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Journal of Applied Mathematics
Volume 2012, Article ID 608681, 35 pages
Research Article

Type-2 Fuzzy Soft Sets and Their Applications in Decision Making

College of Mathematics and Computer Sciences, Hebei University, Hebei, Baoding 071002, Hebei Province, China

Received 23 May 2012; Revised 26 September 2012; Accepted 10 October 2012

Academic Editor: Hector Pomares

Copyright © 2012 Zhiming Zhang and Shouhua Zhang. 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.


Molodtsov introduced the theory of soft sets, which can be used as a general mathematical tool for dealing with uncertainty. This paper aims to introduce the concept of the type-2 fuzzy soft set by integrating the type-2 fuzzy set theory and the soft set theory. Some operations on the type-2 fuzzy soft sets are given. Furthermore, we investigate the decision making based on type-2 fuzzy soft sets. By means of level soft sets, we propose an adjustable approach to type-2 fuzzy-soft-set based decision making and give some illustrative examples. Moreover, we also introduce the weighted type-2 fuzzy soft set and examine its application to decision making.