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Combination of interval-valued fuzzy set and soft set

✍ Scribed by Xibei Yang; Tsau Young Lin; Jingyu Yang; Yan Li; Dongjun Yu

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
513 KB
Volume
58
Category
Article
ISSN
0898-1221

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✦ Synopsis

The soft set theory, proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. By combining the interval-valued fuzzy set and soft set models, the purpose of this paper is to introduce the concept of the interval-valued fuzzy soft set. The complement, ''AND'' and ''OR'' operations are defined on the interval-valued fuzzy soft sets. The DeMorgan's, associative and distribution laws of the interval-valued fuzzy soft sets are then proved. Finally, a decision problem is analyzed by the interval-valued fuzzy soft set. Some numerical examples are employed to substantiate the conceptual arguments.

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The value A(x) for a particular x is typically associated with a degree of belief of some expert. There is now a quite extensive theory of fuzzy sets, the basics involving putting operations on the set ?J'(S) of all fuzzy subsets of the set S. These operations stem from operations on the unit interv