A mathematical treatment of inconsistency in the analytic hierarchy process
Kamran Dadkhah,Fatemeh Zahedi +1 more
TLDR
In this paper, a simple mathematical exposition of some of theorems regarding the treatment of inconsistency in AHP has been presented, and a rigorous mathematical proof that the largest eigenvalue reaches its global minimum when the input matrix is consistent.About:
This article is published in Mathematical and Computer Modelling.The article was published on 1993-02-25 and is currently open access. It has received 37 citations till now. The article focuses on the topics: Mathematical proof.read more
Citations
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Multiple criteria decision making approaches to assessing forest sustainability using criteria and indicators: a case study
Guillermo A. Mendoza,Ravi Prabhu +1 more
TL;DR: Three techniques called ranking, rating, and pairwise comparisons are described and used within the framework of a generic set of criteria and indicators applied in a case study involving a forest concession in Kalimantan, Indonesia, indicating that these techniques are effective tools both for selecting sets of criterion and indicators and eventually for prioritizing them.
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A method for repairing the inconsistency of fuzzy preference relations
TL;DR: An algorithm is developed to repair an inconsistent fuzzy preference relation and to make it become one with weak transitivity, via a synthesis matrix which reflects the relationship between the fuzzy preference relationship with additive consistency and the initial one given by a decision maker.
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Transport planning with multiple criteria: the analytic hierarchy process applications and progress review
TL;DR: In this article, five examples of applications of the Analytic Hierarchy Process (AHP) are made to illustrate the different uses of this ratio scale multicriteria decision method in transportation.
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A quality control approach to consistency paradoxes in AHP
TL;DR: This paper argues against the use of the standard consistency check in the Analytic Hierarchy Process, and suggests a quality control approach is recommended.
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Group decision making in higher education using the analytic hierarchy process
TL;DR: The purpose of this paper is to illustrate how the analytic hierarchy process (AHP) can be applied to those situations in higher education where a group must evaluate a large number of alternatives.
References
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Journal ArticleDOI
A Scaling Method for Priorities in Hierarchical Structures
TL;DR: A method of scaling ratios using the principal eigenvector of a positive pairwise comparison matrix is investigated, showing that λmax = n is a necessary and sufficient condition for consistency.
Book
Matrix Differential Calculus with Applications in Statistics and Econometrics
Jan R. Magnus,Heinz Neudecker +1 more
TL;DR: In this article, the authors discuss the properties of Vectors and Matrices, the Vec-Operator, the Moore-Penrose Inverse Miscellaneous Matrix Results, and the Linear Regression Model.
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Axiomatic foundation of the analytic hierarchy process
TL;DR: In this article, an axiomatic treatment of the Analytic Hierarchy Process (AHP) is presented, which is a special case of axioms for priority setting in systems with feedback which allow for a wide class of dependencies.
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The Analytic Hierarchy Process—A Survey of the Method and its Applications
TL;DR: In this article, the analytic hierarchy process (AHP) and its applications in diverse decision problems are briefly reviewed and some of the major extensions and criticisms of the method are discussed.
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Marketing Applications of the Analytic Hierarchy Process
Yoram Wind,Thomas L. Saaty +1 more
TL;DR: The thrust of the paper is a discussion of a number of illustrative applications of the AHP covering the following areas: the portfolio decisions of a firm whose management is concerned with the determination of the desired target portfolio and allocation of resources among its components.