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Expansions and Reductions on Neutrosophic Classical Soft Set

Year 2018, Volume: 22 Issue: Special, 478 - 486, 05.10.2018

Abstract

In the paper, we first proposed a new notation is called expansion and reduction of the neutrosophic classical soft sets that are based on the linguistic modifiers. By using this new notions, we then developed a neutrosophic classical soft reduction method and present a reel example for the method.

References

  • [1] M.I. Ali, F. Feng, X. Liu, W.K. Min, On some new operations in soft set theory, Comput. Math. Appl. 57(9) (2009) 1547–1553.
  • [2] C. Ashbacher, Introduction to Neutrosophic Logic, American Research Press Rehoboth 2002.
  • [3] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 31 (1989) 343– -349.
  • [4] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87—96.
  • [5] Basset, M.A., Mohamed, M. and Sangaiah, A.K. 2018. Neutrosophic AHP-Delphi Group decision making model based on trapezoidal neutrosophic numbers, J. Ambient. Intell. Human. Comput., DOI 10.1007/s12652-017-0548-7.
  • [6] S. Broumi, Generalized Neutrosophic Soft Set International Journal of Computer Science, Engineering and Information Technology, 3/2 (2013) 17-30.
  • [7] S. Broumi, F. Smarandache, Intuitionistic Neutrosophic Soft Set, Journal of Information and Computing Science 8/2, (2013) 130–140.
  • [8] S. Broumi, I. Deli and F. Smarandache, Relations on Interval Valued Neutrosophic Soft Sets, Journal of New Results in Science, 5 (2014) 1–20.
  • [9] N. Çağman and S. Enginoğlu, Soft set theory and uniint decision making, European Journal of Operational Research, 207, (2010) 848-855.
  • [10] N. Çağman, Contributions to the theory of soft sets, Journal of New Results in Science, 4 (2014) 33–41.
  • [11] N. Çağman, S. Karataş, Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligent and Fuzzy Systems 24/4 (2013) 829–836.
  • [12] N, Çağman, I. Deli, I. Means of FP-Soft Sets and its Applications, Hacettepe Journal of Mathematics and Statistics, 41/5 (2012) 615–625.
  • [13] N, Çağman, I. Deli, Product of FP-Soft Sets and its Applications, Hacettepe Journal of Mathematics and Statistics 41/3 (2012) 365–374.
  • [14] I. Deli, Interval-valued neutrosophic soft sets ant its decision making, arxiv:1402.3130
  • [15] I. Deli, S. Broumi, Neutrosophic Soft Matrices and NSM-decision Making, Journal of Intelligent and Fuzzy Systems, 28 (5) (2015) 2233–2241.
  • [16] Deli I., ¸Suba¸s Y., Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems, Journal of Intelligent and Fuzzy Systems, 32(1) (2017) 291-301, DOI:10.3233/JIFS-151677.
  • [17] Eraslan, S., Reduction theory in soft sets and its applications, PhD Thesis (in Turkish), Graduate School of Natural and Applied Sciences, Gaziosmanpasa University, Tokat, Turkey (2014).
  • [18] F. Feng, Y. Li and N. Çağman, Generalized uni—int decision making schemes based on choice value soft sets, European Journal of Operational Research 220 (2012) 162-–170.
  • [19] F. Feng, Y.M. Li, Soft subsets and soft product operations, Information Sciences, 232 (2013) 44-57.
  • [20] F. Feng, X. Liu , V. L. Fotea, Y. B. Jun, Soft sets and soft rough sets, Information Sciences 181 (2011) 1125–1137.
  • [21] F. Feng, C. Li, B. Davvaz, M. Irfan Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing 14 (2010) 899–911.
  • [22] W. L. Gau, D.J. Buehrer, Vague sets, IEEE Trans. Systems Man and Cy-bernet, 23 (2) (1993) 610-614.
  • [23] I.M. Hanafy, A.A. Salama and K.M. Mahfouz, Neutersophic Classical Events And Its Probability, International Journal of Mathematics and Computer Applications, 3/1 (2013) 171-178.
  • [24] Y. Jiang, Y. Tang, Q. Chen, H. Liu, J.Tang, Intervalvalued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications, 60 (2010) 906–918.
  • [25] F. Karaaslan, I. Deli, On Soft neutrosophic classical sets, International Conference on Mathematics and Mathematics Education (ICMME-2016), 2016, Elazığ, Turkey.
  • [26] Z. Kong, L. Gao and L.Wang, Comment on “A fuzzy soft set theoretic approach to decision making problems”, J. Comput. Appl. Math. 223 (2009) 540–542.
  • [27] D. Molodtsov, Soft set theory first results, Computers and Mathematics with Applications, 37 (1999) 19-31.
  • [28] P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077-1083.
  • [29] P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555–562.
  • [30] P.K. Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics, 5/ 1 (2013) 157-168.
  • [31] P. K. Maji, R.Biswas A.R. Roy, Intuitionistic Fuzzy Soft Sets. The Journal of Fuzzy Mathematics, 9(3) (2001) 677-692.
  • [32] P. K. Maji, A neutrosophic soft set approach to a decision making problem, Annals of Fuzzy Mathematics and Informatics, 3/2, (2012) 313–319.
  • [33] P.K. Maji, R. Biswas and A.R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001) 589-602.
  • [34] Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci. 11 (1982) 341-356.
  • [35] A.R. Roy and P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203 (2007) 412-418.
  • [36] F. Smarandache, "A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic". Rehoboth: American Research Press,(1998).
  • [37] A. Sezgin, A. O. Atagun, On operations of soft sets, Computers and Mathematics with Applications 61 (2011) 1457-1467.
  • [38] R. Şahin, A. Küçük, Generalized neutrosophic soft set and its integration to decision making problem, Applied Mathematics and Information Sciences, 8(6) 1-9 (2014).
  • [39] H. Wang, F. Smarandache, Y.Q. Zhang, R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis; Neutrosophic book series, No: 5, 2005.
  • [40] X. Yang, T.Y. Lin, J. Yang, Y. Li and D. Yu, Combination of interval-valued fuzzy set and soft set, Comput. Math. Appl. 58 (2009) 521-527.
  • [41] J. Ye, Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 27(5) 2014, 2231–2241.
  • [42] J. Ye, Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment, Journal of Intelligent and Fuzzy Systems, 27(6) (2014) 2927–2935.
  • [43] H. Wang, F. Y. Smarandache, Q. Zhang, R. Sunderraman, Single valued neutrosophic sets, Multispace and Multistructure 4 (2010) 410–413.
  • [44] L. A. Zadeh, A fuzzy set-theoretic interpretation of linguistic hedges, J. Cybernet., 2 (1972) 4–34.
  • [45] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning–I, Information Sciences, 8 (1975) 199-249.
  • [46] L. A. Zadeh, Fuzzy Sets, Inform. and Control 8 (1965) 338-353.
  • [47] Z. Zhang, C. Wang, D. Tian, K. Li, A novel approach to interval-valued intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling 38, (2014) 1255–1270.
  • [48] H. Y. Zhang, J. Q. Wang, and X. H. Chen, Interval neutrosophic sets and their application in multicriteria decision making problems, The Scientific World Journal, 2014, http://dx.doi.org/10.1155/2014/645953.
  • [49] P. Zhu, Q. Wen, Operations on Soft Sets Revisited, Journal of Applied Mathematics, (2013) 1-7.
  • [50] Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowl. Base. Syst. 21 (2008) 941-945.
Year 2018, Volume: 22 Issue: Special, 478 - 486, 05.10.2018

