Browse > Article
http://dx.doi.org/10.5831/HMJ.2018.40.1.27

PREPROXIMITY, UNIFORMITY SPACES AND APPLICATIONS OF (E, L) FUZZIFYING MATROID  

Khalaf, Mohammed M. (High Institute of Engineering and Technology, Mathematics Department, Zulfi, Majmaah University)
Publication Information
Honam Mathematical Journal / v.40, no.1, 2018 , pp. 27-46 More about this Journal
Abstract
In this paper, (E, L)-preproximity and uniformity spaces in matriod theory as a generalized to a classical proximity and Uniformity spaces introduced by Csaszar [1] is introduced. Recently, Shi [17]-[18] introduced a new approach to the fuzzification of matroids.Here introduce (E, L)-preproximity and uniformity spaces, Uniformity and strong uniformity on (E, L)-fuzzifying matroid space, Not only study the properties of this new notions, but it has been generated (E, L)-fuzzifying matroid Space from (E, L)-preproximity and uniformity spaces. Next to introduced (E, L)-preproximity continuous in (E, L)-fuzzifying matroid space and used it in more properties. Finally we solve combinatorial optimizations problem via (E, L)-fuzzifying matroid space.
Keywords
(E, L)- fuzzifying matroid Space; (E, L)-preproximity matroid space; (E, L)-uniformity matroid space; optimizations;
Citations & Related Records
연도 인용수 순위
  • Reference
1 F.-G. Shi, (L, M)-fuzzy matroids, Fuzzy Sets and Systems 160 (2009), 2387-2400.   DOI
2 Ying M. S., Fuzzifying topology based on complete residuated Lattice-valued logic(I), Fuzzy Sets and Systems 44 (1993), 227-272.
3 Young sun Kim and Kyung Chan Min, Initial Soft L- Fuzzy preproximities, Information Sciences, Information Sciences 173(1:3) (2005), 93-113.   DOI
4 Artico G., Moresco R., Fuzzy proximities and totally bounded fuzzy uniformities, Journal of Mathematical Analysis and Applications 99:2 (1984), 320-337.   DOI
5 Artico G., Moresco R., Fuzzy proximities compatible with Lowen fuzzy uniformities, Fuzzy Sets and Systems 21:1 (1987), 85-98.   DOI
6 Csaszar A., General topology, A Kademiai Kiado, Budapest (1978).
7 Katsaras A. K., Fuzzy proximity spaces, Journal of Mathematical Analysis and Applications 86:1 (1979), 100-110.
8 Efremovic V. A., Infinitesimal spaces, Doklady Akademii Nauk SSSR (Rus) 76 (1951), 341-343.
9 Efremovic V. A., The geometry of proximity, I. Matematicheskii Sbornik (Rus) 31:73 (1952), 189-200.
10 Hohle U., S.E.Rodabaugh Characterization of L-topologies by L-valued neighborhoods, The Handbooks of Fuzzy Sets Series, Kluwer ACademic Publishers, Dordrecht 2:73 (1999), 289-222.
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 C.V. Negoita and D.A. Ralescu, Zeyada F. M. and Sayed O.R., Interdisciplinary Systems Research Series, Birkhaeuser, Basel, Applications of Fuzzy Sets to Systems Analysis, 11 (1975).
13 Naimpally S. A., Warrack B. D., Proximity Spaces, New York,NY, USA: Cambridge University Press (1970).
14 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.
15 A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and Their Applications (1975), 77-95.
16 Pavelka J., On fuzzy logic II, Z. Math. Logic Gvundlagen Math. 24 (1979), 119-122.
17 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.
18 F.-G. Shi, new approach to the fuzzification of matroids, Fuzzy Sets and Systems 160 (2009), 696-705.   DOI