Geometric consistency based interval weight elicitation from intuitionistic preference relations using logarithmic least square optimization
This paper introduces the notion of intuitionistic fuzzy geometric indices to capture the central tendency of Atanassov’s intuitionistic fuzzy values (A-IFVs). A ratio-based hesitation margin is defined to measure the hesitancy of an A-IFV and used to determine the geometric mean based hesitation margin of an intuitionistic preference relation (IPR). The paper defines geometric consistency of IPRs based on the intuitionistic fuzzy geometric index, and puts forward some properties for geometry consistent IPRs. A parameterized transformation formula is proposed to convert normalization interval weights into geometry consistent IPRs. A logarithmic least square model is developed for constructing the fitted geometry consistent IPR and deriving interval weights from an IPR. Based on the fitted consistent IPR, a method is provided to check the acceptable geometry consistency for IPRs, and an algorithm is further devised to solve multiple criteria decision making problems with IPRs. Two numerical examples and comparisons with existing approaches are provided to illustrate the performance and effectiveness of the proposed models.
KeywordsIntuitionistic preference relation Intuitionistic fuzzy geometric index Geometric consistency Logarithmic least square Multiple criteria decision making
The author would like to thank the Associate Editor and the anonymous reviewers for their constructive comments and suggestions. This research is supported by the National Natural Science Foundation of China (NSFC) under Grant 71271188.
- Liao, H., & Xu, Z. (2014a). Some algorithms for group decision making with intuitionistic fuzzy preference information. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22, 505–529.Google Scholar
- Liao, H., & Xu, Z. (2014b). Priorities of intutionistic fuzzy preference relation based on multiplicative consistency. IEEE Transactions on Fuzzy Systems, 22, 1669–1681.Google Scholar
- Szmidt, E., & Kacprzyk, J. (2009). Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. In E. Rakus-Andersson, R. Yager, N. Ichalkaranje, & L. Jain (Eds.), Recent advances in decision making (Studies in Computational Intelligence) (pp. 7–19). Berlin: Springer.CrossRefGoogle Scholar
- Wu, J., & Chiclana, F. (2014b). Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building. Knowledge-Based Systems, 71, 187–200.Google Scholar