A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

Applied Mathematical Modelling

Volumn 38, Issue 4, 2014, Pages 1255-1270

  Zhang, Zhiming ^a   Wang, Chao ^b   Tian, Dazeng ^a   Li, Kai ^a  

^a HEBEI UNIVERSITY   (China)

^b HEBEI UNIVERSITY OF ENGINEERING   (China)

Author keywords

Decision making; Interval valued intuitionistic fuzzy sets; Interval valued intuitionistic fuzzy soft sets; Level soft sets; Soft sets

Indexed keywords

INTERVAL-VALUED; INTERVAL-VALUED INTUITIONISTIC FUZZY SETS; INTUITIONISTIC FUZZY; INTUITIONISTIC FUZZY SOFT SETS; MATHEMATICAL TOOLS; SOFT SET THEORIES; SOFT SETS;

DECISION MAKING; FUZZY SETS;

SET THEORY;

EID: 84893786054     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2013.08.019     Document Type: Article

References (56)

1. Molodtsov D. Soft set theory-first results. Comput. Math. Appl. 1999, 37:19-31.
2. Zadeh L.A. Fuzzy Sets. Inf. Control 1965, 8:338-353.
3. Pawlak Z. Rough sets. Int. J. Comput. Inf. Sci. 1982, 11:341-356.
4. Aktaş H., Çaǧman N. Soft sets and soft groups. Inf. Sci. 2007, 177:2726-2735.
5. Ali M.I., Feng F., Liu S., Win W.K., Shabir M. On some new operations in soft set theory. Comput. Math. Appl. 2009, 57:1547-1553.
6. Çaǧman N., Enginoǧlu S. Soft matrix theory and its decision making. Comput. Math. Appl. 2010, 59(10):3308-3314.
7. Çaǧman N., Enginoǧlu S. Soft set theory and uni-int decision making. Eur. J. Oper. Res. 2010, 207:848-855.
8. Chen D., Tsang E.C.C., Yeung D.S., Wang X. The parameterization reduction of soft sets and its applications. Comput. Math. Appl. 2005, 49:757-763.
9. Feng F., Jun Y.B., Zhao X.Z. Soft semirings. Comput. Math. Appl. 2008, 56:2621-2628.
10. Gong K., Wang P.P., Xiao Z. Bijective soft set decision system based parameters reduction under fuzzy environments. Appl. Math. Model. 2013, 37:4474-4485.
11. Jun Y.B. Soft BCK/BCI-algebras. Comput. Math. Appl. 2008, 56:1408-1413.
12. Jun Y.B., Park C.H. Applications of soft sets in ideal theory of BCK/BCI-algebras. Inf. Sci. 2008, 178:2466-2475.
13. Kong Z., Gao L., Wang L.F., Li S. The normal parameter of soft sets and its algorithm. Comput. Math. Appl. 2008, 56:3029-3037.
14. Maji P.K., Roy A.R. An application of soft sets in a decision making problem. Comput. Math. Appl. 2002, 44:1077-1083.
15. Maji P.K., Biswas R., Roy A.R. Soft set theory. Comput. Math. Appl. 2003, 45:555-562.
16. Zou Y., Xiao Z. Data analysis approaches of soft sets under incomplete information. Knowl.-Based Syst. 2008, 21:941-945.
17. Ali M.I. A note on soft sets, rough soft sets and fuzzy soft sets. Appl. Soft Comput. 2011, 11(4):3329-3332.
18. Ali M.I. Another view on reduction of parameters in soft sets. Appl. Soft Comput. 2012, 12(6):1814-1821.
19. Aygünoǧlu A., Aygün H. Introduction to fuzzy soft groups. Comput. Math. Appl. 2009, 58:1279-1286.
20. Basu T.M., Mahapatra N.K., Mondal S.K. A balanced solution of a fuzzy soft set based decision making problem in medical science. Appl. Soft Comput. 2012, 12(10):3260-3275.
21. Deng T.Q., Wang X.F. An object-parameter approach to predicting unknown data in incomplete fuzzy soft sets. Appl. Math. Model. 2013, 37:4139-4146.
22. Feng F., Li C., Davvaz B., Ali M.I. Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 2010, 14:899-911.
23. Feng F., Li Y.M., Leoreanu-Fotea V. Application of level soft sets in decision making based on interval-valued fuzzy soft sets. Comput. Math. Appl. 2010, 60(6):1756-1767.
24. Feng F., Liu X.Y., Leoreanu-Fotea V., Jun Y.B. Soft sets and soft rough sets. Inf. Sci. 2011, 181(6):1125-1137.
25. Jiang Y., Tang Y., Chen Q., Liu H., Tang J. Extending fuzzy soft sets with fuzzy description logics. Knowl.-Based Syst. 2011, 24(7):1096-1107.
26. Jiang Y., Tang Y., Liu H., Chen Z. Entropy on intuitionistic fuzzy soft sets and on interval-valued fuzzy soft sets. Inf. Sci. 2013, 240:95-114.
