Integrating Interval Agreement Approach (IAA) with TOPSIS in Multi-Criteria Group Decision Making (MCGDM)

  • Authors

    • Elissa Nadia Madi
    • Binyamin Yusoff
    https://doi.org/10.14419/ijet.v7i3.28.23412
  • Interval Agreement Approach, TOPSIS, MCGDM.

  • Abstract

    This paper presents a proposed method to integrate Interval Agreement Approach (IAA) with Technique for order performance by similarity to ideal solution (TOPSIS) for Multi-Criteria Group Decision Making (MCGDM). The proposed method utilises IAA to model the preferences (word) given by decision maker in the initial step of TOPSIS-MCGDM. In real world, problems preferences may be given as imprecise or incomplete information. An issue has been raised about how to precisely modelling the preferences or word in the context of MCGDM. One of the strengths in IAA technique during the modelling process is it distinguished the two types of uncertainties (intra- and inter-) in different degree of freedom. The proposed method is able to capture the information from one or more intervals (with crisp or uncertain interval endpoints) associated with preferences given by the decision maker. This paper provides an example to illustrate the application of the proposed model.

     

     

  • References

    1. [1] J. M. Mendel, “The perceptual computer: an architecture for computing with words,†Proceedings of the 10th IEEE International Conference on Fuzzy Systems, 2001, pp. 35–38.

      [2] I. B. Türkşen, “Type 2 representation and reasoning for CWW,†Fuzzy Sets Syst., 127, 17–36, 2002.

      [3] J. M. Mendel, “An architecture for making judgments using computing with words,†Int. J. Appl. Math. Comput. Sci., 12(3), 325–335, 2002.

      [4] F. Herrera and E. Herrera-Viedma, “Linguistic decision analysis: Steps for solving decision problems under linguistic information,†Fuzzy Sets Syst., 115(1), 67–82, 2000.

      [5] I. B. Türkşen, “Meta-linguistic axioms as a foundation for computing with words,†Inf. Sci. (Ny)., 177(2), 332–359, 2007.

      [6] C. Wagner and H. Hagras, “Interpreting fuzzy set operations and multi level agreement in a computing with words context,†Proceedings of the IEEE Int. Conf. Fuzzy Syst., pp. 2139–2146, 2011.

      [7] C. Wagner, S. Miller, J. Garibaldi, T. D. Anderson, and C. T. Havens, “From interval-valued data to general type-2 fuzzy sets,†IEEE Trans. Fuzzy Syst., 2014.

      [8] F. Liu and J. M. Mendel, “An interval approach to fuzzistics for interval type-2 fuzzy sets,†Proceedings of the IEEE International Fuzzy Systems Conference, 2007, pp. 1–6.

      [9] S. Miller, C. Wagner, J. M. Garibaldi, and S. Appleby, “Constructing General Type-2 fuzzy sets from interval-valued data,†Proceedings of the IEEE International Conference on Fuzzy Systems, 2012, pp. 1–8.

      [10] A. Bilgin, H. Hagras, A. Malibari, M. J. Alhaddad, and D. Alghazzawi, “Towards a linear general type-2 fuzzy logic based approach for computing with words,†Soft Comput., 17(12), 2203–2222, 2013.

      [11] A. Bilgin, H. Hagras, A. Malibari, M. J. Alhaddad, and D. Alghazzawi, “Towards a general type-2 fuzzy logic approach for computing with words using linear adjectives,†Proceedings of the IEEE International Conference on Fuzzy Systems, 2012, pp. 1–8.

      [12] Y. Dong, G. Zhang, W.-C. Hong, and S. Yu, “Linguistic computational model based on 2-tuples and intervals,†IEEE Trans. Fuzzy Syst., 21, 1006–1018, 2013.

      [13] A. Halder, A. Chakraborty, A. Konar, and A. K. Nagar, “Computing with words model for emotion recognition by facial expression analysis using interval type-2 fuzzy sets,†Proceedings of the IEEE International Conference on Fuzzy Systems, 2013, pp. 1–8.

      [14] A. Kazemzadeh, “Toward a computational approach for natural language description of emotions,†Proceedings of the Lecture Notes in Computer Science, 2011, pp. 216–223.

      [15] A. Kazemzadeh, S. Lee, and S. Narayanan, “Fuzzy logic model for the meaning of emotion words,†IEEE Computational Intelligence Magazine, pp. 34–49, 2013.

      [16] X. Yang, L. Yan, H. Peng, and X. Gao, “Encoding words into Cloud models from interval-valued data via fuzzy statistics and membership function fitting,†Knowledge-Based Syst., 55, 114–124, 2014.

