Advertisement

Evidential Reasoning Approach for MADA under Group and Fuzzy Decision Environment

  • Xin-Bao Liu
  • Mi Zhou
  • Jian-Bo Yang
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 4)

Abstract

Multiple attribute decision analysis (MADA) is common in everyday life of the real word. In a MADA problem, both qualitative attributes with uncertain assessment values and quantitative attributes with accurate assessments are often included in. Evidential reasoning (ER) is one of the MADA approaches that it can tackle issues under ignorance, incompleteness and uncertainty. In this paper, group of experts are involved, and the weights of attributes originated by experts are considered to be triangular fuzzy numbers. Weighted arithmetic mean method is used to combine the triangular fuzzy weights of attributes from each expert. α-cut is then used to transform the combined fuzzy weights to interval weights, and several pairs of evidential reasoning nonlinear programming models are conduct to calculate the total assessments.

Keywords

evidential reasoning fuzzy weight α-cut Multiple Attribute Decision Analysis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yang, J.B., Singh, M.G.: An evidential reasoning approach for multiple attribute decision making with uncertainty. IEEE Trans. Syst., Man, Cybern. 24(1), 1–18 (1994)CrossRefGoogle Scholar
  2. 2.
    Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics 38, 325–339 (1967)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Yang, J.B.: Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties. European Journal of Operational Research 131, 31–61 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Yang, J.B., Xu, D.L.: On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty. IEEE Trans. Syst., Man, Cybern., —Part A: Systems and Humans 32(3), 289–304 (2002)CrossRefGoogle Scholar
  5. 5.
    Wang, Y.M., Yang, J.B., Xu, D.L.: Environmental impact assessment using the evidential reasoning approach. European Journal of Operational Research 174, 1885–1913 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Xu, D.L., Yang, J.B., Wang, Y.M.: The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty. European Journal of Operational Research 174, 1914–1943 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Yang, J.B., Wang, Y.M., Xu, D.L., Chin, K.S.: The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties. European Journal of Operational Research 171, 309–343 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Wang, Y.M., Yang, J.B., Xu, D.L., Chin, K.S.: The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees. European Journal of Operational Research 175, 35–66 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Guo, M., Yang, J.B., Chin, K.S., Wang, H.W.: Evidential reasoning based preference programming for multiple attribute decision analysis under uncertainty. European Journal of Operational Research 182(3), 1294–1312 (2007)zbMATHCrossRefGoogle Scholar
  10. 10.
    Chen, S.M., Wang, C.H.: Fuzzy risk analysis based on ranking fuzzy numbers using-cuts, belief features and signal/noise ratios. Expert systems with applications 36, 5576–5581 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2010

Authors and Affiliations

  • Xin-Bao Liu
    • 1
  • Mi Zhou
    • 1
  • Jian-Bo Yang
    • 1
    • 2
  1. 1.School of ManagementHefei University of Technology
  2. 2.Manchester Business Schoolthe University of Manchester 

Personalised recommendations