MCDMDecision-makingRankingMath steps

BWM + Z-number + Zero-Sum Game — Best Worst Method weighting with Z-number payoff matrix and game-theoretic ranking

OriginatorAdesina, K.A.; Yazdi, M.; Omidvar, M. (hybrid); Rezaei, J. 2015 (BWM); Zadeh, L.A. 2011 (Z-numbers); von Neumann 1928 + Nash 1950 (zero-sum game / Nash equilibrium)Year2022Sources1

BWM-ZNUMBER-GAME (BWM + Z-number + Zero-Sum Game — Best Worst Method weighting with Z-number payoff matrix and game-theoretic ranking) is a ranking multi-criteria decision-making (MCDM) method introduced by Adesina, K.A.; Yazdi, M.; Omidvar, M. (hybrid); Rezaei, J. 2015 (BWM); Zadeh, L.A. 2011 (Z-numbers); von Neumann 1928 + Nash 1950 (zero-sum game / Nash equilibrium) in 2022. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.

Key highlights

  • Follows a transparent, reproducible computational procedure that can be audited step by step.
  • Handles multiple criteria of differing scales and units within a single decision matrix.

Intuition

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How it works

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When to use it

G_i represents the expected payoff under Nash equilibrium. Higher G_i = better alternative. G_i = 0 alternatives are ranked iteratively by re-solving the game after removing G_i ≠ 0 rows. BWM weights w*_j modulate the relative importance of criteria in the payoff computation. Sensitivity analysis on confidence levels (B in Z-numbers) is recommended.

Strengths & limitations

Strengths
  • Follows a transparent, reproducible computational procedure that can be audited step by step.
  • Handles multiple criteria of differing scales and units within a single decision matrix.
Limitations
  • Results depend on the chosen normalisation, weights, and parameter settings.

Common pitfalls

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Sources

  1. 1.
    Adesina, K. A., Yazdi, M., Omidvar, M. (2022). Emergency Decision Making Fuzzy-Expert Aided Disaster Management System. in: Yazdi M. (ed.), Linguistic Methods Under Fuzzy Information in System Safety and Reliability Analysis, Studies in Fuzziness and Soft Computing, Vol. 414, Springer, Cham, pp. 139-150 (Chapter 6)

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Cite this page

ScholarGate. (2026, June 2). BWM-ZNUMBER-GAME. ScholarGate. https://scholargate.app/decision-making/bwm-znumber-game