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Reply to the note on article "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees"

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  • Wang, Ying-Ming

Abstract

In a very recent note by Gao and Ni [B. Gao, M.F. Ni, A note on article "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees", European Journal of Operational Research, in press, doi:10.1016/j.ejor.2007.10.0381], they argued that Yen's combination rule [J. Yen, Generalizing the Dempster-Shafer theory to fuzzy sets, IEEE Transactions on Systems, Man and Cybernetics 20 (1990) 559-570], which normalizes the combination of multiple pieces of evidence at the end of the combination process, was incorrect. If this were the case, the nonlinear programming models we proposed in [Y.M. Wang, J.B. Yang, D.L. Xu, K.S. Chin, The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees, European Journal of Operational Research 175 (2006) 35-66] would also be incorrect. In this reply to Gao and Ni, we re-examine their numerical illustrations and reconsider their analysis of Yen's combination rule. We conclude that Yen's combination rule is correct and our nonlinear programming models are valid.

Suggested Citation

  • Wang, Ying-Ming, 2009. "Reply to the note on article "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees"," European Journal of Operational Research, Elsevier, vol. 197(2), pages 813-817, September.
    • Handle: RePEc:eee:ejores:v:197:y:2009:i:2:p:813-817
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    References listed on IDEAS

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    1. Gao, Bin & Ni, Ming-Fang, 2009. "A note on article "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees"," European Journal of Operational Research, Elsevier, vol. 197(2), pages 809-812, September.
    2. Wang, Ying-Ming & Yang, Jian-Bo & Xu, Dong-Ling & Chin, Kwai-Sang, 2006. "The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees," European Journal of Operational Research, Elsevier, vol. 175(1), pages 35-66, November.
    3. Xu, Dong-Ling & Yang, Jian-Bo & Wang, Ying-Ming, 2006. "The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1914-1943, November.
    4. Wang, Ying-Ming & Yang, Jian-Bo & Xu, Dong-Ling, 2006. "Environmental impact assessment using the evidential reasoning approach," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1885-1913, November.
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