Abstract

References

  • [1] M.I. Ali, F. Feng, X. Liu, W.K. Min, On some new operations in soft set theory, Comput. Math. Appl. 57(9) (2009) 1547–1553.
  • [2] C. Ashbacher, Introduction to Neutrosophic Logic, American Research Press Rehoboth 2002.
  • [3] K. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst. 31 (1989) 343– -349.
  • [4] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87—96.
  • [5] Basset, M.A., Mohamed, M. and Sangaiah, A.K. 2018. Neutrosophic AHP-Delphi Group decision making model based on trapezoidal neutrosophic numbers, J. Ambient. Intell. Human. Comput., DOI 10.1007/s12652-017-0548-7.
  • [6] S. Broumi, Generalized Neutrosophic Soft Set International Journal of Computer Science, Engineering and Information Technology, 3/2 (2013) 17-30.
  • [7] S. Broumi, F. Smarandache, Intuitionistic Neutrosophic Soft Set, Journal of Information and Computing Science 8/2, (2013) 130–140.
  • [8] S. Broumi, I. Deli and F. Smarandache, Relations on Interval Valued Neutrosophic Soft Sets, Journal of New Results in Science, 5 (2014) 1–20.
  • [9] N. Çağman and S. Enginoğlu, Soft set theory and uniint decision making, European Journal of Operational Research, 207, (2010) 848-855.
  • [10] N. Çağman, Contributions to the theory of soft sets, Journal of New Results in Science, 4 (2014) 33–41.
  • [11] N. Çağman, S. Karataş, Intuitionistic fuzzy soft set theory and its decision making, Journal of Intelligent and Fuzzy Systems 24/4 (2013) 829–836.
  • [12] N, Çağman, I. Deli, I. Means of FP-Soft Sets and its Applications, Hacettepe Journal of Mathematics and Statistics, 41/5 (2012) 615–625.
  • [13] N, Çağman, I. Deli, Product of FP-Soft Sets and its Applications, Hacettepe Journal of Mathematics and Statistics 41/3 (2012) 365–374.
  • [14] I. Deli, Interval-valued neutrosophic soft sets ant its decision making, arxiv:1402.3130
  • [15] I. Deli, S. Broumi, Neutrosophic Soft Matrices and NSM-decision Making, Journal of Intelligent and Fuzzy Systems, 28 (5) (2015) 2233–2241.
  • [16] Deli I., ¸Suba¸s Y., Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems, Journal of Intelligent and Fuzzy Systems, 32(1) (2017) 291-301, DOI:10.3233/JIFS-151677.
  • [17] Eraslan, S., Reduction theory in soft sets and its applications, PhD Thesis (in Turkish), Graduate School of Natural and Applied Sciences, Gaziosmanpasa University, Tokat, Turkey (2014).
  • [18] F. Feng, Y. Li and N. Çağman, Generalized uni—int decision making schemes based on choice value soft sets, European Journal of Operational Research 220 (2012) 162-–170.
  • [19] F. Feng, Y.M. Li, Soft subsets and soft product operations, Information Sciences, 232 (2013) 44-57.
  • [20] F. Feng, X. Liu , V. L. Fotea, Y. B. Jun, Soft sets and soft rough sets, Information Sciences 181 (2011) 1125–1137.
  • [21] F. Feng, C. Li, B. Davvaz, M. Irfan Ali, Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft Computing 14 (2010) 899–911.
  • [22] W. L. Gau, D.J. Buehrer, Vague sets, IEEE Trans. Systems Man and Cy-bernet, 23 (2) (1993) 610-614.
  • [23] I.M. Hanafy, A.A. Salama and K.M. Mahfouz, Neutersophic Classical Events And Its Probability, International Journal of Mathematics and Computer Applications, 3/1 (2013) 171-178.
  • [24] Y. Jiang, Y. Tang, Q. Chen, H. Liu, J.Tang, Intervalvalued intuitionistic fuzzy soft sets and their properties, Computers and Mathematics with Applications, 60 (2010) 906–918.
