By Matteo Brunelli
The Analytic Hierarchy method (AHP) has been one of many optimum mathematical equipment for choice making with a number of standards and has been largely studied within the operations examine literature in addition to utilized to unravel numerous real-world difficulties. This e-book is intended to introduce and boost the readers’ wisdom of the AHP, regardless of how normal they're with the topic.
This publication presents a concise, but self-contained, advent to the AHP that makes use of a singular and extra pedagogical method. It starts off with an advent to the foundations of the AHP, overlaying the serious issues of the strategy, in addition to a few of its purposes. subsequent, the booklet explores additional facets of the tactic, together with the derivation of the concern vector, the estimation of inconsistency, and using AHP for workforce judgements. each one of those is brought via enjoyable preliminary assumptions. additionally, this publication covers extensions of AHP, that are mostly ignored in undemanding expositions of the tools. Such extensions hindrance varied numerical representations of personal tastes and the period and fuzzy representations of personal tastes to account for uncertainty. in the course of the entire exposition, an eye fixed is stored at the newest advancements of the method.
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Additional resources for Introduction to the Analytic Hierarchy Process
The problem of the ox was a problem of measurement, and we should not forget that the AHP is a theory of relative measurement. The AHP for group decisions has been acclaimed by some researchers, for instance Dyer and Forman . g. ‘Scientific and mathematical generality’, ‘psychophysical applicability’, and ‘applicability to conflict resolution’, for group decisions with MCDM methods, and according to her qualitative analysis, the AHP is a valuable decision methodology for group decisions. The AHP can be used in many different ways as a group decision making method and it can be implemented in the so-called Delphi method .
The logarithm relates (R> , ·) with (R, +) and is perhaps the most famous group isomorphism. In fact, from basics of calculus we know the rule log(x) + log(y) = log(x · y) ∀x, y > 0 , which exposes the relation between pairwise comparison matrices and additive pairwise comparison matrices. The reader familiar with group theory must have understood the strength and the implication of group isomorphism which, in words, was described by Fraleigh in his textbook  as “the concept of two systems being structurally identical, that is, one being just like the other except for names”.
In fact, from basics of calculus we know the rule log(x) + log(y) = log(x · y) ∀x, y > 0 , which exposes the relation between pairwise comparison matrices and additive pairwise comparison matrices. The reader familiar with group theory must have understood the strength and the implication of group isomorphism which, in words, was described by Fraleigh in his textbook  as “the concept of two systems being structurally identical, that is, one being just like the other except for names”. The existence of group isomorphisms between different representations of preference is not a mere theoretical exercise but a precious result as it helps to naturally extend concepts from one representation to another one.