# The Analytic Hierarchy Process: Structuring, Measurement, and Synthesis

John Wang (Montclair State University, USA), Chandana Chakraborty (Montclair State University, USA) and Huanyu Ouyang (The People’s Hospital of Jiangxi Provence, China)
DOI: 10.4018/978-1-59904-843-7.ch003

## Abstract

The challenges of evaluation and decision making are encountered in every sphere of life and on a regular basis. The nature of the required decisions, however, may vary between themselves. While some decisions may reflect individual solutions on simple problems, others may indicate collaborative solutions on complex issues. Regardless of their distinctive nature, all decisions are outcomes of a mental process. The process involves careful evaluation of merits of all the available options leading ultimately to the choice of a single solution. Numerous efforts have been made in the literature to develop decision models ideal for choosing the best solution for a given problem. The dilemma in using these decision models, however, can hardly be avoided. With differences in underlying methodology, each model serves a specific decision-making need of the decision maker. In the absence of a universal framework suitable for handling a variety of problems, decision makers are often required to identify the model best suited for their particular need. Furthermore, they need to take account of the advantages and disadvantages associated with the chosen model.

## Key Terms in this Chapter

Eigenvector: An Eigenvector is a nonzero vector that is mapped by a given linear transformation of a vector space onto a vector that is the product of a scalar multiplied by the original vector.

Eigenvalue: An eigenvalue is a scalar associated with a given linear transformation of a vector space and having the property that there is some nonzero vector that when multiplied by the scalar is equal to the vector obtained by letting the transformation operate on the vector.

Synthesis: Synthesis is the combining of separate elements to form a coherent whole.

Criteria: These are one of the three main parts of the AHP that need to be defined before solving a problem. A criterion is a standard on which your judgments are based.

Hierarchy: It is a system of ranking and organizing in which each component is a subordinate to another component directly above or below depending on the layout.

Alternatives: They are multiple choices from which you have to choose one based upon their weights on the different criteria. The alternative with the highest overall rating is selected as the most efficient choice in an AHP.

Rank Reversal: This is one of the secondary problems related to AHP that occurs when the rankings for the alternatives are changed with either the addition of or removal of an alternative.

Consistency Measure (CM): Also known as consistency ratio or consistency index, it is an estimated arithmetical indicator of the inconsistencies or intransitivity in a set of pair-wise ratings.

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