Research Article
Year 2021,
Volume: 4 Issue: 2, 259 - 270, 31.07.2021
Abstract
In our study, we gave a new definition for bipolar soft topology and we were able to examine the concept of bipolar soft ordered topology using the base concept we defined on this new bipolar soft topology. We also define the concept of bipolar soft set relation by defining an R relation on a bipolar soft set. Thus, we have defined the concept of bipolar soft interval and presented the bipolar soft ordered topology structure using these intervals in our study. Then, we expressed some applications of bipolar soft order topology.
References
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- Molodtsov. D, Soft set theory first results, Comput. Math. Appl., Vol.37, No.19-31, (1999).
- Shabir. M, Naz. M, On Bipolar Soft Sets, arXiv: 1303.1344v1 [math.LO], (2013).
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- Çağman. N, Karataş. S, Enginoglu. S, Soft topology, Comput. Math. Appl., Vol.62, pp.351-258, (2011).
- Babitha. K. V, Sunil, J. J, Transitive Closures and Ordering on Soft Sets, Comput. Math. Appl., Vol.62, pp.2235-2239, (2011).
- Tanay. B, Yaylalı. G, New structures On Partially Ordered Soft Sets and Soft Scott Topology, Ann. Fuzzy Math. Inform., Vol.7, pp.89-97, (2014).
- Roy. S, Samanta. T. K, An Introduction of a Soft Topological Spaces Proceeding of UGC sponsored National seminar on Recent trends in Fuzzy set theory, Rough set theory and Soft set theory at Uluberia College on 23rd and 24th September, ISBN 978-81-922305-5-9, pp.9-12, (2011).
- Shabir. M, Naz. M, On bipolar soft sets, Retrieved from https://arxiv.org/abs/1303.1344, (2013).
- Shabir. M, Bakhtawar. A, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songklanakari J. Sci. Technol., Vol.39, No.3, pp.359-371, (2017).
- Guan. X, Li. Y, Feng. F, A new order relation on fuzzy soft sets and its applications, Soft Compt., Vol.17, pp.63-70, (2013).
- Onyeozili. I. A, Gwary. T. M, A study the Fundamentals of Soft Set Theory, International of Sciences and Technology Research, Vol.3, No.4, pp.132-143, (2014).
- Sut. D. K, An Application of Fuzzy Soft Relation in Decision Making Problems, International Journal of Mathematics Trends and Technology, Vol.3, No.2, (2012).
- Babitha. K. V, Sunil. J. J, Soft Set Relations and Functions, Comput. Math. Appl., Vol.60, pp.1840-1849, (2010).
- Park. J. H, Kim. O. H, Kwun. Y. C, Some properties of equivalence soft set relations, Comput. Math. Appl., Vol.63, pp.1079-1088, (2012).
- Yang. H, Guo. Z, Kernels and Closures of Soft Set Relations, and Soft Set Relation Mappings, Comput. Math. Appl., Vol.61, pp.651-662, (2011).
- Tanay. B, Yaylalı. G, New structures On Partially Ordered Soft Sets and Soft Scott Topology, Ann. Fuzzy Math. Inform., Vol.7, pp.89-97, (2014).
- Shabir. M, Naz. M, On soft topological spaces, Comput. Math. Appl., Vol.61, pp.1786-1799, (2011).
- Çağman. N, Karataş. S, Enginoğlu. S, Soft topology, Comput. Math. Appl., Vol.62, pp.351-358, (2011).
- Aygünoğlu. A, Aygün. H, Some notes on soft topological spaces, Neural Comput. Appl., Vol.21, No.1, pp.113-119, (2012).
- Zorlutuna. I, Akdağ. M, Min. W. K, Atmaca. S, Remarks On soft topological spaces, Ann. Fuzzy Math. Inf., Vol.3, No.2, pp.171-185, (2012).
- Hussain. S, Ahmad. B, Some properties of soft topological spaces, Comput. Math. Appl., Vol.62, pp.4058-4067, (2011).
- Pazar Varol. B, Aygun. H, On soft hausdorf spaces, Ann. Fuzzy Math. Inf., Vol.5, No.1, pp.15-24, (2013).
- Min. W. K, A note on soft topological spaces, Comput. Math. Appl., Vol.62, pp.3524-3528, (2011).
- Shabir. M, Naz. M, On Bipolar Soft Sets, arXiv: 1303.1344v1 [math.LO], (2013).
- Karaaslan. F, Karatas. S, A new approach to bipolar soft sets and its applications, Discrete Math. Algorithm. Appl., 07, 1550054, (2015).
- Shabir. M, Bakhtawar. A, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songklanakari J. Sci. Technol., Vol.39, No.3, pp.359-371, (2017).
- Öztürk. Y. T, On Bipolar Soft Topological Space, Journal of New Theory, Vol.20, pp.64-75, (2018).
