Research Article
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Year 2019, Issue: 27, 74 - 89, 01.03.2019

Abstract

References

  • [1] Artico G., Moresco R., Fuzzy proximities and totally bounded fuzzy uniformities, Journal of Mathematical Analysis and Applications. 99(2) (1984) 320–337.
  • [2] Artico G., Moresco R., Fuzzy proximities compatible with Lowen fuzzy uniformities, Fuzzy Sets and Systems. 21(1) (1987) 85–98.
  • [3] Csaszar, A., Foundations of general topology, Pergamon Press.
  • [4] Csaszar A., General topology,A Kademiai Kiado, Budapest.
  • [5] El-Ghoul M., Attiya H., The dynamical fuzzy topological space and its folding,Int. Fuzzy Math Institute, USA 12 (2004) 685–93.
  • [6] Efremoviˇc V. A., The geometry of proximity., I. Matematicheskii Sbornik. 31(73) (1952) 189–200. (Rus).
  • [7] Hohle U., Many valued Topology and Its Applications, Kluwer Academic Publishers, Boston, 2001, 22-72.
  • [8] Hohle U., Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl. 78 (1980) 449-472.
  • [9] Hohle U., Characterization of L-topologies by L-valued neighborhoods, in: U. Hohle, S.E.Rodabaugh (Eds.), The Handbooks of Fuzzy Sets Series, Vol.2, Kluwer ACademic Publishers, Dordrecht, 1999, pp. 289-222.
  • [10] Katsaras A. K., Fuzzy proximity spaces. Journal of Mathematical Analysis and Applications, 68(1) (1979) 100–110.
  • [11] Khedr F. H., Abd EL-Hakim K. M., Zeyada F. M. and Sayed O.R. , Fuzzifying Proximity and strong fuzzifying uniformity, Soochow Journal of Mathematics, 29 (2003) 82-92.
  • [12] Markin S. A., Sostak A. P., Another approach to the concept of a fuzzy proximity, Rendiconti del Circolo Matematico di Palermo II. Supplemento. 29 (1992) 529–551.
  • [13] Naimpally S. A., Warrack B. D., Proximity Spaces., New York, NY, USA: Cambridge University Press; 1970.
  • [14] Pavelka J., On fuzzy logic II, Math. Logic Gvundlagen Math. 24 (1979) 119-122.
  • [15] Ramadan A. A., El-Adawy T. M., Abd Alla M. A., On fuzzifying preproximity spaces, Arabian Journal for Science and Engineering. 30(1) (2005) 51–67
  • [16] Ying M. S., A new approach for fuzzy topology (I), Fuzzy Sets and Systems 29 (1991) 202-221
  • [17] Ying M. S., A new approach for fuzzy topology (II),Fuzzy Sets and Systems 27 (1992) 221-222.
  • [18] Ying M. S., A new approach for fuzzy topology (III),Fuzzy Sets and Systems 44 (1992) 192-207
  • [19] Ying M. S., Fuzzifying uniform spaces,Fuzzy Sets and Systems, 42 (1992) 92-102.
  • [20] Ying M. S., Fuzzifying topology based on complete residuated Lattice-valued logic (I), Fuzzy Sets and Systems 44 (1993) 227-272.
  • [21] Yue Y., Lattice-valued induced fuzzy topological spaces,Fuzzy Sets and Systems 158(13) (2007) 1461-1471.

Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer

Year 2019, Issue: 27, 74 - 89, 01.03.2019

Abstract

The main motivation behind this work is to introduce the notion of (2,L)-double fuzzifying topology which is a generalization of the notion of (2,L)-fuzzifying topology and classical topology. We define the notions of (2,L)-double fuzzifying preproximity and (2,L)-fuzzifying syntopogenous structures. Some fundamental properties are also established. These concepts will help in verifying the existing characterizations and also help in achieving new and generalized results. Finally we study a model as an application of fuzzifying topology in biology.

