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Some Geometric Operators for Aggregating Intuitionistic Linguistic Information

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Abstract

With respect to intuitionistic linguistic information aggregation problems, we first define a new score function and a new accuracy function of intuitionistic linguistic number (ILN) and present a simple method for the comparison between two ILNs. Then, based on the intuitionistic linguistic weighted geometric averaging (ILWGA) operator, we propose two new intuitionistic linguistic geometric operators, such as the intuitionistic linguistic ordered weighted geometric (ILOWG) operator and intuitionistic linguistic hybrid geometric (ILHG) operator, and establish various properties of these operators. Furthermore, we apply the ILHG and ILWGA operators to solve multi-criteria group decision making problems, in which the criterion values take the form of ILNs and the criterion weight information is known completely. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed approach.

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References

  1. Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning. Part 1. Inf. Sci. 8(3), 199–249 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst. 78(1), 73–87 (1996)

    Article  MathSciNet  Google Scholar 

  3. Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: A rational consensus model in group decision making under linguistic assessments. Fuzzy Sets Syst. 88(1), 31–49 (1997)

    Article  MathSciNet  Google Scholar 

  4. Xu, Z.S., Da, Q.L.: An overview of operators for aggregating information. Int. J. Intell. Syst. 18(9), 953–969 (2003)

    Article  MATH  Google Scholar 

  5. Herrera, F., Herrera-Viedma, E.: Aggregation operators for linguistic weighted information. IEEE Trans. Syst. Man Cybern. part A: Syst. Hum. 27(5), 646–656 (1997)

    Article  Google Scholar 

  6. Xu, Z.S.: On generalized induced linguistic aggregation operators. Int. J. Gen. Syst. 35(1), 17–28 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  7. Yang, W.E., Wang, J.Q.: Vague linguistic matrix game approach for multi-criteria decision making with uncertain weights. J. Intell. Fuzzy Syst. 25(2), 315–324 (2013)

    MATH  Google Scholar 

  8. Wei, G.W., Zhao, X.F.: Some dependent aggregation operators with 2-tuple linguistic information and their application to multiple attribute group decision making. Expert Syst. Appl. 39(5), 5881–5886 (2012)

    Article  Google Scholar 

  9. Merigó, J.M., Casanovas, M., Martínez, L.: Linguistic aggregation operators for linguistic decision making based on the Dempster-Shafer theory of evidence. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 18(3), 287–304 (2010)

    Article  MATH  Google Scholar 

  10. Wei, G.W.: Some generalized aggregating operators with linguistic information and their application to multiple attribute group decision making. Comput. Ind. Eng. 61(1), 32–38 (2011)

    Article  Google Scholar 

  11. Merigó, J.M., Gil-Lafuente, A.M., Zhou, L.G.: Induced and linguistic generalized aggregation operators and their application in linguistic group decision making. Group Decis. Negot. 21(4), 531–549 (2012)

    Article  Google Scholar 

  12. Wang, J.Q., Wu, J.T., Wang J., et al.: Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems. Inf. Sci. 288, 55–72 (2014)  

    Article  MATH  Google Scholar 

  13. Yang, W.E., Wang, J.Q.: Multi-criteria semantic dominance: a linguistic decision aiding technique based on incomplete preference information. Eur. J. Oper. Res. 231(1), 171–181 (2013)

    Article  Google Scholar 

  14. Herrera, F., Martínez, L.: A 2-Tuple Fuzzy Linguistic Representation Model for Computing with Words. IEEE Trans. Fuzzy Syst. 8(6), 746–752 (2000)

    Article  Google Scholar 

  15. Xu, Z.S.: EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 12(6), 791–810 (2004)

    Article  MATH  Google Scholar 

  16. Xu, Z.S.: A method based on linguistic aggregation operators for group decision making with linguistic preference relations. Inf. Sci. 166(1–4), 19–30 (2004)

    Article  MATH  Google Scholar 

  17. Herrera, F., Herrera-Viedma, E., Verdegay, J.L.: Direct approach processes in group decision making using linguistic OWA operators. Fuzzy Sets Syst. 79(2), 175–190 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Xu, Z.S.: Uncertain Multiple Attribute Decision Making: Methods and Applications. Tsinghua University Press, Beijing (2004)

