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118
First-Level Transitivity Rule Method for Filling in Incomplete Pair-Wise Comparison Matrices in the Analytic Hierarchy Process
, 2014
"... Abstract: The paper discusses the problem of performing the prioritization of decision elements within the multicriteria optimization method, analytic hierarchy process (AHP), with incomplete information. An approach is proposed on how to fill in the gap in the pair-wise comparison matrix generated ..."
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Abstract: The paper discusses the problem of performing the prioritization of decision elements within the multicriteria optimization method, analytic hierarchy process (AHP), with incomplete information. An approach is proposed on how to fill in the gap in the pair-wise comparison matrix generated
MATRIX BALANCING PROBLEM AND BINARY AHP
, 2006
"... Abstract A matrix balancing problem and an eigenvalue problem are transformed into two minimumnorm 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 o ..."
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Cited by 2 (0 self)
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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 χ square estimate from pairwise comparison values
Achieving Matrix Consistency in AHP through Linearization
"... Matrices used in the analytic hierarchy process (AHP) compile expert knowledge as pairwise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent- and sometimes the ..."
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Matrices used in the analytic hierarchy process (AHP) compile expert knowledge as pairwise comparisons among various criteria and alternatives in decision-making problems. Many items are usually considered in the same comparison process and so judgment is not completely consistent- and sometimes
An LP-based inconsistency monitoring of pairwise comparison matrices
"... Abstract A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied ..."
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Abstract A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied
An LP-based inconsistency monitoring of pairwise comparison matrices
, 2011
"... A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The re-sults can be applied in the pr ..."
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A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The re-sults can be applied
A method to estimate results of unknown comparisons in Binary AHP
- Journal of the Operations Research Society of Japan
, 1997
"... Abstract In this paper we propose an algorithm to estimate results of unknown comparisons in binary AHP. For incomplete comparison case, which includes unknown pairwise comparisons, there are various methods to calculate weights, for example, Harker method, Two-Stage method and so on. However these ..."
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Cited by 1 (0 self)
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Abstract In this paper we propose an algorithm to estimate results of unknown comparisons in binary AHP. For incomplete comparison case, which includes unknown pairwise comparisons, there are various methods to calculate weights, for example, Harker method, Two-Stage method and so on. However
A Note on the Multiplicative AHP
"... Abstract: The paper concerns the pairwise comparison method used to rank a finite, usually small number of alternatives, in the Analytic Hierarchy Process (AHP), which belongs to a certain class of multiple attribute decision making methods. Ranking of alternatives is calculated based on expert judg ..."
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Abstract: The paper concerns the pairwise comparison method used to rank a finite, usually small number of alternatives, in the Analytic Hierarchy Process (AHP), which belongs to a certain class of multiple attribute decision making methods. Ranking of alternatives is calculated based on expert
A logical interpretation for eigenvalue method in AHP
- Journal of Operations Research Society of Japan
, 1999
"... Abstract The eigenvalue method (EM), that is to find the principal eigenvector of a pairwise comparison matrix, is widely used and known to be practical in Analytic Hierarchy Process (AHP). However, the validity of EM has never been fully proved. In this article, we present an equilibrium model and ..."
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Cited by 10 (5 self)
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Abstract The eigenvalue method (EM), that is to find the principal eigenvector of a pairwise comparison matrix, is widely used and known to be practical in Analytic Hierarchy Process (AHP). However, the validity of EM has never been fully proved. In this article, we present an equilibrium model
Calculating Weights Methods in Complete Matrices and Incomplete Matrices
"... Abstract—It is well known that the Analytic Hierarchy Process (AHP) of Saaty is one of the most powerful approach for decision aid in solving of a multi criteria decision making (MCDM) problem. Several computing weights methods in AHP are analyzed. Based on least square method, three methods for cal ..."
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Abstract—It is well known that the Analytic Hierarchy Process (AHP) of Saaty is one of the most powerful approach for decision aid in solving of a multi criteria decision making (MCDM) problem. Several computing weights methods in AHP are analyzed. Based on least square method, three methods
Measuring Inconsistency of Pair-wise Comparison Matrix with Fuzzy Elements
, 2013
"... Abstract � This paper deals with measuring inconsistency and incompatibility of pair-wise comparison matrix with fuzzy elements. Here we deal with some properties of such pair-wise comparisons, particularly, reciprocity consistency and compatibility. Moreover, we show how to measure it defining two ..."
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Cited by 6 (1 self)
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new indices. The first index of inconsistency is based on the classical concept of consistency, however, instead of principle eigenvector method used in AHP we apply the logarithmic least squares method. Defining the second index of incompatibility we look for a consistent matrix in the form
Results 1 - 10
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118
