Interval-valued intuitionistic fuzzy hybrid weighted averaging operator based on Einstein operation and its application to decision making

Journal of Intelligent and Fuzzy Systems

Volumn 25, Issue 2, 2013, Pages 279-290

  Wang, Weize ^a   Liu, Xinwang ^a  

^a Southeast University   (China)

Author keywords

arithmetic averaging operator; Atanassov's intuitionistic fuzzy set (AIFS); Einstein t norm; interval valued intuitionistic fuzzy set (IVIFS); multi attribute decision making (MADM)

Indexed keywords

ARITHMETIC AVERAGING; ATANASSOV'S INTUITIONISTIC FUZZY SET (AIFS); EINSTEIN T-NORM; INTERVAL-VALUED INTUITIONISTIC FUZZY SETS; MULTI ATTRIBUTE DECISION MAKING;

DECISION MAKING; MATHEMATICAL OPERATORS; STATISTICAL METHODS;

FUZZY SETS;

EID: 84878837593     PISSN: 10641246     EISSN: 18758967     Source Type: Journal    
DOI: 10.3233/IFS-120635     Document Type: Article

References (59)

1. L.A. Zadeh, Fuzzy sets, Inform Contr 8(3) (1965), 338-353.
2. K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst 20(1) (1986), 87-96.
3. L.A. Zadeh, Outline of a new approach to analysis of complex systems and decision processes interval-valued fuzzy sets, IEEE Transactions on Systems Man and Cybernetics SMC3(1) (1973), 28-44.
4. I.B. Turksen, Interval valued fuzzy sets based on normal forms, Fuzzy Sets Syst 20(2) (1986), 191-210.
5. H. Bustince and P. Burillo, Structures on intuitionistic fuzzy relations, Fuzzy Sets Syst 78(3) (1996), 293-303.
6. G. Deschrijver and E.E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets Syst 133(2) (2003), 227-235.
7. G. Deschrijver and E.E. Kerre, On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision, Inf Sci 177(8) (2007), 1860-1866.
8. Z.S. Xu and R.R. Yager, Some geometric aggregation operators based on intuitionistic fuzzy sets, Int J Gen Syst 35(4) (2006), 417-433.
9. Z.S. Xu, Intuitionistic fuzzy aggregation operators, IEEE Transactions on Fuzzy Systems 15(6) (2007), 1179-1187.
10. H.-W. Liu and G.-J. Wang, Multi-criteria decision-making methods based on intuitionistic fuzzy sets, Eur J Oper Res 179(1) (2007), 220-233.
11. T. Beaubouef and F.E. Petry, Uncertainty modeling for database design using intuitionistic and rough set theory, Journal of Intelligent and Fuzzy Systems 20(3) (2009), 105- 117.
12. Z.S.Xuand R.R.Yager, Intuitionistic fuzzy bonferroni means. Systems, Man, and Cybernetics, Part B: Cybernetics, IEEE Transactions on 41(2) (2011), 568-578.
13. Z.S. Xu and X. Cai, Recent advances in intuitionistic fuzzy information aggregation, Fuzzy Optim Decis Mak 9(4) (2010), 359-381.
14. G. Beliakov, H. Bustince, D.P. Goswami, U.K. Mukherjee, and N.R. Pal, On averaging operators for atanassov's intuitionistic fuzzy sets, Inf Sci 181(6) (2011), 1116-1124.
15. W. Wang and X. Liu, Intuitionistic fuzzy geometric aggregation operators based on Einstein operations, Int J Intell Syst 26(11) (2011), 1049-1075.
16. T. Chaira, Intuitionistic fuzzy color clustering of human cell images on different color models, Journal of Intelligent and Fuzzy Systems 23(2) (2012), 43-51.
17. W. Wang and X. Liu, Intuitionistic fuzzy information aggregation using Einstein operations, IEEE Transactions on Fuzzy Systems 20(5) (2012), 923-938.
18. K. Atanassov and G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst 31(3) (1989), 343-349.
19. K.T. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst 64(2) (1994), 159-174.
20. H. Bustince and P. Burillo, Correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst 74(2) (1995), 237-244.
21. D.H. Hong, A note on correlation of interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst 95(1) (1998), 113-117.
22. W.-L. Hung and J.-W. Wu, Correlation of intuitionistic fuzzy sets by centroid method, Inf Sci 144(1-4) (2002), 219- 225.
23. Z.S. Xu, On correlation measures of intuitionistic fuzzy sets intelligent data engineering and automated learning ́lc ideal 2006. volume 4224 of Lecture Notes in Computer Science, pages 16-24. Springer Berlin/Heidelberg, 2006.
24. T.K. Mondai and S.K. Samanta, Topology of interval-valued intuitionistic fuzzy sets, Fuzzy Sets Syst 119(3) (2001), 483-494.
25. J.A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications 18(1) (1967), 145-174.
26. H.L. Huang and F.G. Shi, L-fuzzy numbers and their properties, Inf Sci 178(4) (2008), 1141-1151.
27. H. Bustince and P. Burillo, Mathematical analysis of intervalvalued fuzzy relations: Application to approximate reasoning, Fuzzy Sets Syst 113(2) (2000), 205-219.
28. D. Glad and V. Annelies, Generalized arithmetic operations in interval-valued fuzzy set theory, Journal of Intelligent and Fuzzy Systems 16(4) (2005), 265-271.
29. G. Deschrijver, Arithmetic operators in interval-valued fuzzy set theory, Inf Sci 177(14) (2007), 2906-2924.
