the analytic hierarchy process (ahp) is a mathematical theory for measurement and decision making...
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The Analytic Hierarchy Process (AHP) is a mathematical theory for measurement and decision making that was developed by Dr. Thomas L. Saaty during the mid-1970's when he was teaching at the Wharton Business School of the University of Pennsylvania. Applications of the Analytic Hierarchy Process can be classified into two major categories: (1) Choice -- the evaluation or prioritization of alternative courses of action, and (2) Forecasting -- the evaluation of alternative future outcomes.
“AHP”
Analytic Hierarchy ProcessA Structured Judgmental Forecasting Method
“AHP”
Analytic Hierarchy ProcessA Structured Judgmental Forecasting Method
AHP Steps to a Decision/Forecast
Setting the Framework:Goals, Criteria, & Alternatives
F orecas t S cen ario 1
C rite rion 1
F orecas t S cen ario 2 F orecas t S cen ario 3
C rite rion 2
F orecas t S cen ario n
C rite rion n
G oa l
Linear Hierarchy
component,cluster(Level)
element
A loop indicates that eachelement depends only on itself.
Goal
Subcriteria
Criteria
Alternatives
Feedback Network with components having Inner and Outer Dependence among Their Elements
C4
C1
C2
C3
Feedback
Loop in a component indicates inner dependence of the elements in that component with respect to a
common property.
Arc from componentC4 to C2 indicates the
outer dependence of the elements in C2 on theelements in C4 with
respectto a common property.
Sample Hierarchy/Network Structures for Modeling
Side Note:
The Use of the Flow Chart is a Very Useful Device to
Conceptualize Your Modeling and Forecasting Problem.
Consider a Simple Hierarchy Example
Six Types of Scales
• Nominal • Positional
• Ordinal• Arbitrary
• Relative or Ratio• Absolute
Nominal Scale
Nominal scales are primarily intended for identification or coding purposes.
For example, a list of employee numbers or social security numbers.
Positional Scale
Positional scales are a refinement of the nominal scale whereby it provides locational or positional information
without necessarily implying ordering. Examples include: home addresses,
geographic positions (latitude or longitude), altitude, musical scale.
Ordinal Scale
Ordinal scales are a way of classifying (for example: hot, warm, tepid, cool,
cold) and imply a magnitude of measurement.
Arbitrary Scale
Arbitrary scales are a way of classifying responses (for example: 1, 2, 3, 4, 5 --
which is known as unipolar or a bipolar version, for example: -3, -2, -1,
0, 1, 2, 3) and imply a degree of strength. It can also take the form of a survey response, where say, strongly
agree (=5), agree (=4), etc.
Relative or Ratio Scale
Relative or ratio scales have uniform interval but with no absolute zero. The
zero point is arbitrary (say, distance from the office or home). The Saaty
pairwise rankings is a form of this scale.
Absolute Scale
Absolute scales has uniform intervals and an absolute zero. (For example,
money in a bank account.) This can be used in the AHP model.
Absolute Scale
Relative Scale
20
Pairwise ComparisonsSize
Apple A Apple B Apple C
SizeComparison
Apple A Apple B Apple C
Apple A 1 2 6 6/10 A
Apple B 1/2 1 3 3/10 B
Apple C 1/6 1/3 1 1/10 C
When the judgments are consistent, as they are here, any normalized column gives the priorities. Also, the judgments can be obtained by forming the appropriate ratios from the priority vector. That is not
true if the judgments are inconsistent.
ResultingPriority Eigenvector
Relative Sizeof Apple
For example, in comparing option 1 to option 2 you might assign a ranking of 5 for option 1 relative to option 2. By transitivity, option 2 is assigned a ranking of [1/5 = 0.20] relative to option 1.