Title: Diminishing Choquet Hesitant 2-Tuple Linguistic Aggregation Operator for Multiple Attributes Group Decision Making
Author(s): Ismat Beg, Raja Noshad Jamil, Tabasam Rashid
Pages: 76-104
Cite as:
Ismat Beg, Raja Noshad Jamil, Tabasam Rashid, Diminishing Choquet Hesitant 2-Tuple Linguistic Aggregation Operator for Multiple Attributes Group Decision Making, Int. J. Anal. Appl., 17 (1) (2019), 76-104.


In this article, we develop a diminishing hesitant 2-tuple averaging operator (DH2TA) for hesitant 2-tuple linguistic arguments. DH2TA work in the way that it aggregate all hesitant 2-tuple linguistic elements and during the aggregation process it also controls the hesitation in translation of the resultant aggregated linguistic term. We develop a scalar product for hesitant 2-tuple linguistic elements and based on the scalar product a weighted diminishing hesitant 2-tuple averaging operator (DWH2TA) is introduced. Moreover, combining Choquet integral with hesitant 2-tuple linguistic information, the diminishing Chouqet hesitant 2-tuple average operator (DCH2TA) is defined. The proposed operators higher reflect the correlations among the elements. After investigating the properties of these operators, a multiple attribute decision making method based on DCH2TA operator is proposed. Finally, an example is given to illustrate the significance and usefulness of proposed method.

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  1. R. D. Andr´es, M. Espinilla and L. Mart´ınez, An extended hierarchical linguistic model for managing integral evaluation, Int. J. Comput. Intell. Syst. 3 (4) (2010), 486–500. Google Scholar

  2. R. D. Andr´es, J.L. Garc´ıa-Lapresta and L. Mart´ınez, A multi-granular linguistic model for management decision-making in performance appraisal, Soft Computing, 14 (1) (2010), 21–34. Google Scholar

  3. C. Araz and I. Ozkarahan, Supplier evaluation and management system for strategic sourcing based on a new multicriteria sorting procedure, Int. J. Production Economics, 106 (2) (2007), 585–606. Google Scholar

  4. I. Beg and T. Rashid, Multi-criteria of bike purchasing using fuzzy choquet integral, J. Fuzzy Math. 22 (3)(2014), 677-694. Google Scholar

  5. I. Beg and T. Rashid, Hesitant 2-tuple linguistic information in multiple attributes group decision making, J. Intell. Fuzzy Syst. 30 (2016), 109–116. Google Scholar

  6. I. Beg and T. Rashid, Modelling uncertainties in multi-criteria decision making using distance measure and TOPSIS for hesitant fuzzy sets, J. Artif. Intell. Soft Comput. Res. 7(2)(2017), 103-109. Google Scholar

  7. C. Bonferroni, Sulle medie multiple di potenze, Bolletino Matematica Italiana, 5 (1950), 267–270. Google Scholar

  8. C. T. Chen, C. T. Lin, and S. F. Huang, A fuzzy approach for supplier evaluation and selection in supply chain management, Int. J. Production Economics, 102 (2) (2006), 289–301. Google Scholar

  9. C.T. Chen, P. F. Pai and W. Z. Hung, An integrated methodology using linguistic promethee and maximum deviation method for third-party logistics supplier selection, Int. J. Comput. Intell. Syst. 3 (4) (2010), 438–451. Google Scholar

  10. Y. Chen, X. Zeng M. Happiette, P. Bruniaux, R. Ng and W. Yu, Optimisation of garment design using fuzzy logic and sensory evaluation techniques, Eng. Appl. Artif. Intell. 22 (2) (2009), 272–282. Google Scholar

  11. G. Choquet, Theory of capacities. Ann. Inst. Fourier, 5 (1953), 131–295. Google Scholar

  12. S. Y. Chou and Y. H. Chang, A decision support system for supplier selection based on a strategy-aligned fuzzy SMART approach, Expert Syst. Appl. 34 (4) (2008), 2241–2253. Google Scholar

  13. R. Degani and G. Bortolan, The problem of linguistic approximation in clinical decision making, Int. J. Approx. Reason. 2 (1988), 143–162. Google Scholar

  14. M. Delgado, J.L. Verdegay and M.A. Vila, On aggregation operations of linguistic labels, Int. J. Intell. Syst. 8 (3) (1993), 351–370. Google Scholar

  15. Y.C. Dong, C.C. Li and F. Herrera, An optimization-based approach to adjusting the unbalanced linguistic preference relations to obtain a required consistency level, Inf. Sci. 292 (2015), 27–38. Google Scholar

  16. D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Kluwer Academic, New York, 1980. Google Scholar

  17. C. X. Feng, J. Wang, and J. S. Wang, An optimization model for concurrent selection of tolerances and suppliers, Comput. Ind. Eng. 40 (1-2) (2001), 15–33. Google Scholar

  18. N. Fenton and W. Wang, Risk and confidence analysis for fuzzy multicriteria decision making, Knowl.based Syst. 19 (6) (2006), 430–437. Google Scholar

