Expansions and Reductions on Neutrosophic Classical Soft Set

İrfan DELİ
802 200


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.

Anahtar kelimeler

Soft sets; Neutrosophic classical soft sets; Expansion; Neutrosophic classical soft reduction

Tam metin:



[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.