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Erschienen in: International Journal of Machine Learning and Cybernetics 3/2014

01.06.2014 | Original Article

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

verfasst von: Xia Liang, Cuiping Wei

Erschienen in: International Journal of Machine Learning and Cybernetics | Ausgabe 3/2014

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Abstract

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.

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Literatur
3.
Zurück zum Zitat Beliakov G, Bustince H et al (2011) On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inf Sci 181:1116–1124CrossRefMATHMathSciNet Beliakov G, Bustince H et al (2011) On averaging operators for Atanassov’s intuitionistic fuzzy sets. Inf Sci 181:1116–1124CrossRefMATHMathSciNet
5.
Zurück zum Zitat Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305–316CrossRefMATHMathSciNet Burillo P, Bustince H (1996) Entropy on intuitionistic fuzzy sets and on interval-valued fuzzy sets. Fuzzy Sets Syst 78:305–316CrossRefMATHMathSciNet
6.
Zurück zum Zitat Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74:217–223CrossRefMATH Chen SM (1995) Measures of similarity between vague sets. Fuzzy Sets Syst 74:217–223CrossRefMATH
7.
Zurück zum Zitat Chen SM, Tan JM (1994) Handling multi-criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172CrossRefMATHMathSciNet Chen SM, Tan JM (1994) Handling multi-criteria fuzzy decision making problems based on vague set theory. Fuzzy Sets Syst 67(2):163–172CrossRefMATHMathSciNet
8.
Zurück zum Zitat 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’03), Zittau, Germany, pp 159–163 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’03), Zittau, Germany, pp 159–163
9.
Zurück zum Zitat De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117(2):209–213CrossRefMATHMathSciNet De SK, Biswas R, Roy AR (2001) An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets Syst 117(2):209–213CrossRefMATHMathSciNet
10.
Zurück zum Zitat Deschrijver G, Kerre EE (2003) On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst 133:227–235CrossRefMATHMathSciNet Deschrijver G, Kerre EE (2003) On the relationship between some extensions of fuzzy set theory. Fuzzy Sets Syst 133:227–235CrossRefMATHMathSciNet
11.
12.
Zurück zum Zitat Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114:103–113CrossRefMATH Hong DH, Choi CH (2000) Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst 114:103–113CrossRefMATH
13.
Zurück zum Zitat Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Huasdorff distance. Pattern Recognit Lett 25:1603–1611CrossRef Hung WL, Yang MS (2004) Similarity measures of intuitionistic fuzzy sets based on Huasdorff distance. Pattern Recognit Lett 25:1603–1611CrossRef
14.
Zurück zum Zitat Li DF, Cheng CT (2002) New similarity measure of intuitionistic fuzzy sets and application to pattern recongnitions. Pattern Recognit Lett 23:221–225CrossRefMATHMathSciNet Li DF, Cheng CT (2002) New similarity measure of intuitionistic fuzzy sets and application to pattern recongnitions. Pattern Recognit Lett 23:221–225CrossRefMATHMathSciNet
15.
Zurück zum Zitat Li YH, Olson DL, Zeng Q (2007) Similarity measures between intuitionistic fuzzy (vague) set: a comparative analysis. Pattern Recognit Lett 28:278–285CrossRef Li YH, Olson DL, Zeng Q (2007) Similarity measures between intuitionistic fuzzy (vague) set: a comparative analysis. Pattern Recognit Lett 28:278–285CrossRef
16.
Zurück zum Zitat Li DF, Wang YC, Liu S, Shan F (2009) Fractional programming methodology for multi-attribute group decision-making using IFS. Appl Soft Comput 9:219–225CrossRef Li DF, Wang YC, Liu S, Shan F (2009) Fractional programming methodology for multi-attribute group decision-making using IFS. Appl Soft Comput 9:219–225CrossRef
17.
Zurück zum Zitat Li F, Xu ZY (2001) Similarity measures between vague sets. Software (in Chinese) 12(6):922–927 Li F, Xu ZY (2001) Similarity measures between vague sets. Software (in Chinese) 12(6):922–927
18.
