theory of fuzzy sets

In our work in this paper, we define intuitionistic fuzzy complex subgroups with respect to t-norm T and s-norm S and investigate some properties of them in detail. Next, we obtain some results about them and give some relationships between them. Later, we introduce the inverse, composition, intersection and normality of them and we prove some basic new results and present some properties of them such that the inverse and composition of two intuitionistic fuzzy complex subgroups with respect to t-norm T and s-norm S will be intuitionistic complex fuzzy subgroups with respect to t-norm T and s-norm S. Also we consider and give some characterizations of them. Finally, we discuss them under group homomorphisms and investigate some related properties such that the image and preimage of two intuitionistic fuzzy complex subgroups with respect to t-norm T and s-norm S will be intuitionistic complex fuzzy subgroups with respect to t-norm T and s-norm S.

In this article, by using norms($T$ and $C$), we present the concept of intuitionistic fuzzy implicative ideals,  intuitionistic fuzzy closed implicative ideals and intuitionistic fuzzy commutative ideals of $BCI$-algebras. Some interesting results of them are given. Characterisations of implicative ideals, closed implicative ideals and commutative ideals of $BCI$-algebras by using them are explored. By using intersections, direct products and homomorphisms, some interesting results are obtained.

In this paper, we use the notion of t-norms to introduce fuzzy subalgebras, fuzzy ideals, fuzzy implicative ideals, fuzzy positive implicative ideals in BCK-algebras. Next, we clarify the links between them and investigate their properties. Finally, we consider them under intersection, cartesian product and homomorphisms(image and pre image) and we study related properties.

In this paper, by using norms (t-norms and t-conorms), we introduce the notions of bifuzzy d-algebras and bifuzzy d-ideals of d-algebras and investigate several interesting properties. Next, we consider their intersection and product. Finally, we obtain some results about them under d-algebra homomorphisms.