Soft elementary bitopological spaces
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this article a notion of soft quasi-pseudo metric is introduced and its underlying soft bitopology is defined where the relevant soft topologies are elementary soft topologies. Considering the ordering of a pair of soft elements two different notions of pairwise soft separation axioms and weak pairwise soft separation axioms are developed. Some properties of this new soft elementary bitopology regarding pairwise soft separation axioms and weak pairwise soft separation axioms are studied. With some examples and counter examples the relations among them have been justified. Further it is seen that under a given condition the soft quasi-pseudo metric space also satisfies the pairwise soft separation properties.
Abstract
In this article a notion of soft quasi-pseudo metric is introduced and its underlying soft bitopology is defined where the relevant soft topologies are elementary soft topologies. Considering the ordering of a pair of soft elements two different notions of pairwise soft separation axioms and weak pairwise soft separation axioms are developed. Some properties of this new soft elementary bitopology regarding pairwise soft separation axioms and weak pairwise soft separation axioms are studied. With some examples and counter examples the relations among them have been justified. Further it is seen that under a given condition the soft quasi-pseudo metric space also satisfies the pairwise soft separation properties.
참고문헌 (36)
- W. A. Wilson, "On quasi-metric space", Amer. J. Math, 53(3), pp.675~684 (1931)
- J. C. Kelly, "Bitopological spaces", Proc. London Math Soc, 13(3), pp.71~89 (1963)
- C. W. Patty, "Bitopological spaces", Duke. Math. J, 34(3), pp.387~392 (1967)
- Saegrove, "On bitopological spaces", pp.1971
- I. L. Reilly, "On bitopological separation properties", Nanta Math, 29, pp.14~25 (1972)
- D. Molodtsov, "Soft set theory first results", Comput. Math. Appl, 37(4-5), pp.19~31 (1999)
- L. A. Zadeh, "Fuzzy sets", Information and Control, 8(3), pp.338~353 (1965)
- P. K. Maji, "An application of soft sets in a decision making problem", Comput. Math. Appl, 44(8-9), pp.1077~1083 (2002)
- P. K. Maji, "Soft set theory", Comput. Math. Appl, 45(4-5), pp.555~562 (2003)
- I. Deli, "Interval-valued neutrosophic soft sets and its decision making", Int J Mach Learn Cyber, 8(2), pp.665~676 (2017)
- T. Herawan, "A soft set approach for association rules mining", Knowl-Based Syst, 24(1), pp.186~195 (2011)
- Y. B. Jun, "Applications of soft sets in ideal theory of BCK", BCI-algebras, 2008, pp.178(11), 2466~2475
- D. Pei, "From soft sets to information systems", 2005 IEEE International conference on Granular Computing, 2, pp.617~621 (2005)
- Y. Zou, "Data analysis approaches of soft sets under incomplete information", Knowl-Basesd Syst, 21(8), pp.941~945 (2016)
- H. Akta¸s, "Soft sets and soft groups", Inform. Sci, 177, pp.2726~2735 (2007)
- F. Feng, "Soft semirings", Comput. Maths. Appl, 56(10), pp.2621~2628 (2008)
- P. Majumdar, "On soft mapping", Comput. Math. Appl, 60(9), pp.2666~2672 (2010)
- M. Shabir, "On soft topological spaces", Comput. Math. Appl, 61(7), pp.1786~1799 (2011)
- M. Chiney, "Soft topology redefined", The Journal of Fuzzy Mathematics, 27(2), pp.459~486 (2019)
- R. Gowri, "Higher separation axioms in soft bicech closure spaces", Advances in Applied Mathematical Analysis, 11(1), pp.55~61 (2016)
- H. Hazra, "Soft topology", Fuzzy Information and Engineering, 4(1), pp.105~115 (2012)
- Sk. Nazmul, "Neighbourhood properties of soft topological spaces", Ann. Fuzzy. Math. Inform, 6(1), pp.1~15 (2013)
- Sk. Nazmul, "Group soft topology", The Journal of Fuzzy Mathematics, 22(2), pp.435~450 (2014)
- S. Das, "On soft metric spaces", The Journal of Fuzzy Mathematics, 21(3), pp.707~734 (2013)
- S. Das, "On soft linear spaces and soft normed linear spaces", Ann. Fuzzy Math. Inform, 9(1), pp.91~109 (2015)
- G. S¸enel, "Soft closed sets on soft bitopological space", Journal of New Results in Science, 3(5), pp.57~66 (2014)
- B. M. Ittanagi, "Soft Bitopological Spaces", Comp. and Math. with App, 107, pp.1~4 (2014)
- G. S¸enel, "The theory of soft ditopological spaces", International Journal of Computer Applications, 150(4), pp.1~5 (2016)[DOI]
- G. S¸enel, "Soft topology generated by L-soft sets", Journal of New Theory, 4(24), pp.88~100 (2018)
- G. S¸enel, "Soft topological subspaces", Ann. Fuzzy Math. Informa, 10(4), pp.525~535 (2015)
- K. Taskopru, "A new approach for soft topology and soft function via soft element", Math. Meth. Appl. Sc. Special Issue:IECMSA 2019-International Eurasian Conference on Mathematical Sciences and Applications, 44(9), pp.7556~7570 (2020)
- S. Dutta, "On neighbourhood system and convergence of soft nets in redefined soft topological spaces", International Journal of Pure and Applied Mathematics, 120(5), pp.1529~1545 (2018)
- S. Roy, "On compactness and connectedness in redefined soft topological spaces", International Journal of Pure and Applied Mathematics, 120(5), pp.1505~1528 (2018)
- S. Roy, "Recent Advances in Intelligent Information Systems and Applied Mathematics. ICITAM 2019", pp.699~712 (2020), Springer
- Z. Ma, "Soft set theory based on its extension", Fuzzy Information and Engineering, 2(4), pp.423~432 (2010)
- S. Das, "soft real numbers and their properties", The Journal of Fuzzy Mathematics, 20(3), pp.551~576 (2012)