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A D Number-Goal Programing Integrated Method for Evaluating Credibility of Complex Simulation Systems

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Modeling, Design and Simulation of Systems (AsiaSim 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 751))

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Abstract

For a complex simulation system with little or no simulation data, the credibility evaluation of simulation system is mainly based on the expert experience to grade the simulation system. However, the existing evaluation methods do not take into account the uncertainty of the evaluation result. To this end, a D number-goal programming method is proposed for complex simulation systems. This method not only handles the uncertainty, but also simplifies the whole evaluation procedure. Finally, the proposed evaluation method is validated by a practical system to illustrate the effectiveness of the proposed method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 61374199) and the National High-Tech Research Development Plan of China (No. 2015AA042101)

Author information

Authors and Affiliations

  1. School of Automation Science and Electrical Engineering, Beihang University, 100191, Beijing, China

    Gengjiao Yang, Lin Zhang, Longfei Zhou & Jin Cui

  2. Engineering Research Center of Complex Product Advanced Manufacturing Systems, Ministry of Education, 100191, Beijing, China

    Gengjiao Yang, Lin Zhang, Longfei Zhou & Jin Cui

Authors
  1. Gengjiao Yang
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  2. Lin Zhang
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  3. Longfei Zhou
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  4. Jin Cui
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Corresponding author

Correspondence to Gengjiao Yang .

Editor information

Editors and Affiliations

  1. Universiti Teknologi Malaysia, Skudai, Malaysia

    Mohamed Sultan Mohamed Ali

  2. Universiti Teknologi Malaysia, Skudai, Malaysia

    Herman Wahid

  3. Universiti Teknologi Malaysia, Skudai, Malaysia

    Nurul Adilla Mohd Subha

  4. Universiti Teknologi Malaysia, Skudai, Malaysia

    Shafishuhaza Sahlan

  5. Universiti Teknologi Malaysia, Skudai, Malaysia

    Mohd Amri Md. Yunus

  6. Universiti Teknologi Malaysia, Skudai, Malaysia

    Ahmad Ridhwan Wahap

Appendix

Appendix

The opinions of expert group on the weight of indicators are as follows.

$$ \begin{aligned} A_{1} & = \left( {\begin{array}{*{20}c} 1& 1& 3\\ 1& 1& 2\\ { 1 / 3} & { 1 / 2} & 1\\ \end{array} } \right),A_{2} = \left( {\begin{array}{*{20}c} 1& 2& 3\\ { 1 / 2} & 1& 2\\ { 1 / 3} & { 1 / 2} & 1\\ \end{array} } \right),A_{3} = \left( {\begin{array}{*{20}c} 1& { 1 / 2} & 3\\ 2& 1& 3\\ { 1 / 3} & { 1 / 3} & 1\\ \end{array} } \right),A_{4} = \left( {\begin{array}{*{20}c} 1& 3& 5\\ { 1 / 3} & 1& 2\\ { 1 / 5} & { 1 / 2} & 1\\ \end{array} } \right), \\ A_{5} & = \left( {\begin{array}{*{20}c} 1& 2& 5\\ { 1 / 2} & 1& 3\\ { 1 / 5} & { 1 / 3} & 1\\ \end{array} } \right),A_{6} = \left( {\begin{array}{*{20}c} 1& 3& 3\\ { 1 / 3} & 1& 2\\ { 1 / 3} & { 1 / 2} & 1\\ \end{array} } \right),A_{7} = \left( {\begin{array}{*{20}c} 1& 1& 5\\ 1& 1& 3\\ { 1 / 5} & { 1 / 3} & 1\\ \end{array} } \right),A_{ 8} = \left( {\begin{array}{*{20}c} 1& 1& 4\\ 1& 1& 3\\ { 1 / 4} & { 1 / 3} & 1\\ \end{array} } \right), \\ A_{ 9} & = \left( {\begin{array}{*{20}c} 1& 3& { 1 / 4} \\ { 1 / 3} & 1& { 1 / 5} \\ 4& 5& 1\\ \end{array} } \right),A_{ 1 0} = \left( {\begin{array}{*{20}c} 1& 4& 3\\ { 1 / 4} & 1& 1\\ { 1 / 3} & 1& 1\\ \end{array} } \right),A_{ 1 1} = \left( {\begin{array}{*{20}c} 1& 4& 3\\ { 1 / 4} & 1& { 1 / 2} \\ { 1 / 3} & 2& 1\\ \end{array} } \right),A_{ 1 2} = \left( {\begin{array}{*{20}c} 1& 4& 5\\ { 1 / 4} & 1& 1\\ { 1 / 5} & 1& 1\\ \end{array} } \right), \\ A_{ 1 3} & = \left( {\begin{array}{*{20}c} 1& { 1 / 4} & 3\\ 4& 1& 5\\ { 1 / 3} & { 1 / 5} & 1\\ \end{array} } \right),A_{ 1 4} = \left( {\begin{array}{*{20}c} 1& { 1 / 3} & 2\\ 3& 1& 5\\ { 1 / 2} & { 1 / 5} & 1\\ \end{array} } \right),A_{ 1 5} = \left( {\begin{array}{*{20}c} 1& { 1 / 2} & 3\\ 2& 1& 5\\ { 1 / 3} & { 1 / 5} & 1\\ \end{array} } \right). \\ \end{aligned} $$