30. X.-D. Liu, S.-H. Zheng and F.-L. Xiong, Entropy and subsethood for general interval-valued intuitionistic fuzzy sets. In 2nd International Conference on Fuzzy Systems and Knowledge Discovery, FSKD 2005, volume 3613 LNAI of Lecture Notes in Computer Science, pp. 42-52, Changsa, China, (2006) Springer Verlag.
31. Z.S. Xu and J. Chen, An overview of distance and similarity measures of intuitionistic fuzzy sets, International Journal of Uncertainty Fuzziness and Knowledge-Based Systems 16(4) (2008), 529-555.
32. Z.S. Xu, J. Chen and J. Wu, Clustering algorithm for intuitionistic fuzzy sets, Inf Sci 178(19) (2008), 3775-3790.
33. G. Wei and G. Lan, Grey relational analysis method for interval-valued intuitionistic fuzzy multiple attribute decision making, Fuzzy Systems and Knowledge Discovery, Fourth International Conference on 1 (2008), 291-295.
34. Z.J. Wang, K.W. Li and W. Wang, An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights, Inf Sci 179(17) (2009), 3026-3040.
35. J. Ye, Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment, Expert Syst Appl 36(3) (2009), 6899-6902.
36. W. Wang, Comments on armulticriteria fuzzy decisionmaking method based on a novel accuracy function under interval-valued intuitionistic fuzzy environmental by jun ye, Expert Syst Appl 38(10) (2011), 13186-13187.
37. D.F. Li, Linear programming method for madm with intervalvalued intuitionistic fuzzy sets, Expert Syst Appl 37(8) (2010), 5939-5945.
38. D.F. Li, Closeness coefficient based nonlinear programming method for interval-valued intuitionistic fuzzy multiat-tribute decision making with incomplete preference information, Appl Soft Comput 11(4) (2011), 3402-3418.
39. D.F. Li, Topsis-based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy sets, Fuzzy Systems, IEEE Transactions on 18(2) (2010), 299-311.
40. D.F. Li, Mathematical-programming approach to matrix games with payoffs represented by atanassov's intervalvalued intuitionistic fuzzy sets, IEEE Transactions on Fuzzy Systems 18(6) (2010), 1112-1128.
41. G.Wei, H.Wang and R. Lin, Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute averaging operator based on IVIFNs decision-making with incomplete weight information, Knowledge and Information Systems 26(2) (2011), 337-349.
42. Z.S. Xu, Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making, Kongzhi yu Juece/Control and Decision 22(2) (2007), 215-219.
43. Z.S. Xu and J. Chen, Approach to group decision making based on interval-valued intuitionistic judgment matrices, Systems Engineering - Theory and Practice 27(4) (2007), 126-133.
44. G. Wei and X. Wang, Some geometric aggregation operators based on interval-valued intuitionistic fuzzy sets and their application to group decision making. Cis: 2007 International Conference on Computational Intelligence and Security, Proceedings, 2007, pp. 495-499.
45. Z.S. Xu and J. Chen, On geometric aggregation ove intervalvalued intuitionistic fuzzy information, Fourth International Conference on Fuzzy Systems and Knowledge Discovery, Vol 2, Proceedings (2007), 466-471.
46. Z.S. Xu and R.R. Yager, Dynamic intuitionistic fuzzy multiattribute decision making, Int J Approx Reasoning 48(1) (2008), 246-262.
47. H. Zhao, Z.S. Xu, M. Ni and S. Liu, Generalized aggregation operators for intuitionistic fuzzy sets, Int J Intell Syst 25(1) (2010), 1-30.
48. G. Wei, Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision making, Appl Soft Comput 10(2) (2010), 423-431.
49. G. Wei and W. Yi, Induced interval-valued intuitionistic fuzzy owg operator, Fuzzy Systems and Knowledge Discovery, Fourth International Conference on 1 (2008), 605-609.
50. Z.S. Xu, Choquet integrals of weighted intuitionistic fuzzy information, Inf Sci 180(5) (2010), 726-736.
51. Z.S. Xu and M.M. Xia, Induced generalized intuitionistic fuzzy operators, Knowledge-Based Syst 24(2) (2011), 197-209.
52. E.P. Klement, R. Mesiar and E. Pap, Triangular norms position paper I: Basic analytical and algebraic properties, Fuzzy Sets Syst 143(1) (2004), 5-26.
53. G. Deschrijver and E. Kerre, A generalization of operators on intuitionistic fuzzy sets using triangular norms and conorms, Notes on Intuitionistic Fuzzy Sets 8(1) (2002), 19-27.
54. G. Beliakov, A. Pradera and T. Calvo, Aggregation Functions: A Guide for Practitioners, Springer, Heidelberg, Berlin, New York, 2007.
55. M. Grabisch, J.-L. Marichal, R. Mesiar and E. Pap, Aggregation Functions, Cambridge University Press, Cambridge, 2009.
56. R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision-making, IEEE Transactions on Systems, Man, and Cybernetics 18(1) (1988), 183-190.
57. J.M. Merigo, A unified model between the weighted average and the induced owa operator, Expert Systems with Applications 38(9) (2011), 11560-11572.
58. A.I. Olçer and A.Y. Odabaşi, A new fuzzy multiple attributive group decision making methodology and its application to propulsion/manoeuvring system selection problem, Eur J Oper Res 166(1) (2005), 93-114.
59. Z.S. Xu, An overview of methods for determining OWA weights, Int J Int Syst 20(8) (2005), 843-865.