Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations


Genc S., BORAN F. E. , AKAY D. , Xu Z.

INFORMATION SCIENCES, cilt.180, sa.24, ss.4877-4891, 2010 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 180 Konu: 24
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1016/j.ins.2010.08.019
  • Dergi Adı: INFORMATION SCIENCES
  • Sayfa Sayıları: ss.4877-4891

Özet

In this paper, the concept of multiplicative transitivity of a fuzzy preference relation, as defined by Tanino [T. Tanino, Fuzzy preference orderings in group decision-making, Fuzzy Sets and Systems 12 (1984) 117-131], is extended to discover whether an interval fuzzy preference relation is consistent or not, and to derive the priority vector of a consistent interval fuzzy preference relation. We achieve this by introducing the concept of interval multiplicative transitivity of an interval fuzzy preference relation and show that, by solving numerical examples, the test of consistency and the weights derived by the simple formulas based on the interval multiplicative transitivity produce the same results as those of linear programming models proposed by Xu and Chen [Z.S. Xu, J. Chen, Some models for deriving the priority weights from interval fuzzy preference relations, European Journal of Operational Research 184 (2008) 266-280]. In addition, by taking advantage of interval multiplicative transitivity of an interval fuzzy preference relation, we put forward two approaches to estimate missing value(s) of an incomplete interval fuzzy preference relation, and present numerical examples to illustrate these two approaches. (C) 2010 Published by Elsevier Inc.