Year 2019, Volume , Issue 27, Pages 74 - 89 2019-03-01

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

Mohammed Mohammed KHALAF [1]


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.

(2;L)-double fuzzifying topology, (2;L)-doublefuzzifying preproximity, L-fuzzifying dynamice topology, breast cancer
  • [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.
Primary Language en
Subjects Mathematics, Applied
Journal Section Research Article
Authors

Author: Mohammed Mohammed KHALAF

Dates

Publication Date : March 1, 2019

Bibtex @research article { jnt560383, journal = {Journal of New Theory}, issn = {2149-1402}, eissn = {2149-1402}, address = {Mathematics Department, Gaziosmanpasa University 60250 Tokat-TURKEY.}, publisher = {Gaziosmanpasa University}, year = {2019}, volume = {}, pages = {74 - 89}, doi = {}, title = {Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer}, key = {cite}, author = {KHALAF, Mohammed Mohammed} }
APA KHALAF, 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 . Retrieved from https://dergipark.org.tr/en/pub/jnt/issue/43609/560383
MLA KHALAF, M . "Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer". Journal of New Theory (2019 ): 74-89 <https://dergipark.org.tr/en/pub/jnt/issue/43609/560383>
Chicago KHALAF, M . "Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer". Journal of New Theory (2019 ): 74-89
RIS TY - JOUR T1 - Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer AU - Mohammed Mohammed KHALAF Y1 - 2019 PY - 2019 N1 - DO - T2 - Journal of New Theory JF - Journal JO - JOR SP - 74 EP - 89 VL - IS - 27 SN - 2149-1402-2149-1402 M3 - UR - Y2 - 2020 ER -
EndNote %0 Journal of New Theory Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer %A Mohammed Mohammed KHALAF %T Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer %D 2019 %J Journal of New Theory %P 2149-1402-2149-1402 %V %N 27 %R %U
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 .
AMA KHALAF M . Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer. JNT. 2019; (27): 74-89.
Vancouver KHALAF M . Double Fuzzifying Topogenous Space, Double Fuzzifying Quasi-Uniform Spaces and Applications of Dynamics Fuzzifying Topology in Breast Cancer. Journal of New Theory. 2019; (27): 89-74.