On interval-valued hesitant fuzzy rough approximation operators

Soft Computing

Volumn 20, Issue 1, 2016, Pages 189-209

  Zhang, Haidong ^a,b   Shu, Lan ^a   Liao, Shilong ^b  

^a UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA   (China)

^b NORTH MINZU UNIVERSITY   (China)

Author keywords

Interval valued hesitant fuzzy relation; Interval valued hesitant fuzzy rough approximation operators; Interval valued hesitant fuzzy rough set; Interval valued hesitant fuzzy set

Indexed keywords

APPROXIMATION ALGORITHMS; FUZZY SETS;

AXIOMATIC APPROACH; CONSTRUCTIVE APPROACH; FUZZY RELATIONS; FUZZY ROUGH APPROXIMATION OPERATORS; FUZZY-ROUGH SETS; INTERVAL-VALUED; INTERVAL-VALUED FUZZY SETS; MEMBERSHIP DEGREES;

ROUGH SET THEORY;

EID: 84952982909     PISSN: 14327643     EISSN: 14337479     Source Type: Journal    
DOI: 10.1007/s00500-014-1490-7     Document Type: Article

References (63)

1. Babitha KV, John SJ (2013) Hesitant fuzzy soft sets. J New Results Sci 3:98–107
2. Chakrabarty K, Gedeon T, Koczy L (1998) Intuitionistic fuzzy rough set. In: Proceedings of fourth joint conference on information sciences (JCIS), Durham, NC, pp 211–214
3. Chen N, Xu ZS, Xia MM (2013a) Interval-valued hesitant preference relations and their applications to group decision making. Knowl-Based Syst 37:528–540
4. Chen N, Xu ZS, Xia MM (2013b) Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Model 37:2197–2211
5. Chuchro M (1993) A certain conception of rough sets in topological boolean algebras. Bull Sect Logic 22(1):9–12
6. Chuchro M (1994) On rough sets in topological Boolean algebras. In: Ziarko W (ed) Rough sets, fuzzy sets and knowledge discovery. Springer, Berlin, pp 157–160
7. Comer S (1991) An algebraic approach to the approximation of information. Fundam Inform 14:492–502
8. Comer S (1993) On connections between information systems, rough sets, and algebraic logic. In: Rauszer C (ed), Algebraic methods in logic and computer science, vol 28. Banach Center Publisher, Polish Academy of Sciences, pp 117–127
9. Cornelis C, Cock MD, Kerre EE (2003) Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Syst Appl 20:260–270
10. Cornelis C, Deschrijver G, Kerre EE (2004) Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: constructive, classification, application. Int J Approx Reason 35:55–95
11. Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191–209
12. Farhadinia B (2013) Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf Sci 240:129–144
13. Jena SP, Ghosh SK (2002) Intuitionistic fuzzy rough sets. Notes Intuit Fuzzy Sets 8:1–18
14. Kortelainen J (1994) On relationship between modified sets, topological space and rough sets. Fuzzy Sets Syst 61:91–95
15. Li TJ, Zhang WX (2008) Rough fuzzy approximations on two universes of discourse. Inf Sci 178:892–906
16. Lin TY (1996) A rough logic formalism for fuzzy controllers: a hard and soft computing view. Int J Approx Reason 15:359–414
17. Liu GL (2013) Using one axiom to characterize rough set and fuzzy rough set approximations. Inf Sci 223:285–296
18. Mi JS, Zhang WX (2004) An axiomatic characterization of a fuzzy generalized of rough sets. Inf Sci 160:235–249
19. Morsi NN, Yakout MM (1998) Axiomatics for fuzzy rough sets. Fuzzy Sets Syst 100:327–342
20. Nanda S, Majumda S (1992) Fuzzy rough sets. Fuzzy Sets Syst 45:157–160
21. Pawlak Z (1982) Rough sets. Int J Comput Inf Sci 11:145–172
22. Pawlak Z (1991) Rough sets—theoretical aspects to reasoning about data. Kluwer, Boston
23. Radzikowska AM, Kerre EE (2002) A comparative study of fuzzy rough sets. Fuzzy Sets Syst 126:137–155
24. Rizvi S, Naqvi HJ, Nadeem D (2002) Rough intuitionistic fuzzy set. In: Proceedings of the sixth joint conference on information sciences (JCIS), Durham, NC, pp 101–104
25. Rodrguez RM, Martnez L, Herrera F (2012) Hesitant fuzzy linguistic term sets for decision making. IEEE Trans Fuzzy Syst 1:109–119
26. Samanta SK, Mondal TK (2001) Intuitionistic fuzzy rough sets and rough intuitionistic fuzzy sets. J Fuzzy Math 9:561–582
27. Skardowska UW (1989) On a generalization of approximation space. Bull Pol Acad Sci Math 37:51–61
28. Sun BZ, Gong ZT, Chen DG (2008) Fuzzy rough set theory for the interval-valued fuzzy information systems. Inf Sci 178:2794–2815
29. Thiele H (2000) On axiomatic characterisation of crisp approximation operators. Inf Sci 129:221–226
