MATRIX BALANCING PROBLEM AND BINARY AHP

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概要

• 論文の詳細を見る

• A matrix balancing problem and an eigenvalue problem are transformed into two minimum-norm point problems whose difference is only a norm. The matrix balancing problem is solved by scaling algorithms that are as simple as the power method of the eigenvalue problem. This study gives a proof of global convergence for scaling algorithms and applies the algorithm to Analytic Hierarchy process (AHP), which derives priority weights from pairwise comparison values by the eigenvalue method (EM) traditionally. Scaling algorithms provide the minimum X square estimate from pairwise comparison values. The estimate has properties of priority weights such as right-left symmetry and robust ranking that are not guaranteed by the EM.

著者

• Sekitani Kazuyuki

  Shizuoka University

• Genma Koichi

  Shizuoka University

• Kato Yutaka

  Hosei University

• Sekitani Kazuyuki

  Shizuoka Univ.

関連論文

• MATHEMATICAL PROPERTIES OF DOMINANT AHP AND CONCURRENT CONVERGENCE METHOD
• Mathematical Structure of Dominant AHP and Concurrent Convergence Method(AHP)
• REMARKS ON THE CONCURRENT CONVERGENCE METHOD FOR A TYPICAL MUTUAL EVALUATION SYSTEM
• A model-based AHP with incomplete pairwise comparisons
• A logical interpretation for the eigenvalue method in AHP : Why is a weight vector in AHP calculated by the eigenvalue method?
• A LOGICAL INTERPRETATION FOR THE EIGENVALUE METHOD IN AHP
• A paradox of concurrent convergence method for a typical mutual evaluation system
• MATRIX BALANCING PROBLEM AND BINARY AHP
• A NEW APPROACH OF REVISING UNSTABLE DATA IN ANP BY BAYES THEOREM
• LEAST DISTANCE BASED INEFFICIENCY MEASURES ON THE PARETO-EFFICIENT FRONTIER IN DEA

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