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Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions

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

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.

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

Abstract

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.
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

İsmail Ibedou

Salah Abbas This is me

Publication Date January 1, 2019
Submission Date May 13, 2018
Published in Issue Year 2019 Issue: 26

Cite

APA Ibedou, İ., & Abbas, S. (2019). Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions. Journal of New Theory(26), 1-12.
AMA Ibedou İ, Abbas S. Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions. JNT. January 2019;(26):1-12.
Chicago Ibedou, İsmail, and Salah Abbas. “Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions”. Journal of New Theory, no. 26 (January 2019): 1-12.
EndNote Ibedou İ, Abbas S (January 1, 2019) Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions. Journal of New Theory 26 1–12.
IEEE İ. Ibedou and S. Abbas, “Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions”, JNT, no. 26, pp. 1–12, January 2019.
ISNAD Ibedou, İsmail - Abbas, Salah. “Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions”. Journal of New Theory 26 (January 2019), 1-12.
JAMA Ibedou İ, Abbas S. Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions. JNT. 2019;:1–12.
MLA Ibedou, İsmail and Salah Abbas. “Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions”. Journal of New Theory, no. 26, 2019, pp. 1-12.
Vancouver Ibedou İ, Abbas S. Generalized Forms of Upper and Lower Continuous Fuzzy Multifunctions. JNT. 2019(26):1-12.


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