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Analytic Hierarchy Process(AHP)
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The Analytic Hierarchy Process (AHP) is a structured technique for organizing and analyzing complex
decisions, based on mathematics and psychology. It was developed by Thomas L. Saaty in the 1970s and has been extensively studied and refined since then.
Analytic Hierarchy Process4 Major Steps of AHP:
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Analytic Hierarchy Process
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Saati Scale
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Analytic Network Process(ANP)
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The Analytic Network Process (ANP) is a more general form of the analytic hierarchy process (AHP) used in multi-criteria decision analysis.
AHP structures a decision problem into a hierarchy with a goal, decision criteria, and alternatives, while the ANP structures it as a
network. Both then use a system of pairwise comparisons to measure the weights of the components of the structure, and finally to rank the
alternatives in the decision.
Analytic Network Process
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In a hierarchy, alternatives affect (depend on) the criteria, criteria affect goal. It is assumed that:– Criteria do not affect alternatives– Criteria do not depend on each other– Alternatives do not depend on each otherIn complex decisions there may be dependence and feedback.Network model with dependence and feedback improves the priorities derived from judgments and makes prediction much more accurate
Analytic Network Process4 Major Steps of ANP:
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Step1: Model Construction and Problem Structuring
Step2: Pairwise Comparison Matrices and Priority Vectors
Step3: Supermatrix Formation
Step4: Selection of The Best Alternatives
Analytic Network Process
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Step1: Model Construction and Problem Structuring
The problem should be stated clearly and be decomposed into a rational system, like a network. This network structure can be obtained by decision-makers through brainstorming or other appropriate methods.
Analytic Network Process
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Step2: Pairwise Comparison Matrices and Priority Vectors
Similar to the comparisons performed in AHP, pairsof decision elements at each cluster are compared with
respect to their importance towards their controlcriteria. The clusters themselves are also compared
pairwise with respect to their contribution to theobjective. Decision-makers are asked to respond to a
series of pairwise comparisons of two elementsor two clusters to be evaluated in terms of their
contribution to their particular upper level criteria.
Analytic Network Process
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Step2: Pairwise Comparison Matrices and Priority Vectors
In addition, interdependencies among elements of a cluster must also be examined pairwise;
the influence of each element on other elements can be represented by an eigenvector. The relative
importance values are determined with Saaty’s 1–9 scale ,where a score of 1 represents equal
importance between the two elements and a score of 9 indicates the extreme importance of one element
(row cluster in the matrix) compared to the other one (column cluster in the matrix).
Analytic Network Process
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Step2: Pairwise Comparison Matrices and Priority Vectors
A reciprocal like with AHP, pairwise comparison in ANP is performed in the framework of a matrix, and a local
priority vector can be derived as an estimate of the relative importance associated with the elements (or clusters)
being compared by solving the following equation:
Where A is the matrix of pairwise comparison, w is the eigenvector, and λ max is the largest eigenvalue of A.
Saaty proposes several algorithms to approximate w. In this paper, Expert Choice is used to compute the eigenvectors from the pairwise
comparison matrices and to determine the consistency ratios.
Analytic Network Process
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Step3: Supermatrix Formation
The Supermatrix concept is similar to the Markov chain process.To obtain global priorities in a system with interdependent influences, the local priority vectors are entered in the appropriate columns of a matrix. As a result, a supermatrix is actually a partitioned matrix, where each matrix segment represents a relationship between two clusters in a system.The local priority vectors obtained in Step 2 are grouped and placed in the appropriate positions in a supermatrix based on the flow of influence from one cluster to another, or from a cluster to itself, as in the loop.
Analytic Network Process
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Step4: Selection of The Best Alternatives
If the supermatrix formed in Step 3 covers the whole network, the priority weights of the alternatives can be found in the column of
alternatives in the normalized supermatrix. On the other hand, if a supermatrix only comprises clusters that are interrelated, additional calculations must be made to obtain the overall
priorities of the alternatives. The alternative with the largest overall priority should be selected, as it is the best alternative as determined by the calculations made using matrix operations.
Case Study
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لیل به کارگیری تکنیک فرآیند تحلیل شبکه ای در تح
نقاط قوت، ضعف، فرصت و تهدید
(مطالعه موردی شرکت سهامی بیمه ایران)
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AHP ANP
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ماتریس مقایسه زوجی گروه SWOTهای
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وابستگی های درونی گروه SWOTهای
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ماتریس درجه اهمیت استراتژی های جایگزین
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اولویت های نهایی گزینه های استراتژی
SO>WO>ST>WT