Zurück zum Zitat Mitchell HB (2003) On the Dengfeng-Chuntain similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104CrossRef Mitchell HB (2003) On the Dengfeng-Chuntain similarity measure and its application to pattern recognition. Pattern Recognit Lett 24:3101–3104CrossRef
19.
Zurück zum Zitat Pal N R, Bustince H et al (2013) Uncertainties with Atanassovs intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf Sci 228:61–74 Pal N R, Bustince H et al (2013) Uncertainties with Atanassovs intuitionistic fuzzy sets: fuzziness and lack of knowledge. Inf Sci 228:61–74
20.
Zurück zum Zitat Pearl PG, Yan H (2012) A hierarchical multilevel thresholding method for edge information extraction using fuzzy entropy. Int J Mach Learn Cybern 3(4):297–305CrossRef Pearl PG, Yan H (2012) A hierarchical multilevel thresholding method for edge information extraction using fuzzy entropy. Int J Mach Learn Cybern 3(4):297–305CrossRef
22.
Zurück zum Zitat Szmidt E, Kacprzyk J (2005) New measures of entropy for intuitionistic fuzzy sets. Ninth Int Conf IFSs Sofia 11(2):12–20 Szmidt E, Kacprzyk J (2005) New measures of entropy for intuitionistic fuzzy sets. Ninth Int Conf IFSs Sofia 11(2):12–20
23.
Zurück zum Zitat Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information—applications to pattern recognition. Pattern Recognit Lett 28:197–206CrossRef Vlachos IK, Sergiadis GD (2007) Intuitionistic fuzzy information—applications to pattern recognition. Pattern Recognit Lett 28:197–206CrossRef
24.
Zurück zum Zitat Vlachos IK, Sergiadis GD (2007) Subsethood, entropy, and cardinality for interval-valued fuzzy sets: an algebraic derivation. Fuzzy Sets Syst 158:1384–1396CrossRefMATHMathSciNet Vlachos IK, Sergiadis GD (2007) Subsethood, entropy, and cardinality for interval-valued fuzzy sets: an algebraic derivation. Fuzzy Sets Syst 158:1384–1396CrossRefMATHMathSciNet
25.
Zurück zum Zitat Wan SP (2010) Determination of experts’ weights based on vague sets for multi-attribute group decision-making. Commun Appl Math Comput 24(1):45–52MATHMathSciNet Wan SP (2010) Determination of experts’ weights based on vague sets for multi-attribute group decision-making. Commun Appl Math Comput 24(1):45–52MATHMathSciNet
26.
Zurück zum Zitat Wang XZ, Dong CR (2009) Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567CrossRef Wang XZ, Dong CR (2009) Improving generalization of fuzzy if-then rules by maximizing fuzzy entropy. IEEE Trans Fuzzy Syst 17(3):556–567CrossRef
28.
Zurück zum Zitat Wei CP, Gao ZH, Guo TT (2012) An intuitionistic fuzzy entropy measure based on the trigonometric function. Control Decis (in Chinese) 27(4):571–574MATHMathSciNet Wei CP, Gao ZH, Guo TT (2012) An intuitionistic fuzzy entropy measure based on the trigonometric function. Control Decis (in Chinese) 27(4):571–574MATHMathSciNet
29.
Zurück zum Zitat 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):1437–1448MATHMathSciNet 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):1437–1448MATHMathSciNet
30.
Zurück zum Zitat 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):1111–1130CrossRefMATH 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):1111–1130CrossRefMATH
31.
Zurück zum Zitat Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 182(19):4273–4286CrossRefMathSciNet Wei CP, Wang P, Zhang YZ (2011) Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications. Inf Sci 182(19):4273–4286CrossRefMathSciNet
32.
Zurück zum Zitat 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):430–452CrossRef 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):430–452CrossRef
33.
Zurück zum Zitat Xia MM, Xu ZS (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13(1):31–47CrossRefMathSciNet Xia MM, Xu ZS (2012) Entropy/cross entropy-based group decision making under intuitionistic fuzzy environment. Inf Fusion 13(1):31–47CrossRefMathSciNet
34.
Zurück zum Zitat Xu ZS (2010) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negot 19:57–76CrossRef Xu ZS (2010) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negot 19:57–76CrossRef
35.
