Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS
Tóm tắt
A generalized trapezoidal-valued intuitionistic fuzzy geometric aggregation operator is proposed which is then used to aggregate decision makers’ opinions in group decision making process. An extension of TOPSIS, a multi-criteria trapezoidal-valued intuitionistic fuzzy decision making technique, to a group decision environment is also proposed, where inter-dependent or interactive characteristics among criteria and preference of decision makers are under consideration. Furthermore, Choquet integral-based distance between trapezoidal-valued intuitionistic fuzzy values is defined. Combining the trapezoidal-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based distance, an extension of TOPSIS method is developed to deal with a multi-criteria trapezoidal-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is provided to understand the proposed method.
Tài liệu tham khảo
Angilella, S., Greco, S., Lamantia, F., Matarazzo, B.: Assessing non-additive utility for multicriteria decision aid. Eur. J. Oper. Res. 158, 734–744 (2004)
Angilella, S., Greco, S., Matarazzo, B.: Non-additive robust ordinal regression: A multiple criteria decision model based on the Choquet integral. Eur. J. Oper. Res. 201, 277–288 (2010)
Ashtiani, B., Haghighirad, F., Makui, A., Montazer, G.: Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets. Appl. Soft. Comput. 9, 457–461 (2009)
Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Atanassov, K.: Operators over interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 64(2), 159–174 (1994)
Atanassov, K.: Intuitionistic fuzzy sets. Theory and applications. Physica-Verlag, Heidelberg (1999)
Atanassov, K., Gargov, G.: Interval-valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 31, 343–349 (1989)
Boran, F.E., Gen, S., Kurt, M., Akay, D.: A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst. Appl. 36, 11363–11368 (2009)
Büyüközkan, G., Ruan, D.: Choquet integral based aggregation approach to software development risk assessment. Inf. Sci. 180, 441–451 (2010)
Chen, C.T.: Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets Syst. 114, 1–9 (2000)
Chen, S.J., Hwang, C.L.: Fuzzy multiple attribute decision making. Springer, Berlin (1992)
Chen, T.-Y., Tsao, C.-Y.: The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst. 159, 1410–1428 (2008)
Choquet, G.: Theory of capacities. Annales del Institut Fourier 5, 131–295 (1953)
Chu, T.-C., Lin, Y.-C.: An interval arithmetic based fuzzy TOPSIS model. Expert Syst. Appl. 36, 10870–10876 (2009)
Demirel, T., Demirel, N.C., Kahraman, C.: Multi-criteria warehouse location selection using Choquet integral. Expert Syst. Appl. 37, 3943–3952 (2010)
Grabisch, M., Labreuche, C.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Ann. Oper. Res. 175(1), 247–286 (2010)
Grabisch, M.: Fuzzy integral in multicriteria decision making. Fuzzy Sets Syst. 69, 279–298 (1995)
Grabisch, M.: A new algorithm for identifying fuzzy measures and its application to pattern recognition. In: International joint conference 4th IEEE international conference on fuzzy systems and the 2nd international fuzzy engineering symposium, Yokohama, pp. 145–150 (1995)
Grabisch, M.: The representation of importance and interaction of features by fuzzy measures. Pattern Recogn. Lett. 17, 567–575 (1996)
Grabisch, M.: The application of fuzzy integrals in multicriteria decision making. Eur. J. Oper. Res. 89, 445–456 (1996)
Grabisch, M.: Alternative representations of discrete fuzzy measures for decision making. Int. J. Uncertain Fuzziness Knowl. Based Syst. 5, 587–607 (1997)
Grabisch, M., Murofushi, T., Sugeno, M.: Fuzzy measure and integrals. Physica-Verlag, New York (2000)
Herrera, F., Herrera-Viedma, E., Martinez, L.: A fusion approach for managing multi-granularity linguistic term sets in decision making. Fuzzy Sets Syst. 114, 43–58 (2000)
Hu, Y.C.: Classification performance evaluation of single-layer perceptron with Choquet integral-based TOPSIS. Appl. Intell. 29(3), 204–215 (2000)
Hwang, C.L., Yoon, K.: Multiple attributes decision making methods and applications. Berlin. Springer, Heidelberg (1981)
Ishii, K., Sugeno, M.: A model human evaluation process using fuzzy measure. Int. J. Man. Mach. Stud. 22, 19–38 (1985)
Jahanshahloo, G.R., Hosseinzadeh, L.otfi., F., Izadikhah, M.: Extension of the TOPSIS method for decision-making problems with fuzzy data. Appl. Math. Comput. 181, 1544–1551 (2006)
Keeney, R.L., Raiffa, H.: Decision with multiple objectives. Wiley, New York (1976)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)
Kojadinovic, I.: Modeling interaction phenomena using fuzzy measures: on the notions of interaction and independence. Fuzzy Sets Syst. 135, 317–340 (2002)
Kuo, M.S., Tzeng, G.H., Huang, W.C.: Group decision-making based on concepts of ideal and anti-ideal points in a fuzzy environment. Math. Comput. Model. 45, 324–339 (2007)
Labreuche, C., Grabisch, M.: The Choquet integral for the aggregation of interval scales in multicriteria decision making. Fuzzy Sets Syst. 137, 11–26 (2003)
