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Soft Connectedness Via Soft Ideals

Year 2014, Volume: 3 Issue: 4, 90 - 108, 01.04.2014

Abstract

The notion of soft topological spaces with soft idealwas studied by Kandil et al. [15]. Applications to various fieldswere further investigated by Kandil et al. [13, 14]. The notionof connectedness in soft topological spaces was initiated by Linin [19]. The purpose of this paper is to introduce and study thenotion of connectedness to soft topological spaces with soft ideals.We study the notions of -soft connected sets, -soft separatedsets ands-soft connected sets in soft topological spaces with softideals

References

  • B. Ahmad and A. Kharal, On fuzzy soft sets, Advances in Fuzzy Systems (2009) 1-6.
  • B. Ahmad and A. Kharal, Mappings of soft classes, to appear in New Math. Nat. Comput.
  • H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences 1 (77) (2007) 2726-2735.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications 57 (2009) 1547- 1553.
  • A. Aygunoglu and H. Aygun, Introduction to fuzzy soft groups, Computers and Mathematics with Applications 58 (2009) 1279-1286.
  • Banu Pazar Varol and Halis Aygun, On soft Hausdorff spaces, Annals of Fuzzy Mathematics and Informatics 5 (2013) 15-24.
  • Bin Chen, Some Local Properties of Soft Semi-Open Sets, Hindawi Publishing Corporation, 2013 (1-6).
  • N. C¸ agman, F.Citak and S. Enginoglu, Fuzzy parameterized fuzzy soft set theory and its applications, Turkish Journal of Fuzzy Systems 1(1)(2010) 21-35.
  • N.Cagman and S. Enginoglu, Soft set theory and uni-int decision making, European Journal of Operational Research 207 (2010) 848-855.
  • S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl., 62 (2011) 4058-4067.
  • D. Jankovic and T.R. Hamlet, New topologies from old via ideals, The American Mathematical Monthly 97 (1990) 295-310.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, γ-operation and decompositions of some forms of soft continuity in soft topological spaces, Annals of Fuzzy Mathematics and Informatics 7 (2014) 181-196.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, γ-operation and decompositions of some forms of soft continuity of soft topological spaces via soft ideal. To appear in the J¨okull Journal.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Semi-soft compactness via soft ideals. , Appl. Math. Inf. Sci. 8 (5) (2014) 1-10.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft ideal theory, Soft local function and generated soft topological spaces, Appl. Math. Inf. Sci. 8 (4) (2014) 1-9.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Supra soft topological spaces. To appear in the J¨okull Journal.
  • K. Kannan, Soft generalized closed sets in soft topological spaces, Journal of The- oretical and Applied Technology 37 (2012) 17-21.
  • D. V. Kovkov, V. M. Kolbanov and D. A. Molodtsov, Soft sets theory-based opti- mization, Journal of Computer and Systems Sciences International 46 (6) (2007) 872-880.
  • F. Lin, Soft connected spaces and soft paracompact spaces, International Journal of Mathematical Science and Engineering, 7 (2) (2013) 1-7.
  • J. Mahanta and P.K. Das, On soft topological space via semi open and semi closed soft sets, arXiv:1203.4133v,2012.
  • P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics 9 (3) (2001) 589-602.
  • P. K. Maji, R. Biswas and A. R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics 9 (3) (2001) 677-691.
  • P. K. Maji,R. Biswas and A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (2003) 555-562.
  • P. Majumdar and S. K. Samanta, Generalised fuzzy soft sets, Computers and Mathematics with Applications 59 (2010) 1425-1432.
  • D. A. Molodtsov, Soft set theory-firs tresults, Computers and Mathematics with Applications 37 (1999) 19-31.
  • D.Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique and its appli- cation, Nechetkie Sistemy i Myagkie Vychisleniya 1(1)(2006) 8-39.
  • A. Mukherjee and S. B. Chakraborty, On intuitionistic fuzzy soft relations, Bulletin of Kerala Mathematics Association 5(1)(2008) 35-42.
  • Sk. Nazmul and S. K. Samanta, Neighbourhood properties of soft topological spaces, Annals of Fuzzy Mathematics and Informatics 6(2012) 1-15.
  • D. Pei and D. Miao, From soft sets to information systems, in: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager, B. Zhang (Eds.), Proceedings of Granular Computing, in: IEEE, vol.2, 2005, pp. 617-621.
  • M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011) 1786-1799.
  • Sujoy Das and S. K. Samanta, Soft metric, Annals of Fuzzy Mathematics and Informatics 6 (2013) 77-94.
  • Weijian Rong, The countabilities of soft topological spaces, International Journal of Computational and Mathematical Sciences 6 (2012) 159-162.
  • Z. Xiao, L. Chen, B. Zhong, S. Ye, Recognition for information based on the theory of soft sets, in: J. Chen(Ed.), Proceeding of ICSSSM-05, vol. 2, IEEE, pp. 1104-1106, 2005.
  • W. Xu, J. Ma, S. Wang and G. Hao, Vague soft sets and their properties, Com- puters and Mathematics with Applications 59 (2010) 787-794.
  • Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete infor- mation, Knowledge-Based Systems 21 (2008) 941-945.
  • I. Zorlutuna, M. Akdag, W.K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics 3 (2012) 171-185.
Year 2014, Volume: 3 Issue: 4, 90 - 108, 01.04.2014

