Abstract

Graphs are a great aid in interpreting multidimensional data. Two examples are employed to illustrate this point. In the first the many dissimilarities generated in the Analytic Network Process (ANP) are anal ysed using Individual Differences Scaling (INDSCAL). This is the first time such a procedure has been used in this context. In the second the single set of dissimilarities that arise from the Analytic Hierarchy Process (AHP) are analysed using Multidimensional Scaling (MDS). The novel approach adopted here replaces a complex iterative procedure with a systematic ap proach that may be readily automated.

Highlights

  • It is often said that a picture is worth a thousand words

  • The Analytic Hierarchy Process (AHP) is a method for formalizing decision making where there are a limited number of choices but each has a number of attributes and it my be difficult to formalize some of those attributes

  • In the AHP procedure the decision maker is required to make pair wise comparisons between n alternatives based on a ratio scale, the choices are made from the integers between 1 and 9 and their reciprocals (I = {1/9, 1/8, 1/7, 1/5, 1/4, 1/3, 1/2, 1, 2, 3, 4, 5, 6, 7, 8, 9})

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Summary

Introduction

It is often said that a picture is worth a thousand words. It is always useful to have diagrams to enhance the interpretation of analytic techniques. In recent years many papers have been written examining the Analytic Hierarchy Process (AHP, Saaty, 2001, for example) as an aid to decision making. This has been extended to the Analytic Network Process (ANP, Saaty, 1996). The first example benefits from the application of the INDSCAL procedure, while for the second a direct procedure is developed which avoids the iterative scheme previously utilised For those not familiar with the numerical procedures employed here: Analytic Hierarchy Process, Analytic Network Process, Individual Differences Scaling, Non-metric Multidimensional Scaling and Procrustes Analysis. These are briefly reviewed; the topics are presented in alphabetic order

Analytic hierarchy process
Analytic network process
Individual differences scaling
Non-metric multidimensional scaling
Procrustes analysis
Example 1 – The Analytic Network Process
How Different Are the Features
Example 2 – The Analytic Hierarchy Process
The Data
Notation
Procedure
Applying Multidimensional Scaling
10. Conclusion

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