期刊
COMPUTERS & INDUSTRIAL ENGINEERING
卷 111, 期 -, 页码 67-78出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.cie.2017.07.002
关键词
Multiplicative consistency; Triangular reciprocal preference relation; Interval reciprocal preference relation; Constrained fuzzy arithmetic; AHP
Extension of Saaty's definition of consistency to interval and fuzzy reciprocal preference relations is studied in the paper. The extensions of the definition to interval and triangular reciprocal preference relations proposed by Wang (2005), Liu (2009), Liu et al. (2014) and Wang (2015a, 2015b) are reviewed and some shortcomings in the definitions are pointed out. Particularly, as was already shown by Wang (2015a, 2015b), the definitions of consistency proposed by Liu (2009) and Liu et al. (2014) are not invariant under permutation of compared objects. Wang's (2015a, 2015b) definitions rectify this drawbacks. However, as is pointed out in this paper, Wang's definitions of consistent interval and triangular reciprocal preference relations do not keep the reciprocity of pairwise comparisons, which is the substance of reciprocal preference relations. In this paper, definitions of consistent interval, triangular and trapezoidal reciprocal preference relations invariant under permutation of compared objects and preserving the reciprocity of pairwise comparisons are introduced. Useful tools for verifying the consistency are proposed and some properties of consistent interval and fuzzy reciprocal preference relations are derived. Furthermore, the new definition of consistency for interval reciprocal preference relations is compared with the definition of consistency proposed by Wang et al. (2005), and numerical examples are provided to illustrate the difference between the consistency definitions. (C) 2017 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据