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Soft Computing
Published in: Soft Computing 14/2017

10-02-2016 | Methodologies and Application

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

Author: Zhiming Zhang

Published in: Soft Computing | Issue 14/2017

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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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Metadata
Title
Logarithmic least squares approaches to deriving interval weights, rectifying inconsistency and estimating missing values for interval multiplicative preference relations
Author
Zhiming Zhang
Publication date
10-02-2016
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 14/2017
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-016-2049-6

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