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Fuzzy Multi-attribute Grey Relational Analysis Using DEA and AHP

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Proceedings of the Eleventh International Conference on Management Science and Engineering Management (ICMSEM 2017)

Part of the book series: Lecture Notes on Multidisciplinary Industrial Engineering ((LNMUINEN))

Abstract

This research applies the method of grey relational analysis (GRA) for multiple attribute decision making (MADM) problems in which the attribute weights are completely unknown and attribute values take the form of fuzzy numbers. In order to obtain the attribute weights, this research proposes an integrated data envelopment analysis (DEA) and analytic hierarchy process (AHP) approach. According to this, we define two sets of weights in a domain of grey relational loss, i.e., a reduction in grey relational grade, between each alternative and the ideal alternative. The first set represents the weights of attributes with the minimal grey relational loss in DEA. The second set represents the priority weights of attributes, bounded by AHP, with the maximal grey relational loss. Using a parametric goal programming model, we explore the various sets of weights in a defined domain of grey relational loss. This may result in various ranking positions for each alternative in comparison to the other alternatives. An illustrated example of a nuclear waste dump site selection is used to highlight the usefulness of the proposed approach.

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Author information

Authors and Affiliations

  1. Faculty of Management, Laurentian University, Sudbury, ON, P3E 2C6, Canada

    Mohammad Sadegh Pakkar

Authors
  1. Mohammad Sadegh Pakkar
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Correspondence to Mohammad Sadegh Pakkar .

Editor information

Editors and Affiliations

  1. Business and Administration, Sichuan University, Chengdu, China

    Jiuping Xu

  2. Fuzzy Logic Systems Institute, Tokyo University of Science, Tokyo, Tokyo, Japan

    Mitsuo Gen

  3. Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    Asaf Hajiyev

  4. Monash University, Clayton, Victoria, Australia

    Fang Lee Cooke

Appendix

Appendix

Table 8. The measure of relative closeness to the priority weights of attributes [\(\varDelta _k(\theta )\)] verses grey relational loss[\(\theta \)] for each nuclear waste dump site
Full size table

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Pakkar, M.S. (2018). Fuzzy Multi-attribute Grey Relational Analysis Using DEA and AHP. In: Xu, J., Gen, M., Hajiyev, A., Cooke, F. (eds) Proceedings of the Eleventh International Conference on Management Science and Engineering Management. ICMSEM 2017. Lecture Notes on Multidisciplinary Industrial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-59280-0_57

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  • DOI: https://doi.org/10.1007/978-3-319-59280-0_57

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59279-4

  • Online ISBN: 978-3-319-59280-0

  • eBook Packages: EngineeringEngineering (R0)

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