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Interval weight generation approaches based on consistency test and interval comparison matrices. (English) Zbl 1082.65525

Summary: A simple yet pragmatic method of consistency test is developed to check whether an interval comparison matrix is consistent or not. The linear programming method is used to derive consistent interval weights from consistent interval comparison matrices and to aggregate local interval weights to generate global interval weights. In cases where an interval comparison matrix is inconsistent, an eigenvector method-based nonlinear programming approach is developed to generate interval weights that can meet predetermined consistency requirements. A simple and effective preference ranking method is utilized to compare the interval weights of criteria or rank alternatives. Three numerical examples including a hierarchical decision problem are provided to illustrate the validity and practicality of the proposed methods.

MSC:

65F30 Other matrix algorithms (MSC2010)
65G30 Interval and finite arithmetic
91B06 Decision theory
62C05 General considerations in statistical decision theory
65K05 Numerical mathematical programming methods
65C60 Computational problems in statistics (MSC2010)
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