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A Multistage Risk Decision Making Method for Normal Cloud Model with Three Reference Points

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Group Decision and Negotiation in an Uncertain World (GDN 2018)

Part of the book series: Lecture Notes in Business Information Processing ((LNBIP,volume 315))

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Abstract

Decision making problems become more complicated due to the dynamically changing environment. Consequently, decision making methods with reference points are increasing. Reference points provide a good basis for decision makers. This paper proposes a multistage risk decision making method for normal cloud model considering three reference points. Firstly, the setting method of three reference points is proposed considering the dimensions of multistate, development and promotion. The value function is defined based on the characteristics of three reference points. Secondly, the aggregation methods for different prospect values are proposed with the preference coefficients, which are calculated by the synthetic degree of grey incidence. Thirdly, a two-stage weight optimization method is proposed to solve the attribute weights and stage weights based on the idea of minimax reference point optimization. Finally, a numerical example illustrates the feasibility and validity of the proposed method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China [71171112, 71502073, 71601002]; Funding of Jiangsu Innovation Program for Graduate Education (“the Fundamental Research Funds for the Central Universities”) [KYZZ16_0147].

Author information

Authors and Affiliations

  1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing, 211106, People’s Republic of China

    Wen Song & Jianjun Zhu

Authors
  1. Wen Song
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  2. Jianjun Zhu
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Corresponding author

Correspondence to Jianjun Zhu .

Editor information

Editors and Affiliations

  1. Nanjing University of Aeronautics and Astronautics, Nanjing, China

    Ye Chen

  2. Concordia University, Montreal, QC, Canada

    Gregory Kersten

  3. University of Vienna, Vienna, Austria

    Rudolf Vetschera

  4. Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu, China

    Haiyan Xu

Appendix

Appendix

 

p1

p2

p3

p1

p2

p3

 

c1

c2

a1

6.69,2.27,0.35

5.7,1.93,0.47

5,1.82,0.55)

0.945,0.022,0.009

0.94,0.03,0.008

0.91,0.03,0.009

a2

8.07,2.75,0.19

5.7,1.93,0.47

5,1.82,0.55)

0.95,0.023,0.009

0.95,0.022,0.01

0.935,0.035,0.01

a3

5.7,1.93,0.47

5,1.82,0.55)

4.3,1.93,0.47

0.925,0.037,0.008

0.92,0.052,0.012

0.905,0.052,0.013

a4

6.69,2.27,0.35

5.7,1.93,0.47

5,1.82,0.55)

0.91,0.03,0.01

0.91,0.06,0.01

0.88,0.065,0.011

a5

5.7,1.93,0.47

5.7,1.93,0.47

5,1.82,0.55)

0.925,0.037,0.009

0.92,0.022,0.011

0.89,0.03,0.012

a6

8.07,2.75,0.19

6.69,2.27,0.35

5.7,1.93,0.47

0.945,0.037,0.008

0.94,0.037,0.01

0.905,0.038,0.011

a7

5,1.82,0.55)

5.7,1.93,0.47

5.7,1.93,0.47

0.94,0.015,0.009

0.94,0.03,0.01

0.91,0.033,0.011

a8

6.69,2.27,0.35

5,1.82,0.55)

5,1.82,0.55)

0.97,0.021,0.009

0.96,0.022,0.01

0.92,0.031,0.01

a9

5.7,1.93,0.47

5.7,1.93,0.47

5.7,1.93,0.47

0.94,0.024,0.008

0.94,0.037,0.009

0.915,0.041,0.01

a10

6.69,2.27,0.35

5.7,1.93,0.47

5.7,1.93,0.47

0.955,0.175,0.009

0.95,0.022,0.009

0.911,0.033,0.011

a11

6.69,2.27,0.35

5.7,1.93,0.47

5.7,1.93,0.47

0.9150.033,0.010

0.91,0.025,0.01

0.89,0.031,0.011

a12

8.07,2.75,0.19

6.69,2.27,0.35

5.7,1.93,0.47

0.925,0.028,0.009

0.92,0.023,0.009

0.905,0.025,0.011

a13

5.7,1.93,0.47

5.7,1.93,0.47

5,1.82,0.55)

