An Atanassov’s intuitionistic fuzzy multi-attribute group decision making method based on entropy and similarity measure

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• 作者：Xia Liang (1)
  Cuiping Wei (2)
  
• 关键词：Multi ; attribute group decision making ; Atanassov’s intuitionistic fuzzy set entropy ; Similarity measure ; Weights of experts
• 刊名：International Journal of Machine Learning and Cybernetics
• 出版年：2014
• 出版时间：June 2014
• 年：2014
• 卷：5
• 期：3
• 页码：435-444
• 全文大小：
• 参考文献：1. Abo-Tabl EA (2012) Rough sets and topological spaces based on similarity. Int J Mach Learn Cybern. doi:10.1007/s13042-012-0107-7
  2. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20(1):87-6 CrossRef
  3. Beliakov G, Bustince H et?al (2011) On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inf Sci 181:1116-124 CrossRef
  4. Burillo P, Bustince H (1996) Vague sets are intuitionistic sets. Fuzzy Sets Syst 79:403-05 CrossRef
  5. Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305-16 CrossRef
  6. Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74:217-23 CrossRef
  7. Chen SM, Tan JM (1994) Handling multi-criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets Syst 67(2):163-72 CrossRef
  8. Cornelis C, Atanassov K, Kerre EE (2003) Intuitionistic fuzzy sets and interval-valued fuzzy sets: a critical comparison. In: Proceedings of third European conference on fuzzy logic and Technology (EUSFLAT-3), Zittau, Germany, pp 159-63
  9. De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117(2):209-13 CrossRef
  10. Deschrijver G, Kerre EE (2003) On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst 133:227-35 CrossRef
  11. Gau WL, Buehrer DJ (1993) Vague sets. IEEE Trans Syst Man Cybern 23(2):610-14 CrossRef
  12. Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114:103-13 CrossRef
  13. Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Huasdorff distance. Pattern Recognit Lett 25:1603-611 CrossRef
  14. Li DF, Cheng CT (2002) New similarity measure of intuitionistic fuzzy sets and application to pattern recongnitions. Pattern Recognit Lett 23:221-25 CrossRef
  15. Li YH, Olson DL, Zeng Q (2007) Similarity measures between intuitionistic fuzzy (vague) set: a comparative analysis. Pattern Recognit Lett 28:278-85 CrossRef
  16. Li DF, Wang YC, Liu S, Shan F (2009) Fractional programming methodology for multi-attribute group decision-making using IFS. Appl Soft Comput 9:219-25 CrossRef
  17. Li F, Xu ZY (2001) Similarity measures between vague sets. Software (in Chinese) 12(6):922-27
  18. Mitchell HB (2003) On the Dengfeng-Chuntain similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101-104 CrossRef
  19. Pal N R, Bustince H et?al (2013) Uncertainties with Atanassovs intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf Sci 228:61-4
  20. Pearl PG, Yan H (2012) A hierarchical multilevel thresholding method for edge information extraction using fuzzy entropy. Int J Mach Learn Cybern 3(4):297-05 CrossRef
  21. Szmidt E, Kacprzyk J (2001) Entropy for intuitionistic fuzzy sets. Fuzzy Sets Syst 118(3):467-77 CrossRef
  22. Szmidt E, Kacprzyk J (2005) New measures of entropy for intuitionistic fuzzy sets. Ninth Int Conf IFSs Sofia 11(2):12-0
  23. Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information—applications to pattern recognition. Pattern Recognit Lett 28:197-06 CrossRef
  24. Vlachos IK, Sergiadis GD (2007) Subsethood, entropy, and cardinality for interval-valued fuzzy sets: an algebraic derivation. Fuzzy Sets Syst 158:1384-396 CrossRef
  25. Wan SP (2010) Determination of experts-weights based on vague sets for multi-attribute group decision-making. Commun Appl Math Comput 24(1):45-2
  26. Wang XZ, Dong CR (2009) Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556-67 CrossRef
  27. Wang XZ, He YL, Wang DD (2013) Non-Naive Bayesian classifiers for classification problems with continuous attributes. IEEE Trans Cybern. doi:10.1109/TCYB.2013.2245891
