Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 60, Issue 3, Pages 906-918Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.05.036
Keywords
Soft sets; Fuzzy soft sets; Interval-valued fuzzy soft sets; Intuitionistic fuzzy soft sets; Interval-valued intuitionistic fuzzy soft sets
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Funding
- The National Natural Science Foundation of China [60663001, 60673135, 60970044, 60736020]
- The Foundation of the State Key Laboratory of Computer Science of Chinese Academy of Sciences [SYSKF0904]
- The Natural Science Foundation of Guangxi Province of China [0991100, 0832103]
- The Science Research and Technology Development Project of Guangdong Province of China [2009B090300326, 2009B010800036]
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Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, the notion of the interval-valued intuitionistic fuzzy soft set theory is proposed. Our interval-valued intuitionistic fuzzy soft set theory is a combination of an interval-valued intuitionistic fuzzy set theory and a soft set theory. In other words, our interval-valued intuitionistic fuzzy soft set theory is an interval-valued fuzzy extension of the intuitionistic fuzzy soft set theory or an intuitionistic fuzzy extension of the interval-valued fuzzy soft set theory. The complement, and, or, union, intersection, necessity and possibility operations are defined on the interval-valued intuitionistic fuzzy soft sets. The basic properties of the interval-valued intuitionistic fuzzy soft sets are also presented and discussed. (C) 2010 Elsevier Ltd. All rights reserved.
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