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TOPSIS with belief structure for group belief multiple criteria decision making

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Abstract

The technique for order performance by similarity to ideal solution (TOPSIS) is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and the belief structure (BS) model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers’ judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.

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References

  1. C. L. Hwang, K. Yoon. Multiple Attribute Decision Making, Springer-Verlag, Berlin, 1981.

    MATH  Google Scholar 

  2. H. S. Shih, H. J. Shyur, E. S. Lee. An extension of TOPSIS for group decision making. Mathematical and Computer Modelling, vol. 45, no. 7, pp. 801–813, 2007.

    Article  MATH  Google Scholar 

  3. C. T. Chen, C. T. Lin, S. F. Huang. A fuzzy approach for supplier evaluation and selection in supply chain management. International Journal of Production Economics, vol. 102, no. 2, pp. 289–301, 2006.

    Article  Google Scholar 

  4. H. Deng, C. H. Yeh, R. J. Willis. Inter-company comparison using modified TOPSIS with objective weights. Computers & Operations Research, vol. 27, no. 10, pp. 963–973, 2000.

    Article  MATH  Google Scholar 

  5. M. F. Chen, G. H. Tzeng. Combining grey relation and TOPSIS concepts for selecting an expatriate host country. Mathematical and Computer Modelling, vol. 40, no. 13, pp. 1473–1490, 2004.

    Article  MATH  Google Scholar 

  6. Y. M. Wang, T. M. S. Elhag. Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment. Expert Systems with Applications, vol. 31, no. 2, pp. 309–319, 2006.

    Article  Google Scholar 

  7. T. C. Chu. Facility location selection using fuzzy TOPSIS under group decisions. International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, vol. 10, no. 6, pp. 687–701, 2002.

    Article  MATH  MathSciNet  Google Scholar 

  8. T. C. Chu, Y. C. Lin. A fuzzy TOPSISmethod for robot selection. International Journal of Advanced Manufacturing Technology, vol. 21, no. 4, pp. 284–290, 2003.

    Article  Google Scholar 

  9. S. Balli, S. Korukoglu. Operating system selection using fuzzy AHP and TOPSIS methods. Mathematical & Computational Applications, vol. 14, no. 2, pp. 119–130, 2009.

    MATH  Google Scholar 

  10. T. C. Wang, H. D. Lee. Developing a fuzzy TOPSIS approach based on subjective weights and objective weights. Expert Systems with Applications, vol. 36, no. 5, pp. 8980–8985, 2009.

    Article  Google Scholar 

  11. F. Ye, Y. N. Li. Group multi-attribute decision model to partner selection in the formation of virtual enterprise under incomplete information. Expert Systems with Applications, vol. 36, no. 5, pp. 9350–9357, 2009.

    Article  Google Scholar 

  12. I. Chamodrakas, N. Alexopoulou, D. Martakos. Customer evaluation for order acceptance using a novel class of fuzzy methods based on TOPSIS. Expert Systems with Applications, vol. 36, no. 4, pp. 7409–7415, 2009.

    Article  Google Scholar 

  13. M. Dagdeviren, S. Yavuz, N. Kilinç. Weapon selection using the AHP and TOPSIS methods under fuzzy environment. Expert Systems with Applications, vol. 36, no. 4, pp. 8143–8151, 2009.

    Article  Google Scholar 

  14. I. Ertugrul, N. Karakasoglu. Performance evaluation of Turkish cement firms with fuzzy analytic hierarchy process and TOPSIS methods. Expert Systems with Applications, vol. 36, no. 1, pp. 702–715, 2009.

    Article  Google Scholar 

  15. C. T. Chen. Extensions of the TOPSIS for group decisionmaking under fuzzy environment. Fuzzy Sets and Systems, vol. 114, no. 1, pp. 1–9, 2000.

    Article  MATH  Google Scholar 

  16. G. R. Jahanshahloo, F. H. Lotfi, M. Izadikhah. An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied Mathematics and Computation, vol. 175, no. 2, pp. 1375–1384, 2006.

    Article  MATH  Google Scholar 

  17. Y. J. Wang, H. S. Lee. Generalizing TOPSIS for fuzzy multiple-criteria group decision-making. Computers & Mathematics with Application, vol. 53, no. 11, pp. 1762–1772, 2007.

    Article  MATH  MathSciNet  Google Scholar 

  18. G. R. Jahanshahloo, F. H. Lotfi, M. Izadikhah. Extension of the TOPSIS method for decision-making problems with fuzzy data. Applied Mathematics and Computation, vol. 181, no. 2, pp. 1544–1551, 2006.

    Article  MATH  Google Scholar 

  19. J. B. Yang, M. G. Singh. An evidential reasoning approach for multiple attribute decision making with uncertainty. IEEE Transactions on Systems, Man, and Cybernetics, vol. 24, no. 1, pp. 1–18, 1994.

