期刊
SOFT COMPUTING
卷 21, 期 14, 页码 3993-4004出版社
SPRINGER
DOI: 10.1007/s00500-016-2049-6
关键词
Goal programming; Interval multiplicative preference relation; Consistency; Prioritization; Completion
资金
- National Natural Science Foundation of China [61375075]
- Natural Science Foundation of Hebei Province of China [F2012201020, F2015402033]
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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