Soft set and multi-fuzzy set have been successfully used as an effective mathematical tool for dealing with uncertainty. In this work, we first extend multi-fuzzy set to multi-vague set. By combining the multi-vague set and soft set models, we then introduce the concept of multi-vague soft sets, which can be regarded as a extension of some existing soft set models. We also define some operations on multi-fuzzy vague soft set and study some of their desirable properties. Furthermore, we discuss the lattice of multi-fuzzy vague soft set.
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