      [17] L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-Part II,†Inf. Sci. (Ny)., 8, 301–357, 1975.

      [18] L. A. Zadeh, “The concept of a linguistic variable and its application to approximate reasoning-Part I,†Inf. Sci. (Ny)., 8(3), 199–249, 1975.

      [19] L. A. Zadeh, “The concept of a linguistic variable and its application to approxirqate reasoning-Part III,†Inf. Sci. (Ny)., 9, 43–80, 1975.

      [20] P. Walley and G. de Cooman, “A behavioral model for linguistic uncertainty,†Inf. Sci. (Ny)., 134(1–4), 1–37, 2001.

      [21] L. Martinez, D. Ruan, and F. Herrera, “Computing with words in decision support systems: An overview on models and applications,†Int. J. Comput. Intell. Syst., 3(4), 382–395, 2010.

      [22] L. Martinez, D. Ruan, F. Herrera, E. Herrera-Viedma, and P. P. Wang, “Linguistic decision making: Tools and applications,†Inf. Sci. (Ny)., 179, 2297–2298, 2009.

      [23] L. A. Zadeh, “Fuzzy logic = Computing with words,†IEEE Trans. Fuzzy Syst., 4(2), 103–111, 1996.

      [24] J. M. Mendel, “Computing with words and its relationships with fuzzistics,†Inf. Sci. (Ny)., 177(4), 988–1006, 2007.

      [25] F. Liu and J. M. Mendel, “Encoding words into interval type-2 fuzzy sets using an interval approach,†IEEE Trans. Fuzzy Syst., 16(6), 1503–1521, 2008.

      [26] S. Coupland, J. M. Mendel, and D. Wu, “Enhanced interval approach for encoding words into interval type-2 fuzzy sets and convergence of the word FOUs,†Proceedings of the IEEE International Conference on Fuzzy Systems, 2010, pp. 1–8.

      [27] D. Wu, J. M. Mendel, and S. Coupland, “Enhanced interval approach for encoding words into interval type-2 fuzzy sets and its convergence analysis,†Fuzzy Syst. IEEE Trans., 20(3), 499–513, 2012.

      [28] T. Ozen, J. M. Garibaldi, and S. Musikasuwan, “Modelling the variation in human decision making,†Proceedings of the IEEE Annu. Meet. Fuzzy Information Process, pp. 617–622, 2004.

      [29] R. E. Bellman and L. A. Zadeh, “Decision-making in a fuzzy environment,†Manag. Sci., 17(4), B141–B164, 1970.

      [30] C.-T. Chen, “Extensions of the TOPSIS for group decision-making under fuzzy environment,†Fuzzy Sets Syst., 114(1), 1–9, 2000.

      [31] L.-W. Lee And S.-M. Chen, “Fuzzy multiple attributes group decision-making based on the extension of topsis method and interval type-2 fuzzy sets,†Proceedings of the Seventh International Conference on Machine Learning and Cybernetics, pp. 3260–3265, 2008.

      [32] G. R. Jahanshahloo, F. H. Lotfi, and M. Izadikhah, “An algorithmic method to extend TOPSIS for decision-making problems with interval data,†Appl. Math. Comput., 175(2), 1375–1384, 2006.

      [33] S.-M. Chen and L.-W. Lee, “Fuzzy multiple attributes group decision-making based on the interval type-2 TOPSIS method,†Expert Syst. Appl., 37(4), 2790–2798, 2010.

      [34] C. Wagner, S. Miller, and J. M. Garibaldi, “Similarity based applications for data-driven concept and word models based on type-1 and type-2 fuzzy sets,†Proceedings of the IEEE Int. Conf. Fuzzy Syst., pp. 1–9, 2013.

      [35] C. Wagner and H. Hagras, “Employing zSlices based general type-2 fuzzy sets to model multi level agreement,†Proceedings of the IEEE Symp. Adv. Type-2 Fuzzy Log. Syst., pp. 50–57, 2011.

      [36] C. Wagner and H. Hagras, “Toward general type-2 fuzzy logic systems based on zSlices,†IEEE Trans. Fuzzy Syst., 18(4), 637–660, 2010.

      [37] T. C. Chu and Y. C. Lin, “A fuzzy TOPSIS method for robot selection,†Int. J. Adv. Manuf. Technol., 21, 284–290, 2003.

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  • How to Cite

    Nadia Madi, E., & Yusoff, B. (2018). Integrating Interval Agreement Approach (IAA) with TOPSIS in Multi-Criteria Group Decision Making (MCGDM). International Journal of Engineering & Technology, 7(3.28), 163-169. https://doi.org/10.14419/ijet.v7i3.28.23412

    Received date: 2018-12-08

    Accepted date: 2018-12-08