    Article  Google Scholar 

  20. J. B. Yang, P. Sen. A general multi-level evaluation process for hybrid MADM with uncertainty. IEEE Transactions on Systems, Man, and Cybernetics, vol. 24, no. 10, pp. 1458–1473, 1994.

    Article  Google Scholar 

  21. J. B. Yang, D. L. Xu. On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty. IEEE Transactions on Systems, Man, and Cybernetics — Part A: Systems and Humans, vol. 32, no. 3, pp. 289–304, 2002.

    Article  Google Scholar 

  22. M. Guo, J. B. Yang, K. S. Chin, H. W. Wang. Evidential reasoning approach for multi-attribute decision analysis under both fuzzy and interval uncertainty. IEEE Transactions on Fuzzy Systems, vol. 17, no. 3, pp. 683–697.

  23. J. B. Yang, Y. M. Wang, D. L. Xu, K. S. Chin. The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties. European Journal of Operational Research, vol. 171, no. 1, pp. 309–343, 2006.

    Article  MATH  MathSciNet  Google Scholar 

  24. Y. M. Wang, J. B. Yang, D. L. Xu. Environmental impact assessment using the evidential reasoning approach. European Journal of Operational Research, vol. 174, no. 3, pp. 1885–1913, 2006.

    Article  MATH  Google Scholar 

  25. K. S. Chin, D. L. Xu, J. B. Yang, J. P. K. Lam. Group-based ER-AHP system for product project screening. Expert Systems with Applications, vol. 35, no. 4, pp. 1909–1929, 2008.

    Article  Google Scholar 

  26. P. K. Lam, K. S. Chin, J. B. Yang, W. Liang. Selfassessment of conflict management in client-supplier collaborative new product development. Industrial Management & Data Systems, vol. 107, no. 5, pp. 688–714, 2007.

    Article  Google Scholar 

  27. K. S. Chin, Y. M. Wang, J. B. Yang, K. K. G. Poon. An evidential reasoning based approach for quality function deployment under uncertainty. Expert Systems with Applications, vol. 36, no. 3, pp. 5684–5694, 2009.

    Article  Google Scholar 

  28. K. S. Chin, Y. M. Wang, G. K. K. Poon, J. B. Yang. Failure mode and effects analysis using a group-based evidential reasoning approach. Computers & Operations Research, vol. 36, no. 6, pp. 1768–1779, 2009.

    Article  MATH  Google Scholar 

  29. S. J. Chen, C. L. Hwang. Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer, 1992.

  30. Q. Shen, R. Jensen. Rough sets, their extensions and applications. International Journal of Automation and Computing, vol. 4, no. 3, pp. 17–228, 2007.

    Article  Google Scholar 

  31. M. Kowal, J. Korbicz. Fault detection under fuzzy model uncertainty. International Journal of Automation and Computing, vol. 4, no. 2, pp. 117–124, 2007.

    Article  Google Scholar 

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Authors and Affiliations

  1. College of Information System and Management, National University of Defense Technology, Changsha, 410073, PRC

    Jiang Jiang & Ying-Wu Chen

  2. Manchester Business School, University of Manchester, Manchester, M15 6PB, UK

    Jiang Jiang, Da-Wei Tang & Yu-Wang Chen

Authors
  1. Jiang Jiang
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  2. Ying-Wu Chen
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  3. Da-Wei Tang
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  4. Yu-Wang Chen
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Corresponding author

Correspondence to Jiang Jiang.

Additional information

This work was supported by National Natural Science Foundation of China (No.70971131, 70901074).

Jiang Jiang received the B. Sc. and M. Sc. degrees in system engineering from National University of Defense Technology, PRC in 2004 and 2006, respectively. He is currently a joint Ph.D. candidate in College of Information System and Management, National University of Defense Technology, PRC, and Manchester Business School, University of Manchester, UK.

His research interests include multiple criteria decision making and risk analysis.

Ying-Wu Chen received the Ph.D. degree in engineering from the National University of Defense Technology, PRC in 1994. He is currently a professor as well as the director of the Department of Management Science and Engineering, College of Information System and Management, National University of Defense Technology, PRC.

His research interests include decisionmaking system of project evaluation, management decision, and artificial intelligence.

Da-Wei Tang received the B. Sc. and M. Sc. degrees in system engineering from Huazhong University of Science and Technology, PRC in 2002 and 2005, respectively. He is currently a Ph. D. candidate in Manchester Business School, University of Manchester, UK.

His research interests include decision science, risk analysis, and security analysis.

Yu-Wang Chen received the Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, PRC in 2008. He is currently a research associate at the Decision and System Science Research Center, University of Manchester, UK.

His research interests include selforganizing optimization, supply chain management, and multi-attribute decision analysis.

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Jiang, J., Chen, YW., Tang, DW. et al. TOPSIS with belief structure for group belief multiple criteria decision making. Int. J. Autom. Comput. 7, 359–364 (2010). https://doi.org/10.1007/s11633-010-0515-7

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  • DOI: https://doi.org/10.1007/s11633-010-0515-7

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