期刊
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 250, 期 2, 页码 628-638出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.ejor.2015.09.010
关键词
Decision analysis; Interval multiplicative comparison matrix; Consistency; Acceptability; Logarithmic least square
资金
- National Natural Science Foundation of China [71572040, 71271188, 71272129]
- Zhejiang Provincial Natural Science Foundation of China [LY15G010004]
- Humanities and Social Science Foundation of Ministry of Education of China [14YJC880069]
- Natural Sciences and Engineering Research Council of Canada
Existing research on acceptability of pairwise interval comparison matrices focuses on acceptable consistency by controlling their inconsistency levels to within a certain threshold. However, a perfectly consistent but highly indeterminate interval comparison matrix can be unacceptable as it contains little (sometimes no) useful decision information. This paper first analyzes the current definition of acceptable consistency for interval multiplicative comparison matrices (IMCMs) and shows its technical deficiencies. We then introduce a new notion of acceptable IMCMs, considering both inconsistency and indeterminacy levels in IMCMs. A geometric-mean-based index is proposed to measure the indeterminacy ratio of an IMCM, and useful properties are derived for consistent IMCMs and acceptable IMCMs. An indeterminacy-ratio and geometric mean-based transformation equation is subsequently put forward to convert normalized acceptable interval multiplicative weights into an acceptable IMCM with consistency. By introducing an auxiliary constraint, a logarithmic least square model is established to generate interval multiplicative weights from acceptable IMCMs. A geometric-mean-based possibility degree formula is designed to compare and rank normalized interval multiplicative weights. Two numerical examples are presented to illustrate how to utilize the proposed framework. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
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