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A Linear Goal Programming Method for Calculating Weights in the Interval AHP

Mu Zeng

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Abstract

Based on the incorporation differences between actual interval and judgment interval given by the experts' pairwise comparison, the problem of calculating weights in the interval AHP is studied in three aspects. And on the basis of the solution to a linear goal programming three new algorithms for the interval weight of each alternative derived from interval judgment matrix are proposed respectively. Finally, the effectiveness of these algorithms is illustrated by the solution to a practical example.

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What this paper is about

Based on the incorporation differences between actual interval and judgment interval given by the experts' pairwise comparison, the problem of calculating weights in the interval AHP is studied in three aspects. And on the basis of the solution to a linear goal programming three new algorithms for the interval weight of each alternative derived from interval judgment matrix are proposed respectively. Finally, the effectiveness of these algorithms is illustrated by the solution to a practical example.

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Available abstract

Based on the incorporation differences between actual interval and judgment interval given by the experts' pairwise comparison, the problem of calculating weights in the interval AHP is studied in three aspects. And on the basis of the solution to a linear goal programming three new algorithms for the interval weight of each alternative derived from interval judgment matrix are proposed respectively. Finally, the effectiveness of these algorithms is illustrated by the solution to a practical example.

Key concepts: Analytic hierarchy process, Interval (graph theory), Pairwise comparison, Goal programming, Linear programming, Mathematical optimization, Matrix (chemical analysis), Basis (linear algebra)

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