The weight of the indicator is obtained by AHP as follows.

$$ \begin{aligned} w_{1} & = [\begin{array}{*{20}c} {0.4434} & {0.3874} & {0.1692} \\ \end{array} ],CR_{1} = 0.0158 < 0.1 \\ w_{ 2} & = [\begin{array}{*{20}c} {0. 5 3 9 6} & {0. 2 9 7 0} & {0.16 3 4} \\ \end{array} ],CR_{ 2} = 0.0 0 7 9< 0.1 \\ w_{ 3} & = [\begin{array}{*{20}c} {0. 3 3 2 5} & {0. 5 2 7 8} & {0.1 3 9 6} \\ \end{array} ],CR_{ 3} = 0.0 4 6 2< 0.1 \\ w_{ 4} & = [\begin{array}{*{20}c} {0. 6 4 8 3} & {0. 2 2 9 7} & {0.1 2 2 0} \\ \end{array} ],CR_{ 4} = 0.0 0 3 2< 0.1 \\ w_{ 5} & = [\begin{array}{*{20}c} {0. 5 8 1 6} & {0. 3 0 9 0} & {0.1 0 9 5} \\ \end{array} ],CR_{ 5} = 0.0 0 3 2< 0.1 \\ w_{ 6} & = [\begin{array}{*{20}c} {0. 5 9 3 6} & {0. 2 4 9 3} & {0.1 5 7 1} \\ \end{array} ],CR_{ 6} = 0.0 4 6 2< 0.1 \\ w_{ 7} & = [\begin{array}{*{20}c} {0. 4 8 0 6} & {0. 4 0 5 4} & {0.1 1 4 0} \\ \end{array} ],CR_{ 6} = 0.0 2 5 1< 0.1 \\ w_{ 8} & = [\begin{array}{*{20}c} {0. 4 5 7 9} & {0. 4 1 6 1} & {0.1 2 6 0} \\ \end{array} ],CR_{ 6} = 0.0 0 7 9< 0.1 \\ w_{ 9} & = [\begin{array}{*{20}c} { 0. 2 2 5 5} & { 0. 1 0 0 7} & { 0. 6 7 3 8} \\ \end{array} ],CR_{ 6} = 0.0 7 3 9< 0.1 \\ w_{ 1 0} & = [\begin{array}{*{20}c} { 0. 6 3 3 7} & { 0. 1 7 4 4} & { 0. 1 9 1 9} \\ \end{array} ],CR_{ 1 0} = 0.0 0 7 9< 0.1 \\ w_{ 1 1} & = [\begin{array}{*{20}c} { 0. 6 2 5 0} & { 0. 1 3 6 5} & { 0. 2 3 8 5} \\ \end{array} ],CR_{ 1 1} = 0.0 1 5 8< 0.1 \\ w_{ 1 2} & = [\begin{array}{*{20}c} { 0. 6 9 0 8} & { 0. 1 6 0 3} & { 0. 1 4 8 8} \\ \end{array} ],CR_{ 1 2} = 0.0 0 4 8< 0.1 \\ w_{ 1 3} & = [\begin{array}{*{20}c} { 0. 2 2 5 5} & { 0. 6 7 3 8} & { 0. 1 0 0 7} \\ \end{array} ],CR_{ 1 3} = 0.0 0 7 3 9< 0.1 \\ w_{ 1 4} & = [\begin{array}{*{20}c} { 0. 2 2 9 7} & { 0. 6 4 8 3} & { 0. 1 2 2 0} \\ \end{array} ],CR_{ 1 4} = 0.0 0 3 2< 0.1 \\ w_{ 1 5} & = [\begin{array}{*{20}c} { 0. 3 0 9 0} & { 0. 5 8 1 6} & { 0.} \\ \end{array} 1 0 9 5],CR_{ 1 5} = 0.0 0 3 2< 0.1 \\ \end{aligned} $$