  • [25] F. Karaaslan, I. Deli, On Soft neutrosophic classical sets, International Conference on Mathematics and Mathematics Education (ICMME-2016), 2016, Elazığ, Turkey.
  • [26] Z. Kong, L. Gao and L.Wang, Comment on “A fuzzy soft set theoretic approach to decision making problems”, J. Comput. Appl. Math. 223 (2009) 540–542.
  • [27] D. Molodtsov, Soft set theory first results, Computers and Mathematics with Applications, 37 (1999) 19-31.
  • [28] P.K. Maji, A.R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077-1083.
  • [29] P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555–562.
  • [30] P.K. Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics, 5/ 1 (2013) 157-168.
  • [31] P. K. Maji, R.Biswas A.R. Roy, Intuitionistic Fuzzy Soft Sets. The Journal of Fuzzy Mathematics, 9(3) (2001) 677-692.
  • [32] P. K. Maji, A neutrosophic soft set approach to a decision making problem, Annals of Fuzzy Mathematics and Informatics, 3/2, (2012) 313–319.
  • [33] P.K. Maji, R. Biswas and A.R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9(3) (2001) 589-602.
  • [34] Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci. 11 (1982) 341-356.
  • [35] A.R. Roy and P.K. Maji, A fuzzy soft set theoretic approach to decision making problems, J. Comput. Appl. Math. 203 (2007) 412-418.
  • [36] F. Smarandache, "A Unifying Field in Logics. Neutrosophy: Neutrosophic Probability, Set and Logic". Rehoboth: American Research Press,(1998).
  • [37] A. Sezgin, A. O. Atagun, On operations of soft sets, Computers and Mathematics with Applications 61 (2011) 1457-1467.
  • [38] R. Şahin, A. Küçük, Generalized neutrosophic soft set and its integration to decision making problem, Applied Mathematics and Information Sciences, 8(6) 1-9 (2014).
  • [39] H. Wang, F. Smarandache, Y.Q. Zhang, R. Sunderraman, Interval Neutrosophic Sets and Logic: Theory and Applications in Computing, Hexis; Neutrosophic book series, No: 5, 2005.
  • [40] X. Yang, T.Y. Lin, J. Yang, Y. Li and D. Yu, Combination of interval-valued fuzzy set and soft set, Comput. Math. Appl. 58 (2009) 521-527.
  • [41] J. Ye, Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making, Journal of Intelligent and Fuzzy Systems, 27(5) 2014, 2231–2241.
  • [42] J. Ye, Multiple attribute group decision-making method with completely unknown weights based on similarity measures under single valued neutrosophic environment, Journal of Intelligent and Fuzzy Systems, 27(6) (2014) 2927–2935.
  • [43] H. Wang, F. Y. Smarandache, Q. Zhang, R. Sunderraman, Single valued neutrosophic sets, Multispace and Multistructure 4 (2010) 410–413.
  • [44] L. A. Zadeh, A fuzzy set-theoretic interpretation of linguistic hedges, J. Cybernet., 2 (1972) 4–34.
  • [45] L. A. Zadeh, The concept of a linguistic variable and its application to approximate reasoning–I, Information Sciences, 8 (1975) 199-249.
  • [46] L. A. Zadeh, Fuzzy Sets, Inform. and Control 8 (1965) 338-353.
  • [47] Z. Zhang, C. Wang, D. Tian, K. Li, A novel approach to interval-valued intuitionistic fuzzy soft set based decision making, Applied Mathematical Modelling 38, (2014) 1255–1270.
  • [48] H. Y. Zhang, J. Q. Wang, and X. H. Chen, Interval neutrosophic sets and their application in multicriteria decision making problems, The Scientific World Journal, 2014, http://dx.doi.org/10.1155/2014/645953.
  • [49] P. Zhu, Q. Wen, Operations on Soft Sets Revisited, Journal of Applied Mathematics, (2013) 1-7.
  • [50] Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowl. Base. Syst. 21 (2008) 941-945.
There are 50 citations in total.

