
[29] K. S. Raja Sethupathy and S. Laksmivarahan, Connectedness in fuzzy topology, Kybernetika,
13(3) (1977), 190-193.
[30] M. R. Safi, H. R. Maleki and E. Zaeimazad, A note on the Zimmermann method for solving
fuzzy linear programming problems, Iranian Journal of Fuzzy Systems, 4(2) (2007), 31-45.
[31] A. Stouti, Fixed points of expanding fuzzy multifunctions, J. Fuzzy Math., 13(1) (2005),
95-99.
[32] A. Stouti, An -fuzzy version of Amann’s fixed point theorem for -fuzzy monotone multifunctions,
J. Fuzzy Math., 14(1) (2006), 175-183
[33] T. Thompson, S-closed spaces, Proc. Amer. Math. Soc., 60 (1976), 335-338.
[34] E. Tsiporkova, B. De Baets and E. Kerre, Continuity of fuzzy multivalued mappings, Fuzzy
Sets and Systems, 94 (1998), 335-348.
[35] R. Viertl and D. Hareter, Fuzzy information and stochastics, Iranian Journal of Fuzzy Systems,
1(1) (2004), 43-56.
[36] C. K. Wong, Fuzzy topology: product and quotient theorems, J. Math. Anal. Appl., 45 (1974),
512-521.

[37] M. A. Yaghoobi and M. A. Tamiz, A short note on the relationship between goal programming
and fuzzy programming for vectormaximum problems, Iranian Journal of Fuzzy Systems, 2(2)
(2005), 31-36.
[38] L. A. Zadeh, Fuzzy sets, Information and Control., 8 (1965), 338-353.
[39] M. M. Zahedi and M. R. Khorashadi-Zadeh, Category of (POM)L-fuzzy graphs and hypergraphs,
Iranian Journal of Fuzzy Systems, 2(1) (2005), 49-63.