0.93,0.035,0.01

0.92,0.025,0.01

0.905,0.031,0.01

a14

6.69,2.27,0.35

6.69,2.27,0.35

5.7,1.93,0.47

0.94,0.033,0.009

0.93,0.023,0.01

0.911,0.025,0.011

a15

6.69,2.27,0.35

6.69,2.27,0.35

5.7,1.93,0.47

0.955,0.031,0.009

0.94,0.028,0.009

0.91,0.031,0.011

 

c3

c4

a1

6.69,2.27,0.35

5.7,1.93,0.47

6.69,2.27,0.35

87.5,0.425,0.849

72.5,3.822,0.833

57.5,3.822,0.283

a2

8.07,2.75,0.19

5.7,1.93,0.47

5.7,1.93,0.47

85.5,0.425,0.849

74.5,1.274,0.849

65.5,0.425,1.416

a3

5.7,1.93,0.47

6.69,2.27,0.35

6.69,2.27,0.35

85,0.849,0.708

73.5,1.274,0.849

68,2.548,0.708

a4

5,1.82,0.55)

4.3,1.93,0.47

5,1.82,0.55)

87.5,1.274,0.566

72,2.548,0.425

65.4.247,0.142

a5

5,1.82,0.55)

4.3,1.93,0.47

5,1.82,0.55)

87,1.699,0.425

72,3.397,0.142

65.5,4.671,1.167

a6

5.7,1.93,0.47

5,1.82,0.55)

4.3,1.93,0.47

84.5,2.123,0.283

72.5,2.123,0.566

68.5,2.973,0.566

a7

8.07,2.75,0.19

5.7,1.93,0.47

5.7,1.93,0.47

82.5,2.123,0.283

76,0.849,0.991

71,0.849,1.274

a8

5.7,1.93,0.47

5,1.82,0.55)

5,1.82,0.55)

85,1.699,0.425

71.5,1.274,0.849

68,1.699,0.991

a9

6.69,2.27,0.35

8.07,2.75,0.19

5.7,1.93,0.47

84.5,2.973,0.667

73,1.699,0.708

67.5,2.973,0.566

a10

5,1.82,0.55)

6.69,2.27,0.35

5,1.82,0.55)

87,1.699,0.425

74.5,1.274,0.849

67,3.397,0.425

a11

5.7,1.93,0.47

8.07,2.75,0.19

6.69,2.27,0.35

80,0.849,0.708

69,2.548,0.425

63.5,3.822,0.283

a12

6.69,2.27,0.35

5.7,1.93,0.47

5.7,1.93,0.47

75,0.849,0.425

70,2.548,0.849

61.5,3.822,0.425

a13

5.7,1.93,0.47

6.69,2.27,0.35

4.3,1.93,0.47

85.5,2.123,0.283

72,0.849,0.991

61,1.699,0.991

a14

6.69,2.27,0.35

6.69,2.27,0.35

4.3,1.93,0.47

84,1.699,0.425

72.5,2.123,0.566

67.5,2.123,0.849

a15

5.7,1.93,0.47

8.07,2.75,0.19

5.7,1.93,0.47

84,1.699,0.425

72,2.548,0.425

64.5,4.671,1.167

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Song, W., Zhu, J. (2018). A Multistage Risk Decision Making Method for Normal Cloud Model with Three Reference Points. In: Chen, Y., Kersten, G., Vetschera, R., Xu, H. (eds) Group Decision and Negotiation in an Uncertain World. GDN 2018. Lecture Notes in Business Information Processing, vol 315. Springer, Cham. https://doi.org/10.1007/978-3-319-92874-6_2

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  • DOI: https://doi.org/10.1007/978-3-319-92874-6_2

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