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An Application of Neutrosophic Set to Relative Importance Assignment in AHP

Author

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  • Napat Harnpornchai

    (Center of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Wiriyaporn Wonggattaleekam

    (Department of Agricultural Economy and Development, Faculty of Agriculture, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market.

Suggested Citation

  • Napat Harnpornchai & Wiriyaporn Wonggattaleekam, 2021. "An Application of Neutrosophic Set to Relative Importance Assignment in AHP," Mathematics, MDPI, vol. 9(20), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2636-:d:659625
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    References listed on IDEAS

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    1. Ramanathan, R., 1997. "Stochastic decision making using multiplicative AHP," European Journal of Operational Research, Elsevier, vol. 97(3), pages 543-549, March.
    2. Vaidya, Omkarprasad S. & Kumar, Sushil, 2006. "Analytic hierarchy process: An overview of applications," European Journal of Operational Research, Elsevier, vol. 169(1), pages 1-29, February.
    3. Ho, William & Ma, Xin, 2018. "The state-of-the-art integrations and applications of the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 267(2), pages 399-414.
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    Cited by:

    1. Jiangbin Zhao & Mengtao Liang & Rongyu Tian & Zaoyan Zhang & Xiangang Cao, 2023. "Reliability Optimization of Hybrid Systems Driven by Constraint Importance Measure Considering Different Cost Functions," Mathematics, MDPI, vol. 11(20), pages 1-21, October.

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