Abstract
By combining type-2 fuzzy set theory and soft set theory, the notion of type-2 fuzzy soft set theory is proposed. In other words, our type-2 fuzzy soft set theory is a type-2 fuzzy extension of the soft set theory. Some operations are defined on type-2 fuzzy soft sets. Two algorithms are given to solve decision making problems under complete type-2 fuzzy soft sets environment and incomplete type-2 fuzzy soft sets environment, respectively.
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