Today, soft computing is a field that is used a lot in solving real-world problems, such as problems in economics, finance, banking... With the aim to serve for solving the real problem, many new theories and/or tools which were proposed, improved to help soft computing used more efficiently. We can mention some theories as fuzzy sets theory (L. Zadeh, 1965), intuitionistic fuzzy set (K Atanasov, 1986). In this paper, we introduce a new notion of support-intuitionistic fuzzy (SIF) set, which is the combination a intuitionistic fuzzy set with a fuzzy set. So, SIF set is a directly extension of fuzzy set and intuitionistic fuzzy sets (Atanassov). Then, we define some operators on support-intuitionistic fuzzy sets, and investigate some properties of these operators.

Fuzzy set theory was introduced by L.A. Zadeh in 1965. Immediately, it has many applications in practice and in building databases, one of which is the construction of a fuzzy relational database based on similar relationship. The study of cases of fuzzy relations in different environments will help us understand its applications. In this paper, the rough fuzzy relation on Cartesian product of two universe sets is defined, and then the algebraic properties of them, such as the max, min, and composition of two rough fuzzy relations are examined. Finally, reflexive, α-reflexive, symmetric and transitive rough fuzzy relations on two universe sets are also defined.