Abstract

References

  • B. Ahmad and A. Kharal, On fuzzy soft sets, Advances in Fuzzy Systems (2009) 1-6.
  • B. Ahmad and A. Kharal, Mappings of soft classes, to appear in New Math. Nat. Comput.
  • H. Aktas and N. Cagman, Soft sets and soft groups, Information Sciences 1 (77) (2007) 2726-2735.
  • M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications 57 (2009) 1547- 1553.
  • A. Aygunoglu and H. Aygun, Introduction to fuzzy soft groups, Computers and Mathematics with Applications 58 (2009) 1279-1286.
  • Banu Pazar Varol and Halis Aygun, On soft Hausdorff spaces, Annals of Fuzzy Mathematics and Informatics 5 (2013) 15-24.
  • Bin Chen, Some Local Properties of Soft Semi-Open Sets, Hindawi Publishing Corporation, 2013 (1-6).
  • N. C¸ agman, F.Citak and S. Enginoglu, Fuzzy parameterized fuzzy soft set theory and its applications, Turkish Journal of Fuzzy Systems 1(1)(2010) 21-35.
  • N.Cagman and S. Enginoglu, Soft set theory and uni-int decision making, European Journal of Operational Research 207 (2010) 848-855.
  • S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl., 62 (2011) 4058-4067.
  • D. Jankovic and T.R. Hamlet, New topologies from old via ideals, The American Mathematical Monthly 97 (1990) 295-310.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, γ-operation and decompositions of some forms of soft continuity in soft topological spaces, Annals of Fuzzy Mathematics and Informatics 7 (2014) 181-196.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, γ-operation and decompositions of some forms of soft continuity of soft topological spaces via soft ideal. To appear in the J¨okull Journal.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Semi-soft compactness via soft ideals. , Appl. Math. Inf. Sci. 8 (5) (2014) 1-10.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Soft ideal theory, Soft local function and generated soft topological spaces, Appl. Math. Inf. Sci. 8 (4) (2014) 1-9.
  • A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh and A. M. Abd El-latif, Supra soft topological spaces. To appear in the J¨okull Journal.
  • K. Kannan, Soft generalized closed sets in soft topological spaces, Journal of The- oretical and Applied Technology 37 (2012) 17-21.
  • D. V. Kovkov, V. M. Kolbanov and D. A. Molodtsov, Soft sets theory-based opti- mization, Journal of Computer and Systems Sciences International 46 (6) (2007) 872-880.
  • F. Lin, Soft connected spaces and soft paracompact spaces, International Journal of Mathematical Science and Engineering, 7 (2) (2013) 1-7.
  • J. Mahanta and P.K. Das, On soft topological space via semi open and semi closed soft sets, arXiv:1203.4133v,2012.
  • P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics 9 (3) (2001) 589-602.
  • P. K. Maji, R. Biswas and A. R. Roy, Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics 9 (3) (2001) 677-691.
  • P. K. Maji,R. Biswas and A. R. Roy, Soft set theory, Computers and Mathematics with Applications 45 (2003) 555-562.