  28. Wei CP, Gao ZH, Guo TT (2012) An intuitionistic fuzzy entropy measure based on the trigonometric function. Control Decis (in Chinese) 27(4):571-74
  29. Wei CP, Liang X, Zhang YZ (2012) A comparative analysis and improvement of entropy measures for intuitionistic fuzzy sets. J Syst Sci Math Sci 32(11):1437-448
  30. Wei CP, Tang XJ (2011) An intuitionistic fuzzy group decision making approach based on entropy and similarity measures. Int J Inf Technol Decis Mak 10(6):1111-130 CrossRef
  31. Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 182(19):4273-286 CrossRef
  32. Xia MM, Xu ZS (2011) Some new similarity measures for intuitionistic fuzzy values and their application in group decision making. J Syst Sci Syst Eng 19(4):430-52 CrossRef
  33. Xia MM, Xu ZS (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13(1):31-7 CrossRef
  34. Xu ZS (2010) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negot 19:57-6 CrossRef
  35. Xu ZS (2008) An overview of distance and similarity measures of intuitionistic sets. Int J Uncertain Fuzziness Knowl-Based Syst 16(4):529-55 CrossRef
  36. Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl-Based Syst 24:749-60 CrossRef
  37. Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179-187 CrossRef
  38. Xu ZS (2007) On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions. J Southeast Univ (English Ed) 23(1):139-43
  39. Xu ZS (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22(2):215-19
  40. Xu ZS (2007) Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optim Decis Mak 6(3):221-36 CrossRef
  41. Xu ZS (2007) Multiple attribute decision making with intuitionistic fuzzy preference information. Syst Eng-Theory Pract 27(11):62-1 CrossRef
  42. Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180:726-36 CrossRef
  43. Xu ZS, Cai XQ (2010) Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst 25:489-13
  44. Xu ZS, Hu H (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(2):267-80 CrossRef
  45. Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417-33 CrossRef
  46. Xu ZS, Yager RR (2008) Dynamic intuitionistic fuzzy multi-attribute decision making. Int J Approx Reason 48:246-62 CrossRef
  47. Ye J (2010) Two effective measures of intuitionistic fuzzy entropy. Comput Lett 87(1-):55-2 CrossRef
  48. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338-56 CrossRef
  49. Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199-49
  50. Zeng WY, Li HX (2006) Relationship between similarity measure and entropy of interval-valued fuzzy sets. Fuzzy Sets Syst 157:1477-484 CrossRef
  51. Zhang QS, Jiang SY (2008) A note on information entropy measures for vague sets and its application. Inf Sci 178:4184-191 CrossRef
  52. Zhang HY, Zhang WX, Mei CL (2009) Entropy of interval-valued fuzzy sets based on distance and its relationship with similarity measure. Knowl-Based Syst 22:449-54 CrossRef
  
• 作者单位：Xia Liang (1)
  Cuiping Wei (2)
  
  1. School of Business Administration, Northeastern University, Shenyang, Liaoning, 110819, China
  2. Institute of Operations Research, Qufu Normal University, Rizhao, Shandong, 276826, China
  
• ISSN：1868-808X

文摘

In this paper, we propose a new similarity measure for Atanassov’s intuitionistic fuzzy sets by the relationship between entropy and similarity measure. With respect to multi-attribute group decision making problem, we then give an approach to derive the relative importance weights of experts. This approach takes into account decision information from three aspects: the uncertainty degrees of individual expert’s assessing information for alternatives, the similarity degree of the assessing information for alternatives provided by individual expert, and the similarity degree of the individual expert’s assessing information to all the others- Finally, we establish a method for handling multi-attribute group decision making problem with Atanassov’s intuitionistic fuzzy information, and adopt an illustrative example to demonstrate its rationality and effectiveness.