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Logarithmic least squares approaches to deriving interval weights, rectifying inconsistency and estimating missing values for interval multiplicative preference relations

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Abstract

The aim of this paper is to develop logarithmic least squares prioritization and completion methods for interval multiplicative preference relations. A parameterized transformation formula is proposed to convert a normalized interval weight vector into a consistent interval multiplicative preference relation. A logarithmic least squares model is established to derive a normalized interval weight vector from an interval multiplicative preference relation and construct the optimized consistent interval multiplicative preference relation. Subsequently, a logarithmic least squares model is built to rectify inconsistency for a complete interval multiplicative preference relation without consistency, and a logarithmic least squares completion model is developed to estimate missing values for an incomplete interval multiplicative preference relation. Several numerical examples are examined to illustrate the validity and applicability of the proposed methods, and comparisons with other existing methods are also made.

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Acknowledgments

The author thanks the anonymous referees for their valuable suggestions in improving this paper. This work is supported by the National Natural Science Foundation of China (Grant No. 61375075) and the Natural Science Foundation of Hebei Province of China (Grant Nos. F2012201020 and F2015402033).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Hebei University, Baoding, 071002, Hebei, China

    Zhiming Zhang

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  1. Zhiming Zhang
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Correspondence to Zhiming Zhang.

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Communicated by V. Loia.

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Zhang, Z. Logarithmic least squares approaches to deriving interval weights, rectifying inconsistency and estimating missing values for interval multiplicative preference relations. Soft Comput 21, 3993–4004 (2017). https://doi.org/10.1007/s00500-016-2049-6

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  • DOI: https://doi.org/10.1007/s00500-016-2049-6

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