DOI QR코드

DOI QR Code

Decomposition of fuzzy ideal continuity via fuzzy idealization

  • Received : 2008.12.28
  • Accepted : 2009.05.16
  • Published : 2009.06.30

Abstract

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy $\alpha$-I-open and r-fuzzy $\beta$-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy $\alpha$-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal $\alpha$-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.

Keywords

References

  1. Chang C.L. "Fuzzy topological spaces." J. Math. Anal. Appl. vol. 24, pp. 182–190, 1968
  2. Chattopadhyay K.C, Hazra R.N, Samanta S.K. "Gradation of openness: fuzzy topology," Fuzzy Sets and Systems, vol. 49, pp. 237–42, 1992
  3. Chattopadhyay K.C, Samanta S.K. "Fuzzy topology: fuzzy closure operator, fuzzy compactness and fuzzy connectedness," Fuzzy Sets and Systems, vol. 54, pp. 207–12, 1993
  4. El-baki S.A, Zahran A.M, Abbas S.E, Saber Y.M. "On Fuzzy ideal topological spaces," to appear in Applied Mathematical Sciences, 2008
  5. El Gayyar M.K, Kerre E.E. Ramadan A.A. "Almost compactness and near compactness in smooth topological spaces," Fuzzy Sets and Systems, vol. 62,pp. 193–202, 1994
  6. EL Naschie M.S, Rossler Oed G. "Information and diffusion in quantum physics." Chaos, Solitons & Fractals, vol. 7, no.5, [special issue] 1996
  7. El Naschie M.S. "On the uncertainty of Cantorian geometry and the two-slit experiment." Chaos, Solitons & Fractals, vol. 9, pp. 517-29, 1998 https://doi.org/10.1016/S0960-0779(97)00150-1
  8. El Naschie M.S. "On the unification of heterotic strings, M theory and $\varepsilon^{(\infty)}$ theory." Chaos, Solitons & Fractals, vol. 11, pp. 2397-2408, 2000 https://doi.org/10.1016/S0960-0779(00)00108-9
  9. El Naschie M.S. "A review of E-infinity theory and the mass spectrum of high energy particle physics." Chaos, Solitons & Fractals, vol. 19, pp. 209-236, 2004 https://doi.org/10.1016/S0960-0779(03)00278-9
  10. El Naschie M.S. "Quantum gravity from descriptive set theory." Chaos, Solitons & Fractals, vol. 19, pp. 1339-1344, 2004 https://doi.org/10.1016/j.chaos.2003.08.009
  11. El Naschie M.S. "Quantum gravity, Clifford algebras, fuzzy set theory and the fundamental constants of nature." Chaos, Solitons & Fractals, vol. 20, pp. 437-450, 2004 https://doi.org/10.1016/j.chaos.2003.09.029
  12. El Naschie M.S. "The simplistic vacuum, exotic quasiparticles and gravitational instanton." Chaos, Solitons & Fractals, vol. 22, pp. 1-11, 2004 https://doi.org/10.1016/j.chaos.2004.01.015
  13. El Naschie M.S. "On a fuzzy Kahler-like manifold which is consistent with the two slit experiment." Int J Nonlinear Sci Numer Simulat, vol. 6, pp. 95-98, 2005
  14. El Naschie M.S. "Topics in the mathematical physics of E-infinity theory." Chaos, Solitons & Fractals, vol. 30, pp. 656-663, 2006. https://doi.org/10.1016/j.chaos.2006.04.043
  15. El Naschie M.S. "Elementary prerequisite for E-infinity (recommended background readings in nonlinear dynamics, geometry and topology)." Chaos, Solitons & Fractals, vol. 30, no.3, pp. 579-605, 2006 https://doi.org/10.1016/j.chaos.2006.03.030
  16. El Naschie M.S. "Advanced prerequisite for E-infinity theory." Chaos, Solitons & Fractals, vol. 30, pp. 636-641, 2006 https://doi.org/10.1016/j.chaos.2006.04.044
  17. Hatir H, Jafari S. "Fuzzy semi-I-open and Fuzzy semi-I-continuity via fuzzy idealization," Chaos, Solitons & Fractals, vol. 34, no.4, pp. 1220–1224, 2007
  18. Hutton B, Reilly I. "Separation axioms in fuzzy topological spaces," Fuzzy Sets and Systems, vol. 3, pp. 93-104, 1980 https://doi.org/10.1016/0165-0114(80)90007-X
  19. Kim Y.C. Ko J.M. "r-generalized fuzzy closed sets." J Fuzzy Math, vol. 12, no.1, pp. 7–21, 2004
  20. Kim Y.C. "r-fuzzy semi-open sets in fuzzy bitopolgical space," Far East J. Math. Sic Spiecial, FJMS vol. 11, pp. 221–236, 2000
  21. Lowen R. "Fuzzy topological spaces and fuzzy compactness," J. Math. Anal. Appl, vol. 56, pp. 621-633, 1976 https://doi.org/10.1016/0022-247X(76)90029-9
  22. Nasef A.A, Mahmoud R.A. "Some topological applications via fuzzy ideals." Chaos, Solitons & Fractals, vol. 13, pp. 825–831, 2002
  23. Ramadan A.A. "Smooth topological spaces," Fuzzy Sets and Systems, vol. 48, pp. 371-375, 1992 https://doi.org/10.1016/0165-0114(92)90352-5
  24. Ramadan A.A, Abbas S.E, Kim Y.C. "Fuzzy irresolute functions in smooth fuzzy topological space." J Fuzzy Math, vol.9, no.4, pp. 865–877, 2001
  25. Ramadan A.A, Abbas S.E, Kim Y.C. "On weaker forms of continuity is $\hat{S}$ostak's fuzzy topology," Indian J. Pure and Appl, vol. 34, no.2, pp. 311-333, 2003
  26. Ramadan A.A, Abde-Sattar M.A, El Gayyar M.K. Smooth L-ideal, Quaestiones Mathematicae 2000
  27. Sarkar D. "Fuzzy ideal theory, fuzzy local function and generated fuzzy topology, fuzzy topology." Fuzzy Sets and Systems, vol. 87, pp. 117–123, 2001
  28. Sostak A.P. "On a fuzzy topological structure." Suppl. Rend. Circ. Mat Palermo Ser II, vol. 11, pp. 89-103, 1985
  29. Sostak A.P. "On some modifications of fuzzy topologies." Mat Vesnik, vol. 41, pp. 51-64, 1989