  19. J.L. Garc´ıa-Lapresta, B. Llamazares and M. Mart´ınez-Panero, A social choice analysis of the Borda rule in a general linguistic framework, Int. J. Comput. Intell. Syst. 3 (4) (2010), 501–513. Google Scholar

  20. R. E. Gregory, Source selection: a matrix approach, J. Purchas. Mater. Manag. 22 (2) (1986), 24–29. Google Scholar

  21. S. H. Ha and R. Krishnan, A hybrid approach to supplier selection for the maintenance of a competitive supply chain, Expert Syst. Appl. 34 (2) (2008), 1303–1311. Google Scholar

  22. F. Herrera and L. Mart´ınez, A 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst. 8 (2000), 746–752. Google Scholar

  23. F. Herrera and L. Mart´ınez, The 2-tuple linguistic computational model advantages of its linguistic description, accuracy and consistency, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 9 (2001), 33–48. Google Scholar

  24. F. Herrera, E. Herrera-Viedma and L. Mart´ınez, A fuzzy linguistic methodology to deal with unbalanced linguistic term sets, IEEE Trans. Fuzzy Syst. 16(2) (2008), 354–370. Google Scholar

  25. E. Herrera-Viedma, A.G. L´opez-Herrera, M. Luque and C. Porcel, A fuzzy linguistic IRS model based on a 2-tuple fuzzy linguistic approach, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 15 (2) (2007), 225–250. Google Scholar

  26. V.N. Huynh and Y. Nakamori, A satisfactory-oriented approach to multi-expert decision-making under linguistic assessments, IEEE Trans. Syst. Man Cybern. 35 (2) (2005), 184–196. Google Scholar

  27. H. Ishibuchi, T. Nakashima and M. Nii, Classification and Modeling with Linguistic Information Granules: Advanced Approaches to Linguistic Data Mining, Springer, Berlin, 2004. Google Scholar

  28. Y.P. Jiang and Z.P. Fan, Property analysis of the aggregation operators for 2-tuple linguistic information, Control Decision, 18(6) (2003), 754–757. Google Scholar

  29. D.K. Joshi, I. Beg and S. Kumar, Hesitant probabilistic fuzzy linguistic sets with applications in multi-criteria group decision making problems, Mathematics 6(4)(2018), Article ID 47. Google Scholar

  30. A. Khalid and I. Beg, Incomplete hesitant fuzzy preference relations in group decision making, Int. J. Fuzzy Syst. 19(3)(2017), 637-645. Google Scholar

  31. G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall PTR, 1995. Google Scholar

  32. C. Labreuche and M. Grabisch, Generalized Choquet-like aggregation functions for handling bipolar scales, Eur. J. Oper. Res. 172 (3) (2006), 931–955. Google Scholar

  33. J. Lawry, A framework for linguistic modelling, Artif. Intell. 155 (1–2) (2004), 1–39. Google Scholar

  34. C. C. Li, Y. Donga, F. Herrera, E. H. Viedm and L. Mart´ınez, Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching, Inf. Fusion, 33 (2017), 29-40. Google Scholar

  35. J. Lu, G. Zhang and F. Wu, Team situation awareness using web-based fuzzy group decision support systems, Int. J. Comput. Intell. Syst. 1 (1) (2008), 51–60. Google Scholar

  36. J. Lu, Y. Zhu, X. Zeng, L. Koehl, J. Ma and G. Zhang, A linguistic multi-criteria group decision support system for fabric hand evaluation, Fuzzy Optim. Decis. Mak. 8 (4) (2009), 395–413. Google Scholar

  37. O. Martin and G.J. Klir, On the problem of retranslation in computing with perceptions, Int. J. General Syst. 35 (6) (2006), 655–674. Google Scholar

  38. L. Mart´ınez, D. Ruan, F. Herrera, E. Herrera-Viedma and P.P. Wang, Linguistic decision making: tools and applications, Inf. Sci. 179 (14) (2009), 2297–2298. Google Scholar

  39. L. Mart´ınez, J. Liu, D. Ruan and J.B. Yang, Dealing with heterogeneous information in engineering evaluation processes, Inf. Sci. 177 (7) (2007), 1533–1542. Google Scholar

  40. L. Mart´ınez, J. Liu, J. B. Yang and F. Herrera, A multigranular hierarchical linguistic model for design evaluation based on safety and cost analysis, Int. J. Intell. Syst. 20 (12) (2005), 1161–1194. Google Scholar

  41. L. Mart´ınez, R. M. Rodr´ıguez and F. Herrera, 2-tuple Linguistic Model Computing with words in Decision Making, Springer (2015). Google Scholar

  42. J.M. Mendel and D. Wu, Perceptual Computing: Aiding People in Making Subjective Judgments, IEEE-Wiley, (2010). Google Scholar

  43. R. Mesiar and A. Kolesarova, On the fuzzy set theory and aggregation functions: Histor and some recent advances, Iran. J. Fuzzy Syst. in press. Google Scholar

