##### Title: Diminishing Choquet Hesitant 2-Tuple Linguistic Aggregation Operator for Multiple Attributes Group Decision Making

##### 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.#### Abstract

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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#### References

- 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.
- 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.
- 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.
- I. Beg and T. Rashid, Multi-criteria of bike purchasing using fuzzy choquet integral, J. Fuzzy Math. 22 (3)(2014), 677-694.
- I. Beg and T. Rashid, Hesitant 2-tuple linguistic information in multiple attributes group decision making, J. Intell. Fuzzy Syst. 30 (2016), 109–116.
- 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.
- C. Bonferroni, Sulle medie multiple di potenze, Bolletino Matematica Italiana, 5 (1950), 267–270.
- 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.
- 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.
- 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.
- G. Choquet, Theory of capacities. Ann. Inst. Fourier, 5 (1953), 131–295.
- 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.
- R. Degani and G. Bortolan, The problem of linguistic approximation in clinical decision making, Int. J. Approx. Reason. 2 (1988), 143–162.
- M. Delgado, J.L. Verdegay and M.A. Vila, On aggregation operations of linguistic labels, Int. J. Intell. Syst. 8 (3) (1993), 351–370.
- 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.
- D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, Kluwer Academic, New York, 1980.
- 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.
- N. Fenton and W. Wang, Risk and confidence analysis for fuzzy multicriteria decision making, Knowl.based Syst. 19 (6) (2006), 430–437.
- 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.
- R. E. Gregory, Source selection: a matrix approach, J. Purchas. Mater. Manag. 22 (2) (1986), 24–29.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- H. Ishibuchi, T. Nakashima and M. Nii, Classification and Modeling with Linguistic Information Granules: Advanced Approaches to Linguistic Data Mining, Springer, Berlin, 2004.
- 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.
- 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.
- A. Khalid and I. Beg, Incomplete hesitant fuzzy preference relations in group decision making, Int. J. Fuzzy Syst. 19(3)(2017), 637-645.
- G.J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications, Prentice-Hall PTR, 1995.
- C. Labreuche and M. Grabisch, Generalized Choquet-like aggregation functions for handling bipolar scales, Eur. J. Oper. Res. 172 (3) (2006), 931–955.
- J. Lawry, A framework for linguistic modelling, Artif. Intell. 155 (1–2) (2004), 1–39.
- 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.
- 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.
- 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.
- O. Martin and G.J. Klir, On the problem of retranslation in computing with perceptions, Int. J. General Syst. 35 (6) (2006), 655–674.
- 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.
- 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.
- 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.
- L. Mart´ınez, R. M. Rodr´ıguez and F. Herrera, 2-tuple Linguistic Model Computing with words in Decision Making, Springer (2015).
- J.M. Mendel and D. Wu, Perceptual Computing: Aiding People in Making Subjective Judgments, IEEE-Wiley, (2010).
- R. Mesiar and A. Kolesarova, On the fuzzy set theory and aggregation functions: Histor and some recent advances, Iran. J. Fuzzy Syst. in press.
- W.R.W. Mohd and L. Abdullah, Aggregation methods in group decision making: A decade survey, Informatica 41 (2017), 71–86.
- 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.
- 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.
- R. Narasimhan, An analytic approach to supplier selection, J. Purchas. Supply Manag. 1 (1983), 27–32.
- 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.
- 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
- 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.
- 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.
- W. R. Soukup, Supplier selection strategies, J. Purchas. Mat. Manag. 23 (3) (1987), 7–12.
- C. Q. Tan and X. H. Chen, Intuitionistic fuzzy Choquet integral operator for multi-criteira decision making, Expert Syst. Appl. 37 (2010), 149–157.
- Thompson, Vendor prole analysis, J. Purchas. Mat. Manag. 26 (1) (1990), 11–18.
- V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst. 25 (2010), 529–539.
- 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.
- P. Wakker, Additive representations of preferences, Kluwer Academic Publishers, (1999).
- Z. Wang and G. Klir, Fuzzy measure theory, New York: Plenum press, (1992).
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- R.R. Yager, A new methodology for ordinal multi objective decisions based on fuzzy sets, Decision Sci. 12 (1981), 589–600.
- 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.
- R.R. Yager, Induced aggregation operators, Fuzzy Sets Syst. 137 (2003), 59–69.
- 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.
- R.R. Yager, OWA aggregation of intuitionistic fuzzy sets, Int. J. General Syst. 38 (6) (2009), 617–641.
- 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
- L. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338–353.
- L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning, Part III, Inf. Sci. 9 (1) (1975), 43–80.
- 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.
- B. Zhu, Z. S. Xu and M. M. Xia, Hesitant fuzzy geometric Bonferroni means, Inf. Sci. 205 (2012), 72–85.