27. Kong Z., Wang L.F., Wu Z.X. Application of fuzzy soft set in decision making problems based on grey theory. J. Comput. Appl. Math. 2011, 236(6):1521-1530.
28. Mao J.J., Yao D.B., Wang C.C. Group decision making methods based on intuitionistic fuzzy soft matrices. Appl. Math. Model. 2013, 37:6425-6436.
29. Meng D., Zhang X.H., Qin K.Y. Soft rough fuzzy sets and soft fuzzy rough sets. Comput. Math. Appl. 2011, 62(12):4635-4645.
30. Shabir M., Ali M.I., Shaheen T. Another approach to soft rough sets. Knowl.-Based Syst. 2013, 40:72-80.
31. Tanay B., Kandemir M.B. Topological structure of fuzzy soft sets. Comput. Math. Appl. 2011, 61(10):2952-2957.
32. Xiao Z., Chen W.J., Li L.L. An integrated FCM and fuzzy soft set for supplier selection problem based on risk evaluation. Appl. Math. Model. 2012, 36:1444-1454.
33. Xiao Z., Xia S.S., Gong K., Li D. The trapezoidal fuzzy soft set and its application in MCDM. Appl. Math. Model. 2012, 36:5844-5855.
34. Xiao Z., Yang X.L., Niu Q., Dong Y.X., Gong K., Xia S.S., Pang Y. A new evaluation method based on D-S generalized fuzzy soft sets and its application in medical diagnosis problem. Appl. Math. Model. 2012, 36:4592-4604.
35. Yang Y., Tan X., Meng C.C. The multi-fuzzy soft set and its application in decision making. Appl. Math. Model. 2013, 37(7):4915-4923.
36. Yin Y.Q., Li H.J., Jun Y.B. On algebraic structure of intuitionistic fuzzy soft sets. Comput. Math. Appl. 2012, 64(9):2896-2911.
37. Zhang Z.M. A rough set approach to intuitionistic fuzzy soft set based decision making. Appl. Math. Model. 2012, 36:4605-4633.
38. Zhang Z.M., Zhang S.H. Type-2 fuzzy soft sets and their applications in decision making. J. Appl. Math. 2012, 2012:1-35.
39. Zhang Z.M., Zhang S.H. A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets. Appl. Math. Model. 2013, 37:4948-4971.
40. Maji P.K., Biswas R., Roy A.R. Fuzzy soft sets. J. Fuzzy Math. 2001, 9:589-602.
41. Majumdar P., Samanta S.K. Generalised fuzzy soft sets. Comput. Math. Appl. 2010, 59:1425-1432.
42. Yang X., Lin T.Y., Yang J., Dongjun Y.L.A. Combination of interval-valued fuzzy set and soft set. Comput. Math. Appl. 2009, 58:521-527.
43. Xu W., Ma J., Wang S.Y., Hao G. Vague soft sets and their properties. Comput. Math. Appl. 2010, 59:787-794.
44. Maji P.K. More on intuitionistic fuzzy soft sets. Lect. Notes Comput. Sci. 2009, 5908:231-240.
45. Maji P.K., Biswas R., Roy A.R. Intuitionistic fuzzy soft sets. J. Fuzzy Math. 2001, 9:677-692.
46. Maji P.K., Biswas R., Roy A.R. On intuitionistic fuzzy soft sets. J. Fuzzy Math. 2004, 12:669-683.
47. Roy A.R., Maji P.K. A fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 2007, 203:412-418.
48. Kong Z., Gao L.Q., Wang L.F. Comment on a fuzzy soft set theoretic approach to decision making problems. J. Comput. Appl. Math. 2009, 223:540-542.
49. Feng F., Jun Y.B., Liu X.Y., Li L.F. An adjustable approach to fuzzy soft set based decision making. J. Comput. Appl. Math. 2010, 234:10-20.
50. Jiang Y., Tang Y., Chen Q. An adjustable approach to intuitionistic fuzzy soft sets based decision making. Appl. Math. Model. 2011, 35:824-836.
51. Zadeh L.A. The concept of a linguistic variable and its application to approximate reasoning-I. Inf. Sci. 1975, 8:199-249.
52. Atanassov K. Intuitionistic fuzzy sets. Fuzzy Sets Syst. 1986, 20:87-96.
53. Atanassov K., Gargov G. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 1989, 31:343-349.
54. Jiang Y., Tang Y., Chen Q., Liu H., Tang J. Interval-valued intuitionistic fuzzy soft sets and their properties. Comput. Math. Appl. 2010, 60:906-918.
55. Gau W.L., Buehrer D.J. Vague sets. IEEE Trans. Syst. Man Cybern. 1993, 23:610-614.
56. Cao Q.W., Wu J. The extended COWG operators and their application to multiple attributive group decision making problems with interval numbers. Appl. Math. Model. 2011, 35:2075-2086.