30. Thiele H (2001a) On axiomatic characterisation of fuzzy approximation operators: I. The fuzzy rough set based case. In: RSCTC 2000, lecture notes in computer science, vol 205, Springer, Berlin, pp 239–247
31. Thiele H (2001b) On axiomatic characterisation of fuzzy approximation operators: II. The rough fuzzy set based case. In: Proceedings of the 31st IEEE international symposium on multiple-valued logic, pp 330–335
32. Thiele H (2001c) On axiomatic characterisation of fuzzy approximation operators: III. The fuzzy diamond and fuzzy box case. In: Proceedings of the 10th IEEE international conference on fuzzy systems, vol 2, pp 1148–1151
33. Tiwari SP, Srivastava AK (2013) Fuzzy rough sets, fuzzy preorders and fuzzy topologies. Fuzzy Sets Syst 210:63–68
34. Torra V (2010) Hesitant fuzzy sets. Int J Intell Syst 25:529–539
35. Torra V, Narukawa Y (2009) On hesitant fuzzy sets and decision. In: The 18th IEEE international conference on fuzzy systems, Jeju Island, Korea, pp 1378–1382
36. Vakarelov D (1991) A modal logic for similarity relations in Pawlak knowledge representation systems. Fundam Inform 15:61C79.
37. Wei GW, Zhao XF, Lin R (2013) Some hesitant interval-valued fuzzy aggregation operators and their applications to multiple attribute decision making. Knowl-Based Syst 46:43–53
38. Wu WZ, Zhang WX (2002) Neighborhood operator systems and approximations. Inf Sci 144:201–217
39. Wu WZ, Zhang WX (2004) Constructive and axiomatic approaches of fuzzy approximation operators. Inf Sci 159:233–254
40. Wu WZ, Leung Y, Zhang WX (2002) Connections between rough-set theory and Dempster–Shafer theory of evidence. Int J Gen Syst 31:405–430
41. Wu WZ, Mi JS, Zhang WX (2003) Generalized fuzzy rough sets. Inf Sci 151:263–282
42. Wu WZ, Leung Y, Mi JS (2005) On characterizations of (I, T)-fuzzy rough approximation operators. Fuzzy Sets Syst 154:76–102
43. Wu WZ, Leung Y, Zhang WX (2006) On generalized rough fuzzy approximation operators. Transactions on Rough sets V, Lecture notes in computer science, vol 4100, pp 263–284
44. Xia MM, Xu ZS (2011) Hesitant fuzzy information aggregation in decision making. Int J Approx Reason 52:395–407
45. Xu ZS, Da QL (2002) The uncertain OWA operator. Int J Intell Syst 17:569–575
46. Xu ZS, Xia MM (2011) Distance and similarity measures for hesitant fuzzy sets. Inf Sci 181:2128–2138
47. Yang XP (2007) Minimization of axiom sets on fuzzy approximation operators. Inf Sci 177:3840–3854
48. Yang XP, Li TJ (2006) The minimization of axiom sets characterizing generalized approximation operators. Inf Sci 176:887–899
49. Yang XB, Song XN, Qi YS, Yang JY (2014) Constructive and axiomatic approaches to hesitant fuzzy rough set. Soft Comput 18:1067–1077
50. Yao YY (1996) Two views of the theory of rough sets on finite universes. Int J Approx Reason 15:291–317
51. Yao YY (1998a) Constructive and algebraic methods of the theory of rough sets. Inf Sci 109:21–47
52. Yao YY (1998b) Relational interpretations of neighborhood operators and rough set approximation operators. Inf Sci 111:239–259
53. Yao YY (1998c) Generalized rough set model. In: Polkowski L, Skowron A (eds) Rough sets in knowledge discovery 1. Methodology and applications. Physica-Verlag, Heidelberg, pp 286–318
54. Yao YY, Lin TY (1996) Generalization of rough sets using modal logic. Intell Autom Soft Comput Int J 2:103–120
55. Yeung DS, Chen DG, Tsang ECC, Lee JWT, Wang XZ (2005) On the generalization of fuzzy rough sets. IEEE Trans Fuzzy Syst 13:343–361
56. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
57. Zhang HY, Zhang WX, Wu WZ (2009) On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse. Int J Approx Reason 51:56–70
58. Zhang XH, Zhou B, Li P (2012) A general frame for intuitionistic fuzzy rough sets. Inf Sci 216:34–49
59. Zhang ZM (2012a) Generalized intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings. Inf Sci 198:186–206
60. Zhang ZM (2012b) On interval type-2 rough fuzzy sets. Knowl-Based Syst 35:1–13
61. Zhang ZM (2013) On characterization of generalized interval type-2 fuzzy rough sets. Inf Sci 219:124–150
62. Zhou L, Wu WZ (2008) On generalized intuitionistic fuzzy approximation operators. Inf Sci 178:2448–2465
63. Zhou L, Wu WZ (2009) On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators. Inf Sci 179:883–898