  44. W.R.W. Mohd and L. Abdullah, Aggregation methods in group decision making: A decade survey, Informatica 41 (2017), 71–86. Google Scholar

  45. G.A. Miller, The magical number seven, plus or minus two: some limits on our capacity of processing information, Psychol. Rev. 63 (1956), 81–97. Google Scholar

  46. R. F. Muirhead, Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters, Proc. Edinburgh Math. Soc. 21(3) (1902), 144–162. Google Scholar

  47. R. Narasimhan, An analytic approach to supplier selection, J. Purchas. Supply Manag. 1 (1983), 27–32. Google Scholar

  48. R. L. Nydick and R. P. Hill, Using the Analytic Hierarchy Process to structure the supplier selection procedure, Int. J. Purchas. Mat. Manag. 28 (2) (1992), 31–36. Google Scholar

  49. L. P´erez-Dom´ınguez, L. Rodr´ıguez-Pic´on, A. Alvarado-Iniesta, D.L. Cruz and Z.S. Xu, MOORA under Pythagorean fuzzy set for multiple criteria decision making, Complexity, 2018 (2008), Article ID 2602376, 10 pages Google Scholar

  50. I. Saad, S. Hammadi, M. Benrejeb and P. Borne, Choquet integral for criteria aggregation in the flexible job-shop scheduling problems, Math. Comput. Simul. 76 (2008), 447–462. Google Scholar

  51. H. Shi, H. C. Liu, P. Li, X. and G. Xu, An integrated decision making approach for assessing healthcare waste treatment technologies from a multiple stakeholder, Waste Manag. 59 (2017), 508-517. Google Scholar

  52. W. R. Soukup, Supplier selection strategies, J. Purchas. Mat. Manag. 23 (3) (1987), 7–12. Google Scholar

  53. C. Q. Tan and X. H. Chen, Intuitionistic fuzzy Choquet integral operator for multi-criteira decision making, Expert Syst. Appl. 37 (2010), 149–157. Google Scholar

  54. Thompson, Vendor prole analysis, J. Purchas. Mat. Manag. 26 (1) (1990), 11–18. Google Scholar

  55. V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529–539. Google Scholar

  56. R. J. Vokurka, J. Choobineh, and L. Vadi, A prototype expert system for the evaluation and selection of potential suppliers, Int. J. Oper. Prod. Manag. 16 (12) (1996), 106–127. Google Scholar

  57. P. Wakker, Additive representations of preferences, Kluwer Academic Publishers, (1999). Google Scholar

  58. Z. Wang and G. Klir, Fuzzy measure theory, New York: Plenum press, (1992). Google Scholar

  59. J.H. Wang and J.Y. Hao, A new version of 2-tuple fuzzy linguistic representation model for computing with words, IEEE Trans. Fuzzy Syst. 14(3) (2006), 435–445. Google Scholar

  60. G.W. Wei, Method for two-tuple linguistic group decision making based on the ET-WG and ET-OWG operators, Expert Syst. Appl. 37 (2010), 7895–7900. Google Scholar

  61. M.M. Xia, Z.S. Xu and B. Zhu, Geometric Bonferroni means with their application in multi-criteria decision making, Knowl. based Syst. 40 (2013), 88-100. Google Scholar

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

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

  64. Z. Xu, S. Shang, W. Qian and W. Shu, A method for fuzzy risk analysis based on the new similarity of trapezoidal fuzzy numbers, Expert Syst. Appl. 37 (3) (2010), 1920–1927. Google Scholar

  65. R.R. Yager, A new methodology for ordinal multi objective decisions based on fuzzy sets, Decision Sci. 12 (1981), 589–600. Google Scholar

  66. R.R. Yager, Computing with Words and Information/Intelligent Systems 2: Applications, Chapter Approximate Reasoning as a Basis for Computing with Words, Physica Verlag, (1999), 50–77. Google Scholar

  67. R.R. Yager, Induced aggregation operators, Fuzzy Sets Syst. 137 (2003), 59–69. Google Scholar

  68. R.R. Yager, On the retranslation process in Zadeh’s paradigm of computing with words, IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics, 34 (2) (2004), 1184–1195. Google Scholar

  69. R.R. Yager, OWA aggregation of intuitionistic fuzzy sets, Int. J. General Syst. 38 (6) (2009), 617–641. Google Scholar

  70. W. Yang and Z. Chen, New aggregation operators based on the Choquet integral and 2-tuple linguistic information, Expert Syst. Appl. 39 (2012), 2662–2668 Google Scholar

  71. L. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353. Google Scholar

  72. L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Part III, Inf. Sci. 9 (1) (1975), 43–80. Google Scholar

  73. Y. Zhang and Z.P. Fan, An approach to linguistic multiple attribute decision-making with linguistic information based on ELOWA operator, Syst. Eng. 24(12) (2006), 324–339. Google Scholar

  74. B. Zhu, Z. S. Xu and M. M. Xia, Hesitant fuzzy geometric Bonferroni means, Inf. Sci. 205 (2012), 72–85. Google Scholar


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