    Google Scholar 

  19. Wang, J.Q., Lu, P., Zhang, H.Y., et al.: Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic information. Inf. Sci. 274, 177–191 (2014)

    Article  Google Scholar 

  20. Wei, G.W.: A method for multiple attribute group decision making based on the ET-WG and ET-OWG operators with 2-tuple linguistic information. Expert Syst. Appl. 37(12), 7895–7900 (2010)

    Article  Google Scholar 

  21. Wei, G.W.: Some harmonic aggregation operators with 2-tuple linguistic assessment information and their application to multiple attribute group decision making. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 19(6), 977–998 (2011)

    Article  MATH  Google Scholar 

  22. Wang, J.Q., Wang, D.D., Zhang, H.Y., et al.: Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators. Soft. Comput. 19(2), 389–405 (2015)

  23. Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  24. Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–356 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  25. Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Trans. Syst. Man Cybern. 23(2), 610–614 (1993)

    Article  MATH  Google Scholar 

  26. Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst. 79(3), 403–405 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  27. Xu, Z.S., Cai, X.Q.: Recent advances in intuitionistic fuzzy information aggregation. Fuzzy Optim. Decis. Mak. 9(4), 359–381 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  28. Atanassov, K.T.: Intuitionistic Fuzzy Sets: Thoery and Applications. Physica, Heidelberg (1999)

    Book  Google Scholar 

  29. Bustince, H., Herrera, F., Montero, J.: Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Physica, Heidelberg (2007)

    Google Scholar 

  30. Xu, Z.S., Cai, X.Q.: Intuitionistic Fuzzy Information Aggregation: Theory and Applications. Springer, New York (2012)

    Book  Google Scholar 

  31. Xu, Z.S., Yager, R.R.: Some geometric aggregation operators based on intuitionistic fuzzy sets. Int. J. Gen Syst. 35(4), 417–433 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  32. Hong, D.H., Choi, C.H.: Multicriteria fuzzy decision-making problems based on vague set theory. Fuzzy Sets Syst. 114, 103–113 (2000)

    Article  MATH  Google Scholar 

  33. Xu, Z.S.: Intuitionistic fuzzy aggregation operators. IEEE Trans. Fuzzy Syst. 15(6), 1179–1187 (2007)

    Article  Google Scholar 

  34. Wang, J.Q., Zhang, H.Y.: Multicriteria decision-making approach based on atanassov’s intuitionistic fuzzy sets with incomplete certain information on weights. IEEE Trans. Fuzzy Syst. 21(3), 510–515 (2013)

    Article  Google Scholar 

  35. Tan, C.Q.: Generalized intuitionistic fuzzy geometric aggregation operator and its application to multi-criteria group decision making. Soft. Comput. 15(5), 867–876 (2011)

    Article  MATH  Google Scholar 

  36. Grzegorzewski, P.: Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric. Fuzzy Sets Syst. 148(2), 319–328 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  37. Xu, Z.S., Chen, J.: An overview of distance and similarity measures of intuitionistic fuzzy sets. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 16(4), 529–555 (2008)

    Article  MATH  Google Scholar 

  38. Xu, Z.S., Chen, J., Wu, J.J.: Clustering algorithm for intuitionistic fuzzy sets. Inf. Sci. 178(19), 3775–3790 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  39. Yue, Z.L., Jia, Y.Y., Ye, G.D.: An approach for multiple attribute group decision making based on intuitionistic fuzzy information. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 17(3), 317–332 (2009)

    Article  MATH  Google Scholar 

  40. Szmidt, E., Kacprzyk, J.: Distances between intuitionistic fuzzy sets. Fuzzy Sets Syst. 114(3), 505–518 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  41. Vlachos, I.K., Sergiadis, G.D.: Intuitionistic fuzzy information—Applications to pattern recognition. Pattern Recogn. Lett. 28(2), 197–206 (2007)

    Article  Google Scholar 

  42. Zhao, H., Xu, Z.S., Ni, M.F., et al.: Generalized aggregation operators for intuitionistic fuzzy sets. Int. J. Intell. Syst. 25(1), 1–30 (2010)

    Article  MATH  Google Scholar 

  43. Xia, M.M., Xu, Z.S.: Generalized point operators for aggregating intuitionistic fuzzy information. Int. J. Intell. Syst. 25(11), 1061–1080 (2010)

