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RESEARCH 0N CONSTBUCTING SYNTHETIC MATRIX IN AHP

Xu, Ze-shui

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Abstract

This paper presents a new method for constructing synthetic matrix which is obtained by extending the given judgement matrices in the Analytic Hierarchy Process(AHP).The consistency relationship among the given matrices and therir synthetic matrix is studied.The method can be used to deal with situations where the number of the given alternatives is larger than nine,and needs less pairwise comparisons thanany others.Thus it will aid in the design of the AHP,which will reduce the information overload of decision maker,a major drawback of the original AHP algorithm.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

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What this paper is about

This paper presents a new method for constructing synthetic matrix which is obtained by extending the given judgement matrices in the Analytic Hierarchy Process(AHP).The consistency relationship among the given matrices and therir synthetic matrix is studied.The method can be used to deal with situations where the number of the given alternatives is larger than nine,and needs less pairwise comparisons thanany others.Thus it will aid in the design of the AHP,which will reduce the information overload of decision maker,a major drawback of the original AHP algorithm.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

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Available abstract

This paper presents a new method for constructing synthetic matrix which is obtained by extending the given judgement matrices in the Analytic Hierarchy Process(AHP).The consistency relationship among the given matrices and therir synthetic matrix is studied.The method can be used to deal with situations where the number of the given alternatives is larger than nine,and needs less pairwise comparisons thanany others.Thus it will aid in the design of the AHP,which will reduce the information overload of decision maker,a major drawback of the original AHP algorithm.Finally,a numerical example is given to show the feasibility and effectiveness of the method.

Key concepts: Analytic hierarchy process, Judgement, Pairwise comparison, Matrix (chemical analysis), Consistency (knowledge bases), Decision maker, Computer science, Operations research

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