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Comprehensive Interval-Induced Weights Allocation with Bipolar Preference in Multi-Criteria Evaluation

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Listed:
  • Xu Jin

    (School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China)

  • Ronald R. Yager

    (Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Machine Intelligence Institute, Iona College, New Rochelle, NY 10801, USA)

  • Radko Mesiar

    (Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 81005 Bratislava, Slovakia
    Department of Algebra and Geometry, Faculty of Science, Palacký University, Olomouc 17, Listopadu 12, 77 146 Olomouc, Czech Republic)

  • Surajit Borkotokey

    (Department of Mathematics, Dibrugarh University, Dibrugarh 786004, India)

  • Lesheng Jin

    (School of Business, Nanjing Normal University, Nanjing 210023, China)

Abstract

Preferences-involved evaluation and decision making are the main research subjects in Yager’s decision theory. When the involved bipolar preferences are concerned with interval information, some induced weights allocation and aggregation methods should be reanalyzed and redesigned. This work considers the multi-criteria evaluation situation in which originally only the interval-valued absolute importance of each criterion is available. Firstly, based on interval-valued importance, upper bounds, lower bounds, and the mean points of each, we used the basic unit monotonic function-based bipolar preference weights allocation method four times to generate weight vectors. A comprehensive weighting mechanism is proposed after considering the normalization of the given absolute importance information. The bipolar optimism–pessimism preference-based weights allocation will also be applied according to the magnitudes of entries of any given interval input vector. A similar comprehensive weighting mechanism is still performed. With the obtained weight vector for criteria, we adopt the weighted ordered weighted averaging allocation on a convex poset to organically consider both two types of interval-inducing information and propose a further comprehensive weights allocation mechanism. The detailed comprehensive evaluation procedures with a numerical example for education are presented to show that the proposed models are feasible and useful in interval, multi-criteria, and bipolar preferences-involved decisional environments.

Suggested Citation

  • Xu Jin & Ronald R. Yager & Radko Mesiar & Surajit Borkotokey & Lesheng Jin, 2021. "Comprehensive Interval-Induced Weights Allocation with Bipolar Preference in Multi-Criteria Evaluation," Mathematics, MDPI, vol. 9(16), pages 1-10, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:2002-:d:618833
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    References listed on IDEAS

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    2. Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 32(7), pages 841-855, July.
    3. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
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