Measure of fuzzy \((i; j)-s\)-compactness

Downloads

DOI:

https://doi.org/10.26637/MJM0803/0055

Abstract

In this paper, the notion of fuzzy \((i, j)-s\)-compactness degrees is introduced in \(L\)-fuzzy topological spaces by means of the implication operation of \(L\). Characterizations of fuzzy \((i, j)-s\)-compactness degrees in \(L\)-fuzzy topological spaces are obtained, and some properties of fuzzy \((i, j)-s\)-compactness degrees are researched.

Keywords:

\(L\)-bitopological spaces , fuzzy \((i; j)-s\)-compactness, Fuzzy \((i; j)-s\)-compactness degree

Mathematics Subject Classification:

Mathematics
  • P. Gomathi Sundari Department of Mathematics, Rajah Serfoji Government College (Affiliated to Bharathidasan University), Thanjavur-613005, Tamil Nadu, India.
  • R. Menaga Department of Mathematics, Sengamala Thayaar Educational Trust Women’s College (Affiliated to Bharathidasan University), Mannargudi-614016, Tamil Nadu, India.
  • Pages: 1050-1054
  • Date Published: 01-07-2020
  • Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

H. Aygun and S. E. Abbas, On characterization of some covering properties in L-fuzzy topological spaces in Sostak sense, Information Sciences, 165 (2004), 221233.

H. Aygun and S. E. Abbas, Some good extensions of compactness in Sostak's L-fuzzy topology, Hacett. J. Math. Stat., 36(2)(2007), 115-125.

C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24(1968), 39-90.

P. Dwinger, Characterizations of the complete homomorphic images of a completely distributive complete lattice I, IndagationesMathematicae (Proceedings), 85(1982), 403-414.

R. Erturk and M. Demirci, On the compactness in fuzzy topological spaces in Sostak's sense, Mat. Vesnik, 50(1998), 75-81.

A. Es and D. Coker, On several types of degree of fuzzy compactness, Fuzzy Sets and Systems, 87 (1997), 349359.

J. M. Fang, Categories isomorphic to L-FTOP, Fuzzy Sets and Systems, 157(2006), 820-831.

J. M. Fang and Y. L. Yue, Base and subbase in I-fuzzy topological spaces, J. Math. Res. Expositon, 26(2006), 89-95.

T. E. Gantner, R. C. Steinlage and R. H. Warren, Compactness in fuzzy topological spaces, J. Math. Anal. Appl., $62(1978), 547-562$.

G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, A Compendium of Continuous Lattices, Springer Verlag, Berlin, 1980.

P. Gomathisundari and R. Menaga, On Fuzzy $(i, j)$-semiopen sets in $L$-fuzzy bitopological spaces (submitted).

P. Gomathisundari and R. Menaga, Generalization of $L$-fuzzy bitopological compact spaces (submitted).

U. Hohle, Upper semicontinuous fuzzy sets and applications, J. Math. Anal. Appl., 78 (1980), 659-673.

U. Hohle and S. E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Boston/Dordrecht/ London, 3, 1999.

T. Kubiak, On Fuzzy Topologies, Ph.D. Thesis, Adam Mickiewicz, Poznan, Poland, 1985.

H. Y. Li and F. G. Shi, Measures of fuzzy compactness in L-fuzzy topological spaces, Comput. Math. Appl., 59 (2010), 941-947.

Y. M. Liu, Compactness and Tychono theorem in fuzzy topological spaces, Acta Math. Sinica, 24 (1981), 260268

Y. M. Liu and M. K. Luo, Fuzzy Topology, World Scientific Publishing, Singapore, 1997.

R. Lowen, Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl., 56(1976), 621-633.

R. Lowen, A comparision of diffierent compactness notions in fuzzy topological spaces, J.Math. Anal. Appl., 64 (1978), 446-454.

A. A. Ramadan and S. E. Abbas, On L-smooth compactness, J. Fuzzy Math., 9(1)(2001), 59-73.

F. G. Shi, Measures of compactness in L-topological spaces, Annals of Fuzzy Mathematics and Informatics, 2(2011), 183-192.

A. P. Sostak, On a fuzzy topological structure, Rend. Ciec. Mat. Palermo, 11(2) (1985), 89-103.

A. P. Sostak, Two decades of fuzzy topology: Basic ideas, notions and results, Russian Math. Surveys, 44 (1989), $125-186$.

G. J. Wang, Theory of L-Fuzzy Topological Spaces, Shaanxi Normal University Press, Xi'an, in Chinese, 1988.

M. S. Ying, A new approach to fuzzy topology I, Fuzzy Sets and Systems, 39(3)(1991), 303-321.

Y. L. Yue and J. M. Fang, Generated I-fuzzy topological spaces, Fuzzy Sets and Systems, 154(2005), 103-117.

  • NA

Metrics

Metrics Loading ...

Published

01-07-2020

How to Cite

P. Gomathi Sundari, and R. Menaga. “Measure of Fuzzy \((i; J)-s\)-Compactness”. Malaya Journal of Matematik, vol. 8, no. 03, July 2020, pp. 1050-4, doi:10.26637/MJM0803/0055.