Fuzzy ??-almost continuous and fuzzy ??-continuous functions in mixed fuzzy ideal topological spaces
Keywords:Fuzzy δ-preopen set, Fuzzy δ-regular open set, Fuzzy δ-pre neighbourhood, Fuzzy δ-regular neighbourhood
AbstractIn this paper we introduce two new classes of functions between mixed fuzzy topological spaces, namely fuzzy ??-almost continuous and fuzzy ??-continuous functions and investigate some of their properties. The description of these two types of functions facilitated by the introduction of generalized open sets, called fuzzy ?-preopen sets, fuzzy ?-precluster point, fuzzy preopen sets, fuzzy ?-pre-q-neighbourhoods.
A. Alexiewicz and Z. Semadeni, “A generalization of two norm spaces”, Bulletin of the Polish Academy of Sciences Mathematics, vol. 6, pp. 135-139, 1958.
C. I. Chang, “Fuzzy topological spaces”, Journal of mathematical analysis and applications, vol. 24, no. 1, pp. 182–190, Oct. 1968, doi: 10.1016/0022-247x(68)90057-7.
A. Chilana, “The space of bounded sequences with the mixed topology”, Pacific journal of mathematics, vol. 48, no. 1, pp. 29–33, Sep. 1973, doi: 10.2140/pjm.1973.48.29.
J. B. Cooper, “The strict topology and spaces with mixed topologies”, Proceedings of the American Mathematical Society, vol. 30, no. 3, pp. 583–583, Nov. 1971, doi: 10.1090/s0002-9939-1971-0284789-2.
J. B. Cooper, “The Mackey topology as a mixed topology”, Proceedings of the American Mathematical Society, vol. 53, no. 1, pp. 107–112, Jan. 1975, doi: 10.1090/s0002-9939-1975-0383059-5.
N. R. Das and P. B. Baishya, “Mixed fuzzy topological spaces”, Journal of fuzzy mathematics, vol. 3, no. 4, pp. 777-784, 1995.
M. Ganster, D. N. Georgiou, S. Jafari, and S. P. Moshokoa, “On some applications of fuzzy points”, Applied general topology, vol. 6, no. 2, pp. 119–133, Oct. 2005, doi: 10.4995/agt.2005.1951.
S. Ganguly and D. Singha, “Mixed topology for a bi-topological spaces”, Bulletin of the Calcutta Mathematical Society , vol. 76, pp. 304-314, 1984.
S. Ganguly and S. Saha, “A note on δ-continuity and δ-connected sets in fuzzy set theory”, Simon Stevin, vol. 62, pp. 127-141, 1988.
M. Alam and V. D. Esteruch, “A contribution to fuzzy subspaces”, Applied general topology, vol. 1, no. 3, pp. 13-23, 2002. [On line]. Available: https://bit.ly/3f0G8sl
K. Shravan and B. C. Tripathy, “Multiset mixed topological space”, Soft computing, vol. 23, no. 20, pp. 9801–9805, Feb. 2019, doi: 10.1007/s00500-019-03831-9.
B. C. Tripathy and G. C. Ray, “On mixed fuzzy topological spaces and countability”, Soft computing, vol. 16, no. 10, pp. 1691–1695, May 2012, doi: 10.1007/s00500-012-0853-1.
B. C. Tripathy and G. C. Ray, “Mixed fuzzy ideal topological spaces”, Applied mathematics and computation, vol. 220, pp. 602–607, Sep. 2013 doi: 10.1016/j.amc.2013.05.072.
B. C. Tripathy and G. C. Ray, “On δ-continuity in mixed fuzzy topological spaces”, Boletim da Sociedade Paranaense de matemática, vol. 32, no. 2, pp. 175–187, Sep. 2014, doi: 10.5269/bspm.v32i2.20254.
R. H. Warren, “Neighborhoods, bases and continuity in fuzzy topological spaces”, Rocky mountain journal of mathematics, vol. 8, no. 3, pp. 459–470, Sep. 1978, doi: 10.1216/rmj-1978-8-3-459.
A. Wiweger, “Linear spaces with mixed topology”, Studia mathematica, vol. 20, no. 1, pp. 47–68, 1961, doi: 10.4064/sm-20-1-47-68.
L. A. Zadeh, “Fuzzy sets”, Information and control, vol. 8, no. 3, pp. 338–353, Jun. 1965, doi: 10.1016/s0019-9958(65)90241-x.