    MATH  Google Scholar 

  44. Tan, C.Q., Chen, X.H.: Induced intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Int. J. Intell. Syst. 26(7), 659–686 (2011)

    Article  Google Scholar 

  45. Tan, C.Q., Jiang, Z.Z., Chen, X.H.: Some issues on quasi-arithmetic intuitionistic fuzzy OWA operators. Appl. Math. Inf. Sci. 7(3), 955–961 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  46. Wang, J.Q., Han, Z.Q., Zhang, H.Y.: Multi-criteria group decision-making method based on intuitionistic interval fuzzy information. Group Decis. Negot. 23, 715–733 (2014)

    Article  Google Scholar 

  47. Shu, M.H., Cheng, C.H., Chang, J.R.: Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly. Microelectron. Reliab. 46(12), 2139–2148 (2006)

    Article  Google Scholar 

  48. Wang, J.Q., Zhang, Z.: Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems. J. Syst. Eng. Electron. 20(2), 321–326 (2009)

    Google Scholar 

  49. Wang, J.Q., Li, H.B.: Multi-criteria decision-making method based on aggregation operators for intuitionistic linguistic fuzzy numbers. Control Decis. 25(10), 1571–1584 (2010)

    MathSciNet  Google Scholar 

  50. Wang, J.Q., Nie, R.R., Zhang, H.Y., et al.: New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis. Inf. Sci. 251, 79–95 (2013)

    Article  MathSciNet  Google Scholar 

  51. Wu, J., Cao, Q.W.: Same families of geometric aggregation operators with intuitionistic trapezoidal fuzzy numbers. Appl. Math. Model. 37(1–2), 318–327 (2013)

    Article  MathSciNet  Google Scholar 

  52. Wan, S.P., Dong, J.Y.: Method of intuitionistic trapezoidal fuzzy number for multi-attribute group decision. Control Decis. 25(5), 773–776 (2010)

    MathSciNet  Google Scholar 

  53. Liu, P.D.: Some generalized dependent aggregation operators with intuitionistic linguistic numbers and their application to group decision making. J. Comput. Syst. Sci. 79(1), 131–143 (2013)

    Article  MATH  Google Scholar 

  54. Wang, X.F., Wang, J.Q., Yang, W.E.: Multi-criteria group decision making method based on intuitionistic linguistic aggregation operators. J. Intell. Fuzzy Syst. 26(1), 115–125 (2014)

    MATH  Google Scholar 

  55. Wang, J.Q., Wang, P., Wang, J., et al.: Atanassov’s interval-valued intuitionistic linguistic multi-criteria group decision-making method based on trapezium cloud model. IEEE Trans. Fuzzy Syst. (2014). doi:10.1109/TFUZZ.2014.2317500

    Google Scholar 

  56. Xu, Z.S.: Group decision making based on multiple types of linguistic preference relations. Inf. Sci. 178(2), 452–467 (2008)

    Article  MATH  Google Scholar 

  57. Xu, Z.S.: An overview of methods for determining OWA weights. Int. J. Intell. Syst. 20(8), 843–865 (2005)

    Article  MATH  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (No. 71271218, 71221061 and 61174075), the Humanities and Social Science Foundation of the Ministry of Education of China (No. 12YJA630114 and 13YJC630200), and the Natural Science Foundation of Hunan Province of China (No. 2015JJ2047). The authors are very grateful to the editors and the anonymous reviewers for their constructive comments and suggestions that have led to an improved version of this paper.

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  1. School of Business, Central South University, Changsha, 410083, China

    Jianqiang Wang

  2. School of Science, Hunan University of Technology, Zhuzhou, 412007, China

    Xinfan Wang & Shengyue Deng

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  1. Xinfan Wang
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  2. Jianqiang Wang
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  3. Shengyue Deng
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Correspondence to Jianqiang Wang.

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Wang, X., Wang, J. & Deng, S. Some Geometric Operators for Aggregating Intuitionistic Linguistic Information. Int. J. Fuzzy Syst. 17, 268–278 (2015). https://doi.org/10.1007/s40815-015-0007-6

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  • DOI: https://doi.org/10.1007/s40815-015-0007-6

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