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On convergence in \(L\)-valued fuzzy topological spaces. (English) Zbl 1347.54022

Summary: We introduce the concept of \(L\)-fuzzy neighborhood systems using complete MV-algebras and present important links with the theory of \(L\)-fuzzy topological spaces. We investigate the relationships among the degrees of \(L\)-fuzzy \(r\)-adherent points (\(r\)-convergent, \(r\)-cluster, and \(r\)-limit, resp.) in an \(L\)-fuzzy topological spaces. Also, we investigate the concept of \(LF\)-continuous functions and their properties.

MSC:

54A40 Fuzzy topology
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[1] Šostak, A. P., On a fuzzy topological structure, Rendiconti del Circolo Matematico di Palermo II, 11, 89-103 (1985) · Zbl 0638.54007
[2] Šostak, A. P., On the neighborhood structure of a fuzzy topological spaces, Zbornik Radova, 4, 7-14 (1990) · Zbl 0713.54008
[3] Šostak, A. P., Basic structures of fuzzy topology, Journal of Mathematical Sciences, 78, 6, 662-701 (1996) · Zbl 0857.54003 · doi:10.1007/bf02363065
[4] Chang, C. L., Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 24, 182-190 (1968) · Zbl 0167.51001 · doi:10.1016/0022-247X(68)90057-7
[5] Demirci, M., Neighborhood structures of smooth topological spaces, Fuzzy Sets and Systems, 92, 1, 123-128 (1997) · Zbl 0924.54007 · doi:10.1016/s0165-0114(96)00132-7
[6] Hazra, R. N.; Samanta, S. K.; Chattopadhyay, K. C., Fuzzy topology redefined, Fuzzy Sets and Systems, 45, 1, 79-82 (1992) · Zbl 0756.54002 · doi:10.1016/0165-0114(92)90093-j
[7] Chattopadhyay, K. C.; Hazra, R. N.; Samanta, S. K., Gradation of openness: fuzzy topology, Fuzzy Sets and Systems, 49, 2, 237-242 (1992) · Zbl 0762.54004 · doi:10.1016/0165-0114(92)90329-3
[8] Höhle, U., Many Valued Topology and Its Application (2001), Boston, Mass, USA: Kluwer Academic, Boston, Mass, USA · Zbl 0988.54001 · doi:10.1007/978-1-4615-1617-0
[9] Höhle, U.; Rodabaugh, S. E., Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory. Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, 3 (1999), Dordrecht, The Netherlands: Kluwer Academic Publishers, Dordrecht, The Netherlands · Zbl 0942.00008
[10] Höhle, U.; Šostak, A. P., Axiomatic foundations of fixed-basis fuzzy topology, Mathematics of Fuzzy Sets. Mathematics of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, 3, 123-272 (1999), Boston, Mass, USA: Kluwer Academic, Boston, Mass, USA · Zbl 0977.54006 · doi:10.1007/978-1-4615-5079-2_5
[11] Pao-Ming, P.; Ying-Ming, L., Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, Journal of Mathematical Analysis and Applications, 76, 2, 571-599 (1980) · Zbl 0447.54006 · doi:10.1016/0022-247x(80)90048-7
[12] Liu, Y.-M.; Luo, M.-K., Fuzzy Topology (1997), Singapore: World Scientific, Singapore · Zbl 0906.54006
[13] Ying, M. S., On the method of neighborhood systems in fuzzy topology, Fuzzy Sets and Systems, 68, 2, 227-238 (1994) · Zbl 0843.54004 · doi:10.1016/0165-0114(94)90048-5
[14] Chen, S. L.; Cheng, J. S., On convergence of nets of \(L\)-fuzzy sets, Journal of Fuzzy Mathematics, 2, 3, 517-524 (1994) · Zbl 0828.54007
[15] Chen, S. L.; Cheng, J. S., \( \theta \)-convergence of nets of L-fuzzy sets and its applications, Fuzzy Sets and Systems, 86, 235-240 (1997) · Zbl 0913.54011
[16] Fang, J., Relationships between \(L\)-ordered convergence structures and strong \(L\)-topologies, Fuzzy Sets and Systems, 161, 22, 2923-2944 (2010) · Zbl 1271.54030 · doi:10.1016/j.fss.2010.07.010
[17] Georgiou, D. N.; Papadopoulos, B. K., Convergences in fuzzy topological spaces, Fuzzy Sets and Systems, 101, 3, 495-504 (1999) · Zbl 0930.54009 · doi:10.1016/s0165-0114(97)00112-7
[18] Yao, W., On many-valued stratified \(L\)-fuzzy convergence spaces, Fuzzy Sets and Systems, 159, 19, 2503-2519 (2008) · Zbl 1206.54012 · doi:10.1016/j.fss.2008.03.003
[19] Ramadan, A. A., Smooth topological spaces, Fuzzy Sets and Systems, 48, 3, 371-375 (1992) · Zbl 0783.54007 · doi:10.1016/0165-0114(92)90352-5
[20] Gierz, G.; Hofmann, K. H., Continuous Lattices and 305 Domains (2003), Cambridge, UK: Cambridge University Press, Cambridge, UK · Zbl 1088.06001
[21] Hájek, P., Metamathematics of Fuzzy Logic. Metamathematics of Fuzzy Logic, Trends in Logic, 4 (1998), Dordrecht, The Netherlands: Kluwer Academic Publishers, Dordrecht, The Netherlands · Zbl 0937.03030 · doi:10.1007/978-94-011-5300-3
[22] Turunen, E., Algebraic structures in fuzzy logic, Fuzzy Sets and Systems, 52, 2, 181-188 (1992) · Zbl 0791.03010 · doi:10.1016/0165-0114(92)90048-9
[23] Turunen, E., Mathematics Behind Fuzzy Logic (1999), New York, NY, USA: Springer, New York, NY, USA · Zbl 0940.03029
[24] Jinming, F., Stratified \(L\)-ordered convergence structures, Fuzzy Sets and Systems, 161, 16, 2130-2149 (2010) · Zbl 1197.54015 · doi:10.1016/j.fss.2010.04.001
[25] Lai, H.; Zhang, D., Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems, 157, 14, 1865-1885 (2006) · Zbl 1118.54008 · doi:10.1016/j.fss.2006.02.013
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