References

  • [1] Artico G., Moresco R., Fuzzy proximities and totally bounded fuzzy uniformities, Journal of Mathematical Analysis and Applications. 99(2) (1984) 320–337.
  • [2] Artico G., Moresco R., Fuzzy proximities compatible with Lowen fuzzy uniformities, Fuzzy Sets and Systems. 21(1) (1987) 85–98.
  • [3] Csaszar, A., Foundations of general topology, Pergamon Press.
  • [4] Csaszar A., General topology,A Kademiai Kiado, Budapest.
  • [5] El-Ghoul M., Attiya H., The dynamical fuzzy topological space and its folding,Int. Fuzzy Math Institute, USA 12 (2004) 685–93.
  • [6] Efremoviˇc V. A., The geometry of proximity., I. Matematicheskii Sbornik. 31(73) (1952) 189–200. (Rus).
  • [7] Hohle U., Many valued Topology and Its Applications, Kluwer Academic Publishers, Boston, 2001, 22-72.
  • [8] Hohle U., Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl. 78 (1980) 449-472.
  • [9] Hohle U., Characterization of L-topologies by L-valued neighborhoods, in: U. Hohle, S.E.Rodabaugh (Eds.), The Handbooks of Fuzzy Sets Series, Vol.2, Kluwer ACademic Publishers, Dordrecht, 1999, pp. 289-222.
  • [10] Katsaras A. K., Fuzzy proximity spaces. Journal of Mathematical Analysis and Applications, 68(1) (1979) 100–110.
  • [11] Khedr F. H., Abd EL-Hakim K. M., Zeyada F. M. and Sayed O.R. , Fuzzifying Proximity and strong fuzzifying uniformity, Soochow Journal of Mathematics, 29 (2003) 82-92.
  • [12] Markin S. A., Sostak A. P., Another approach to the concept of a fuzzy proximity, Rendiconti del Circolo Matematico di Palermo II. Supplemento. 29 (1992) 529–551.
  • [13] Naimpally S. A., Warrack B. D., Proximity Spaces., New York, NY, USA: Cambridge University Press; 1970.
  • [14] Pavelka J., On fuzzy logic II, Math. Logic Gvundlagen Math. 24 (1979) 119-122.
  • [15] Ramadan A. A., El-Adawy T. M., Abd Alla M. A., On fuzzifying preproximity spaces, Arabian Journal for Science and Engineering. 30(1) (2005) 51–67
  • [16] Ying M. S., A new approach for fuzzy topology (I), Fuzzy Sets and Systems 29 (1991) 202-221
  • [17] Ying M. S., A new approach for fuzzy topology (II),Fuzzy Sets and Systems 27 (1992) 221-222.
  • [18] Ying M. S., A new approach for fuzzy topology (III),Fuzzy Sets and Systems 44 (1992) 192-207
  • [19] Ying M. S., Fuzzifying uniform spaces,Fuzzy Sets and Systems, 42 (1992) 92-102.
  • [20] Ying M. S., Fuzzifying topology based on complete residuated Lattice-valued logic (I), Fuzzy Sets and Systems 44 (1993) 227-272.
  • [21] Yue Y., Lattice-valued induced fuzzy topological spaces,Fuzzy Sets and Systems 158(13) (2007) 1461-1471.
There are 21 citations in total.

Details

Primary Language English
Subjects Applied Mathematics
Journal Section Research Article
Authors

Mohammed Mohammed Khalaf This is me

Publication Date March 1, 2019
Submission Date May 29, 2018
Published in Issue Year 2019 Issue: 27

Cite

APA Khalaf, M. M. (2019). Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer. Journal of New Theory(27), 74-89.
AMA Khalaf MM. Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer. JNT. March 2019;(27):74-89.
Chicago Khalaf, Mohammed Mohammed. “Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer”. Journal of New Theory, no. 27 (March 2019): 74-89.
EndNote Khalaf MM (March 1, 2019) Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer. Journal of New Theory 27 74–89.
IEEE M. M. Khalaf, “Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer”, JNT, no. 27, pp. 74–89, March 2019.
ISNAD Khalaf, Mohammed Mohammed. “Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer”. Journal of New Theory 27 (March 2019), 74-89.
JAMA Khalaf MM. Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer. JNT. 2019;:74–89.
MLA Khalaf, Mohammed Mohammed. “Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer”. Journal of New Theory, no. 27, 2019, pp. 74-89.
Vancouver Khalaf MM. Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer. JNT. 2019(27):74-89.


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