Additional Information

AHP (along with other multiple objective methods --discussed below) differs in a significant way from most/all other Management Science/Operations Research methods which focus on an "objective" function – singular.  Taking the "best" course of actio...

The Math of AHP -- Computing priorities from pairwise comparisons Eigenvector computation Priorities for the elements in a cluster are derived from the relative pairwise comparisons by normalizing the principle right eigenvector of the matrix co...

In conformity with the second of the three AHP axioms originally proposed by Saaty, the elements of any cluster should be "homogeneous," meaning that they should differ in importance from one another by no more than an order of magnitude. This req...

Humans have difficulty dealing with more than seven - plus or minus two - factors at a time.  To overcome this cognitive limitation, objectives can be structured into a hierarchy of clusters of elements.  One of the axioms of AHP is that the element...

Originally, AHP was based on three relatively simple axioms. The first axiom, the reciprocal axiom , requires that, if PC(EA,EB) is a paired comparison of elements A and B with respect to their parent, element C, representing how many times more t...

Compensatory decision methodologies, such as AHP are the most effective way to prioritize alternatives.  A rational decision is one that best achieves an individual's or group's objectives -- their wants.  However, there are sometimes constraints, p...

Criteria, Objectives, and Attributes are terms that are often used interchangeably when making decisions.   Traditionally, people speak of criteria. We recommend focusing on "objectives" instead of criteria.  This helps clarify what should and sho...

A major challenge of almost all organizations today is to find a way to integrate the knowledge and expertise of their personnel in decision making and forecasting.  In The Wisdom of Crowds , James Surowiecki shows that under certain conditions -...

The ability for AHP to aggregate (synthesize) and filter (assign roles) is important for several reasons. Governance and Roles Power and control are distributed in organizations in a wide variety of ways.  An effective decision process must r...

Not all numbers have the same meaning in terms of what operations can be legitimately performed on them.  In order for operations like addition and multiplication with numbers to be mathematically meaningful, the numbers must possess certain proper...

Relative measurement in AHP is performed by comparing two elements, e.g., objectives or alternatives, one to another; whereas absolute measurement is performed on each element, e.g., alternatives, one at a time.  There are several ways this is done ...

Relative measurement consists of pairwise comparisons of two elements with respect to some higher level element in the hierarchy.   For example, a judgment can be made about the relative importance of two objectives with respect to the goal, or ...

A minimum spanning set of judgments for a cluster of n elements consists of a set of n -1 judgments, in that every element can be "reached" from every other element.  It is necessary to have a spanning set of judgments in order to compute the pri...

The number of judgments in a cluster, n ( n -1) divided by 2, refers to the maximum number of pairwise comparisons in a cluster.  However, Expert Choice can compute priorities from an eigenvector equation when there are missing judgments.  At a min...

The accuracy of the priorities computed from pairwise relative comparisons has been validated over the years in numerous studies.   First, it has been shown that for a pairwise comparison matrix A = [ a     ij ] that is consistent (sometimes cal...

Expert Choice employs an algorithm to determine when a spanning set of judgments has been entered for a cluster of elements, at which point priorities can be derived.  A spanning set of judgments is such that every element can be "reached" from eve...

Brightness of Light Experiment Area Validation Experiment The relative areas of different geometric shapes (each within an order of magnitude) were derived from pairwise verbal judgments for shapes such as the following:  This experiment...

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Originally, AHP had only one synthesis mode – later called the "distributive" synthesis mode.  A distributive synthesis distributes priorities from the goal down through the alternatives and is analogous to dividing priorities in a pie chart, which...

Overview The theory of AHP does not demand perfect consistency.  AHP allows inconsistency but provides a measure of the inconsistency in each set of judgments.  This measure is an important by-product of the process of deriving priorities base...

Important decisions and resource allocations involve some combination of hard data and judgment.  Expert Choice has effective ways for you to synthesize hard data and judgment into rational, defensible, convincing decisions.  This is accomplished b...

When an individual or small group derives priorities in an AHP model, they can evaluate either from the top down (from goal to objectives to alternatives) or bottom up (from alternatives, to covering objectives, to top level objectives).    A to...

Prioritization and decision making is often performed in a group context.  There are two ways to aggregate individuals' judgments and preferences with AHP, depending on whether the group is assumed to act together as a synergistic group in achievin...

Two types of means and two types of variances are used in Expert Choice Comparion: An Arithmetic Mean is the average interval -- and is the mean or average used in common practice.  It is computed as the sum of the values divided by the number o...

There are some places in Comparion where a new window or tab will need to be opened.  Browsers often prevent these pop-ups from displaying unless you give permission to do so. Google Chrome By default, Google Chrome blocks pop-ups from automat...