Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making

Authors:
Guiwu Wei;Xiaofei Zhao
Affiliations:
School of Economics and Management, Chongqing University of Arts and Sciences, Yongchuan, China;School of Economics and Management, Chongqing University of Arts and Sciences, Yongchuan, China
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2013

Citing 24
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Abstract

In this paper, we investigate the multiple attribute decision making MADM problems with hesitant interval-valued fuzzy information. We first introduce some operations on hesitant fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and propose the hesitant interval-valued fuzzy sets. Then, we further develop some new Einstein aggregation operators with hesitant interval-valued fuzzy information, such as the hesitant interval-valued fuzzy Einstein weighted average HIVFEWA operator, hesitant interval-valued fuzzy Einstein weighted geometric HIVFEWG operator, hesitant interval-valued fuzzy Einstein ordered weighted average HIVFEOWA operator, hesitant interval-valued fuzzy Einstein ordered weighted geometric HIVFEOWG operator, induced hesitant interval-valued fuzzy Einstein ordered weighted averaging I-HIVFEOWA operator and induced hesitant interval-valued fuzzy Einstein ordered weighted geometric I-HIVFEOWG operator. Then, we apply the induced hesitant interval-valued fuzzy Einstein ordered weighted averaging I-HIVFEOWA operator and induced hesitant interval-valued fuzzy Einstein ordered weighted geometric I-HIVFEOWG operator to deal with multiple attribute decision making under the hesitant interval-valued fuzzy environments. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.