Details

Journal Section Articles
Authors

İrfan Deli

Publication Date October 5, 2018
Published in Issue Year 2018 Volume: 22 Issue: Special

Cite

APA Deli, İ. (2018). Expansions and Reductions on Neutrosophic Classical Soft Set. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22, 478-486.
AMA Deli İ. Expansions and Reductions on Neutrosophic Classical Soft Set. J. Nat. Appl. Sci. October 2018;22:478-486.
Chicago Deli, İrfan. “Expansions and Reductions on Neutrosophic Classical Soft Set”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22, October (October 2018): 478-86.
EndNote Deli İ (October 1, 2018) Expansions and Reductions on Neutrosophic Classical Soft Set. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 478–486.
IEEE İ. Deli, “Expansions and Reductions on Neutrosophic Classical Soft Set”, J. Nat. Appl. Sci., vol. 22, pp. 478–486, 2018.
ISNAD Deli, İrfan. “Expansions and Reductions on Neutrosophic Classical Soft Set”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (October 2018), 478-486.
JAMA Deli İ. Expansions and Reductions on Neutrosophic Classical Soft Set. J. Nat. Appl. Sci. 2018;22:478–486.
MLA Deli, İrfan. “Expansions and Reductions on Neutrosophic Classical Soft Set”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, 2018, pp. 478-86.
Vancouver Deli İ. Expansions and Reductions on Neutrosophic Classical Soft Set. J. Nat. Appl. Sci. 2018;22:478-86.

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