Labreuche, C., Grabisch, M.: Generalized Choquet-like aggregation functions for handling bipolar scales. Eur. J. Oper. Res. 172(3), 931–955 (2006)
Liginlal, D., Ow, T.T.: Modeling attitude to risk in human decision processes: An application of fuzzy measures. Fuzzy Sets Syst. 157, 3040–3054 (2006)
Li, D.F., Wang, Y.C., Liu, S., Shan, F.: Fractional programming methodology for multi-attribute group decision making using IFS. Appl. Soft Comput. 8(1), 219–225 (2008)
Mahdavi, I., Mahdavi-Amiri, N., Heidarzade, A., Nourifar, R.: Designing a model of fuzzy TOPSIS in multiple criteria decision making. Appl. Math. Comput. 206, 607–617 (2008)
Meyer, P., Roubens, M.: On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support. Fuzzy Sets Syst. 157, 927–938 (2006)
Negi, D.S.: Fuzzy analysis and optimization. PhD thesis. Department of Industrial Engineering, Kansas State University (1989)
Onisawa, T., Sugeno, M., Nishiwaki, Y., Kawai, H., Harima, Y.: Fuzzy measure analysis of public attitude towards the use of nuclear energy. Fuzzy Sets Syst. 120, 259–289 (1986)
Roubens, M.: Interaction between criteria and definition of weights in MCDA problems. In: Proceedings of the 44th meeting of the european working group multicriteria aid for decisions, Brussels, Belgium (1996)
Saad, I., Hammadi, S., Benrejeb, M., Borne, P.: Choquet integral for criteria aggregation in the flexible job-shop scheduling problems. Math. Comput. Simul. 76, 447–462 (2008)
Schnatter, S.F.: On statistical inference for fuzzy data with applications to descriptive statistics. Fuzzy Sets Syst. 50, 143–165 (1992)
Shieh, J.I., Wu, H.H., Liu, H.C.: Applying a complexity-based Choquet integral to evaluate students’ performance. Expert Syst. Appl. 36, 5100–5106 (2009)
Su, Z.X., Xia, G.P., Chen, M.Y., Wang, L.: Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making. Expert Syst. Appl. 39, 1902–1920 (2012)
Sugeno, M.: Theory of fuzzy integral and its application. Tokyo Institute of Technology, Doctorial Dissertation (1974)
Tan, C., Zhang, Q.: Fuzzy multiple attribute decision making based on interval-valued intuitionistic fuzzy sets. In: Proceeding of the 2006 IEEE international conference on system, man, and cybernetics, October, Taipei, pp. 1404–1407 (2006)
Tan, C.: A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS. Expert Syst. Appl. 38, 3023–3033 (2011)
Tan, C.Q., Chen, X.H.: Intuitionistic fuzzy Choquet integral operator for multi-criteira decision making. Expert Syst. Appl. 37, 149–157 (2010a)
Tan, C.Q., Chen, X.H.: Induced Choquet ordered averaging operator and its application to group decision making. Int. J. Intell. Syst. 25, 59–82 (2010b)
Tseng, M.L., Chiang, J.H., Lan, L.W.: Selection of optimal supplier in supply chain management strategy with analytic network process and Choquet integral. Comput. Ind. Eng. 57, 330–340 (2009)
Tseng, M.L., Yang, Y.P.O., Lin, C.T., Chen, C.B.: Hierarchical MADM with fuzzy integral for evaluating enterprise intranet web sites. Inf. Sci. 169(3–4), 409–426 (2005)
Wakker, P.: Additive representations of preferences. Kluwer Academic Publishers (1999)
Wang, J.H., Hao, J.Y.: A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans. Fuzzy Syst. 14(3), 435–445 (2006)
Wang, T.C., Chang, T.H.: Application of TOPSIS in evaluating initial training aircraft under a fuzzy environment. Expert Syst. Appl. 33, 870–880 (2007)
Wang, Y.J., Lee, H.S.: Generalizing TOPSIS for fuzzy multiple-criteria group decision-making. Comput. Math. Appl 53, 1762–1772 (2007)
Wang, Z., Klir, G.: Fuzzy measure theory. Plenum press, New York (1992)
Wei, G.W.: Some geometric aggregation functions and their application to dynamic multiple attribute decision making in the intuitionistic fuzzy setting. International Journal of Uncertainty. Fuzziness Knowl.-Based Sys. 17(2), 179–196 (2009)
Xu, Z.S.: Methods for aggregating interval-valued intuitionistic fuzzy information and their application to decision making. Control and Decision 22(2), 215–219 (2007)
Xu, Z.S.: Correlated linguistic information aggregation. Int. J. Uncertainty Fuzziness Knowl.-Based Syst. 17(5), 633–647 (2009)
Xu, Z.S.: Choquet integrals of weighted intuitionistic fuzzy information. Inf. Sci. 180, 726–736 (2010)
Xu, Z., Xia, M.: Induced generalized intuitionistic fuzzy operators. Knowl.-Based Syst. 24, 197–209 (2011)
Yager, R.R.: Induced aggregation operators. Fuzzy Sets Syst. 137, 59–69 (2003)
Yager, R.R.: OWA aggregation of intuitionistic fuzzy sets. Int. J. Gen. Syst. 38(6), 617–641 (2009)
Yang, W., Chen, Z.: The quasi-arithmetic intuitionistic fuzzy OWA operators. Knowl.-Based Syst. 27, 219–233 (2012)
Yeh, C.H., Deng, H.: A practical approach to fuzzy utilities comparison in fuzzy multicriteria analysis. Int. J. Approx. Reason. 35, 179–194 (2004)
Yeh, C.H., Deng, H., Chang, Y.H.: Fuzzy multicriteria analysis for performance evaluation of bus companies. Eur. J. Oper. Res. 126, 459–473 (2000)
Zadeh, L.A.: Fuzzy sets. Inf. Control. 8, 338–356 (1965)
Zimmermann, H.J.: Fuzzy Set Theory and Its Applications. Kluwer, Dordrecht (1991)