Year 2021,
Volume: 4 Issue: 2, 259 - 270, 31.07.2021
Abstract
References
- Maji. P. K, Biswas. R, Roy. A. R, Soft set theory, Computers and Mathematics with Applications, Vol.45 No.4-5, pp.555-562, (2003).
- Molodtsov. D, Soft set theory first results, Comput. Math. Appl., Vol.37, No.19-31, (1999).
- Shabir. M, Naz. M, On Bipolar Soft Sets, arXiv: 1303.1344v1 [math.LO], (2013).
- Babitha. K. V, Sunil. J. J, Soft Set Relations and Functions, Comput. Math. Appl., Vol.60, pp.1840-1849, (2010).
- Çağman. N, Karataş. S, Enginoglu. S, Soft topology, Comput. Math. Appl., Vol.62, pp.351-258, (2011).
- Babitha. K. V, Sunil, J. J, Transitive Closures and Ordering on Soft Sets, Comput. Math. Appl., Vol.62, pp.2235-2239, (2011).
- Tanay. B, Yaylalı. G, New structures On Partially Ordered Soft Sets and Soft Scott Topology, Ann. Fuzzy Math. Inform., Vol.7, pp.89-97, (2014).
- Roy. S, Samanta. T. K, An Introduction of a Soft Topological Spaces Proceeding of UGC sponsored National seminar on Recent trends in Fuzzy set theory, Rough set theory and Soft set theory at Uluberia College on 23rd and 24th September, ISBN 978-81-922305-5-9, pp.9-12, (2011).
- Shabir. M, Naz. M, On bipolar soft sets, Retrieved from https://arxiv.org/abs/1303.1344, (2013).
- Shabir. M, Bakhtawar. A, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songklanakari J. Sci. Technol., Vol.39, No.3, pp.359-371, (2017).
- Guan. X, Li. Y, Feng. F, A new order relation on fuzzy soft sets and its applications, Soft Compt., Vol.17, pp.63-70, (2013).
- Onyeozili. I. A, Gwary. T. M, A study the Fundamentals of Soft Set Theory, International of Sciences and Technology Research, Vol.3, No.4, pp.132-143, (2014).
- Sut. D. K, An Application of Fuzzy Soft Relation in Decision Making Problems, International Journal of Mathematics Trends and Technology, Vol.3, No.2, (2012).
- Babitha. K. V, Sunil. J. J, Soft Set Relations and Functions, Comput. Math. Appl., Vol.60, pp.1840-1849, (2010).
- Park. J. H, Kim. O. H, Kwun. Y. C, Some properties of equivalence soft set relations, Comput. Math. Appl., Vol.63, pp.1079-1088, (2012).
- Yang. H, Guo. Z, Kernels and Closures of Soft Set Relations, and Soft Set Relation Mappings, Comput. Math. Appl., Vol.61, pp.651-662, (2011).
- Tanay. B, Yaylalı. G, New structures On Partially Ordered Soft Sets and Soft Scott Topology, Ann. Fuzzy Math. Inform., Vol.7, pp.89-97, (2014).
- Shabir. M, Naz. M, On soft topological spaces, Comput. Math. Appl., Vol.61, pp.1786-1799, (2011).
- Çağman. N, Karataş. S, Enginoğlu. S, Soft topology, Comput. Math. Appl., Vol.62, pp.351-358, (2011).
- Aygünoğlu. A, Aygün. H, Some notes on soft topological spaces, Neural Comput. Appl., Vol.21, No.1, pp.113-119, (2012).
- Zorlutuna. I, Akdağ. M, Min. W. K, Atmaca. S, Remarks On soft topological spaces, Ann. Fuzzy Math. Inf., Vol.3, No.2, pp.171-185, (2012).
- Hussain. S, Ahmad. B, Some properties of soft topological spaces, Comput. Math. Appl., Vol.62, pp.4058-4067, (2011).
- Pazar Varol. B, Aygun. H, On soft hausdorf spaces, Ann. Fuzzy Math. Inf., Vol.5, No.1, pp.15-24, (2013).
- Min. W. K, A note on soft topological spaces, Comput. Math. Appl., Vol.62, pp.3524-3528, (2011).
- Shabir. M, Naz. M, On Bipolar Soft Sets, arXiv: 1303.1344v1 [math.LO], (2013).
- Karaaslan. F, Karatas. S, A new approach to bipolar soft sets and its applications, Discrete Math. Algorithm. Appl., 07, 1550054, (2015).
- Shabir. M, Bakhtawar. A, Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces, Songklanakari J. Sci. Technol., Vol.39, No.3, pp.359-371, (2017).
- Öztürk. Y. T, On Bipolar Soft Topological Space, Journal of New Theory, Vol.20, pp.64-75, (2018).
There are 28 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | July 31, 2021 |
| Submission Date | February 25, 2021 |
| Acceptance Date | July 29, 2021 |
| Published in Issue | Year 2021 Volume: 4 Issue: 2 |
