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Mathematical Problems in Engineering
Volume 2015, Article ID 254764, 17 pages
Research Article

On Interval-Valued Hesitant Fuzzy Soft Sets

1School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou, Gansu 730030, China
2School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, Yunnan 650500, China

Received 16 October 2014; Revised 13 January 2015; Accepted 19 January 2015

Academic Editor: Shuming Wang

Copyright © 2015 Haidong Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


By combining the interval-valued hesitant fuzzy set and soft set models, the purpose of this paper is to introduce the concept of interval-valued hesitant fuzzy soft sets. Further, some operations on the interval-valued hesitant fuzzy soft sets are investigated, such as complement, “AND,” “OR,” ring sum, and ring product operations. Then, by means of reduct interval-valued fuzzy soft sets and level hesitant fuzzy soft sets, we present an adjustable approach to interval-valued hesitant fuzzy soft sets based on decision making and some numerical examples are provided to illustrate the developed approach. Finally, the weighted interval-valued hesitant fuzzy soft set is also introduced and its application in decision making problem is shown.