The opinion of expert group on the credibility scores of indicators are as follows.

$$ \begin{array}{*{20}l} \begin{aligned} S_{ 1} & = \left[ {\begin{array}{*{20}c} { 9 5} & { 8 0} & { 9 7} \\ \end{array} } \right];S_{ 2} = \left[ {\begin{array}{*{20}c} { 9 7} & { 8 5} & { 9 0} \\ \end{array} } \right];S_{ 3} = \left[ {\begin{array}{*{20}c} { 7 5} & { 7 0} & { 8 5} \\ \end{array} } \right];S_{ 4} = [\begin{array}{*{20}c} { 9 6} & { 9 2} & { 9 6} \\ \end{array} ]; \\ S_{5} & = [\begin{array}{*{20}c} { 7 8} & { 9 0} & { 7 6} \\ \end{array} ];S_{6} = \left[ {\begin{array}{*{20}c} { 8 5} & { 7 5} & { 9 6} \\ \end{array} } \right]; \, S_{7} = \left[ {\begin{array}{*{20}c} { 8 4} & { 9 2} & { 9 1} \\ \end{array} } \right]; \, S_{8} = [\begin{array}{*{20}c} { 7 3} & { 7 9} & { 8 6} \\ \end{array} ]; \\ \end{aligned} \hfill \\ \begin{aligned} S_{9} & = [\begin{array}{*{20}c} { 9 2} & { 8 9} & { 9 8} \\ \end{array} ];S_{10} = \left[ {\begin{array}{*{20}c} { 9 1} & { 9 0} & { 9 9} \\ \end{array} } \right];S_{ 1 1} = \left[ {\begin{array}{*{20}c} { 9 0} & { 8 9} & { 9 2} \\ \end{array} } \right];S_{ 1 2} = \left[ {\begin{array}{*{20}c} { 7 5} & { 8 8} & { 9 0} \\ \end{array} } \right]; \\ S_{13} & = [\begin{array}{*{20}c} { 9 6} & { 8 9} & { 7 8} \\ \end{array} ];S_{14} = [\begin{array}{*{20}c} { 8 5} & { 8 7} & { 9 3} \\ \end{array} ];S_{15} = [\begin{array}{*{20}c} { 8 4} & { 8 9} & { 9 4} \\ \end{array} ] \\ \end{aligned} \hfill \\ \end{array} $$

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Yang, G., Zhang, L., Zhou, L., Cui, J. (2017). A D Number-Goal Programing Integrated Method for Evaluating Credibility of Complex Simulation Systems. In: Mohamed Ali, M., Wahid, H., Mohd Subha, N., Sahlan, S., Md. Yunus, M., Wahap, A. (eds) Modeling, Design and Simulation of Systems. AsiaSim 2017. Communications in Computer and Information Science, vol 751. Springer, Singapore. https://doi.org/10.1007/978-981-10-6463-0_18

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  • DOI: https://doi.org/10.1007/978-981-10-6463-0_18

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