Zurück zum Zitat Xu ZS (2008) An overview of distance and similarity measures of intuitionistic sets. Int J Uncertain Fuzziness Knowl-Based Syst 16(4):529–555CrossRefMATH Xu ZS (2008) An overview of distance and similarity measures of intuitionistic sets. Int J Uncertain Fuzziness Knowl-Based Syst 16(4):529–555CrossRefMATH
36.
Zurück zum Zitat Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl-Based Syst 24:749–760CrossRef Xu ZS (2011) Approaches to multiple attribute group decision making based on intuitionistic fuzzy power aggregation operators. Knowl-Based Syst 24:749–760CrossRef
37.
Zurück zum Zitat Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRef Xu ZS (2007) Intuitionistic fuzzy aggregation operators. IEEE Trans Fuzzy Syst 15:1179–1187CrossRef
38.
Zurück zum Zitat 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):139–143MATHMathSciNet 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):139–143MATHMathSciNet
39.
Zurück zum Zitat Xu ZS (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22(2):215–219 Xu ZS (2007) Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control Decis 22(2):215–219
40.
Zurück zum Zitat Xu ZS (2007) Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optim Decis Mak 6(3):221–236CrossRefMATHMathSciNet Xu ZS (2007) Multi-person multi-attribute decision making models under intuitionistic fuzzy environment. Fuzzy Optim Decis Mak 6(3):221–236CrossRefMATHMathSciNet
41.
Zurück zum Zitat Xu ZS (2007) Multiple attribute decision making with intuitionistic fuzzy preference information. Syst Eng-Theory Pract 27(11):62–71CrossRef Xu ZS (2007) Multiple attribute decision making with intuitionistic fuzzy preference information. Syst Eng-Theory Pract 27(11):62–71CrossRef
42.
Zurück zum Zitat Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180:726–736CrossRefMATH Xu ZS (2010) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180:726–736CrossRefMATH
43.
Zurück zum Zitat Xu ZS, Cai XQ (2010) Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst 25:489–513MATHMathSciNet Xu ZS, Cai XQ (2010) Nonlinear optimization models for multiple attribute group decision making with intuitionistic fuzzy information. Int J Intell Syst 25:489–513MATHMathSciNet
44.
Zurück zum Zitat Xu ZS, Hu H (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(2):267–280CrossRefMATH Xu ZS, Hu H (2010) Projection models for intuitionistic fuzzy multiple attribute decision making. Int J Inf Technol Decis Mak 9(2):267–280CrossRefMATH
45.
Zurück zum Zitat Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433CrossRefMATHMathSciNet Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35(4):417–433CrossRefMATHMathSciNet
46.
49.
Zurück zum Zitat Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249MATHMathSciNet Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning-I. Inf Sci 8:199–249MATHMathSciNet
50.
Zurück zum Zitat Zeng WY, Li HX (2006) Relationship between similarity measure and entropy of interval-valued fuzzy sets. Fuzzy Sets Syst 157:1477–1484CrossRefMATHMathSciNet Zeng WY, Li HX (2006) Relationship between similarity measure and entropy of interval-valued fuzzy sets. Fuzzy Sets Syst 157:1477–1484CrossRefMATHMathSciNet
51.
Zurück zum Zitat Zhang QS, Jiang SY (2008) A note on information entropy measures for vague sets and its application. Inf Sci 178:4184–4191CrossRefMATH Zhang QS, Jiang SY (2008) A note on information entropy measures for vague sets and its application. Inf Sci 178:4184–4191CrossRefMATH
52.
Zurück zum Zitat 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 22:449–454CrossRef 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 22:449–454CrossRef
Metadaten
Titel
An Atanassov’s intuitionistic fuzzy multi-attribute group decision making method based on entropy and similarity measure
verfasst von
Xia Liang
Cuiping Wei
Publikationsdatum
01.06.2014
Verlag
Springer Berlin Heidelberg
Erschienen in
International Journal of Machine Learning and Cybernetics / Ausgabe 3/2014
Print ISSN: 1868-8071
Elektronische ISSN: 1868-808X
DOI
https://doi.org/10.1007/s13042-013-0178-0

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