Fuzzy Optimization and Decision Making

, Volume 14, Issue 3, pp 289–310

# Geometric consistency based interval weight elicitation from intuitionistic preference relations using logarithmic least square optimization

• Zhou-Jing Wang
Article

## Abstract

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.

## Keywords

Intuitionistic preference relation Intuitionistic fuzzy geometric index Geometric consistency Logarithmic least square Multiple criteria decision making

## Notes

### Acknowledgments

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.

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