  • P. Majumdar and S. K. Samanta, Generalised fuzzy soft sets, Computers and Mathematics with Applications 59 (2010) 1425-1432.
  • D. A. Molodtsov, Soft set theory-firs tresults, Computers and Mathematics with Applications 37 (1999) 19-31.
  • D.Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique and its appli- cation, Nechetkie Sistemy i Myagkie Vychisleniya 1(1)(2006) 8-39.
  • A. Mukherjee and S. B. Chakraborty, On intuitionistic fuzzy soft relations, Bulletin of Kerala Mathematics Association 5(1)(2008) 35-42.
  • Sk. Nazmul and S. K. Samanta, Neighbourhood properties of soft topological spaces, Annals of Fuzzy Mathematics and Informatics 6(2012) 1-15.
  • D. Pei and D. Miao, From soft sets to information systems, in: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager, B. Zhang (Eds.), Proceedings of Granular Computing, in: IEEE, vol.2, 2005, pp. 617-621.
  • M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011) 1786-1799.
  • Sujoy Das and S. K. Samanta, Soft metric, Annals of Fuzzy Mathematics and Informatics 6 (2013) 77-94.
  • Weijian Rong, The countabilities of soft topological spaces, International Journal of Computational and Mathematical Sciences 6 (2012) 159-162.
  • Z. Xiao, L. Chen, B. Zhong, S. Ye, Recognition for information based on the theory of soft sets, in: J. Chen(Ed.), Proceeding of ICSSSM-05, vol. 2, IEEE, pp. 1104-1106, 2005.
  • W. Xu, J. Ma, S. Wang and G. Hao, Vague soft sets and their properties, Com- puters and Mathematics with Applications 59 (2010) 787-794.
  • Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete infor- mation, Knowledge-Based Systems 21 (2008) 941-945.
  • I. Zorlutuna, M. Akdag, W.K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics 3 (2012) 171-185.
There are 36 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

A. Kandil This is me

Publication Date April 1, 2014
Published in Issue Year 2014 Volume: 3 Issue: 4

Cite

APA Kandil, A. (2014). Soft Connectedness Via Soft Ideals. Journal of New Results in Science, 3(4), 90-108.
AMA Kandil A. Soft Connectedness Via Soft Ideals. JNRS. April 2014;3(4):90-108.
Chicago Kandil, A. “Soft Connectedness Via Soft Ideals”. Journal of New Results in Science 3, no. 4 (April 2014): 90-108.
EndNote Kandil A (April 1, 2014) Soft Connectedness Via Soft Ideals. Journal of New Results in Science 3 4 90–108.
IEEE A. Kandil, “Soft Connectedness Via Soft Ideals”, JNRS, vol. 3, no. 4, pp. 90–108, 2014.
ISNAD Kandil, A. “Soft Connectedness Via Soft Ideals”. Journal of New Results in Science 3/4 (April 2014), 90-108.
JAMA Kandil A. Soft Connectedness Via Soft Ideals. JNRS. 2014;3:90–108.
MLA Kandil, A. “Soft Connectedness Via Soft Ideals”. Journal of New Results in Science, vol. 3, no. 4, 2014, pp. 90-108.
Vancouver Kandil A. Soft Connectedness Via Soft Ideals. JNRS. 2014;3(4):90-108.


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