Representation and application of Fuzzy soft sets in type-2 environment

This paper has represented a soft-set in the type-2 environment by its simplest form as an augmentation to soft-set theories. Furthermore, we have applied the type-2 fuzzy soft set(T2FSS) by using our most straightforward representation to find the solution of a decision-making-problem (DMP) based-on T2FSS as well as weighted type-2 fuzzy soft set (WT2FSS). We have proposed two definitions, namely, Mid-$$\alpha $$ α -threshold fuzzy-set of a T2FSS and Mid-$$\lambda $$ λ -threshold fuzzy-set of a T2FSS. Furthermore, we have presented the definition, namely, level fuzzy-soft-set(LFSS) of a T2FSS. Using this concept, we have prepared two algorithms to select one object in T2FSS as well as WT2FSS based on DMP, which take regret disinclination and expectation preference of decision-makers into consideration in the decision procedure. Also, we have presented two numerical examples at the end.