In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries....

In this note the notion of interval-valued fuzzy BF -algebras (briefly, i-v fuzzy BF -algebras), the level and strong level BF -subalgebra is introduced. Then we state and prove some theorems which determine the relationship between these notions and BF -subalgebras. The images and inverse images of i-v fuzzy BF -subalgebras are defined, and how the homomorphic images and inverse images of i-v ...

In this note the notion of interval-valued fuzzy QS-algebra (briefly, i-v fuzzy QS-algebra), as well as the i-v level and strong i-v level QS-subalgebra is introduced. Several theorems which determine the relationship between these notions and QS-subalgebras are stated and proved. The images and inverse images of i-v fuzzy QS-subalgebras are defined, and how the homomorphic images and inverse i...

In this paper, the notion of $L$-convex fuzzy sublattices is introduced and their characterizations are given. Furthermore,  the notion of the degree to which an $L$-subset is an $L$-convex fuzzy sublattice is proposed and its some  characterizations are given. Besides, the $L$-convex fuzzy sublattice degrees of the homomorphic image and pre-image of an $L$-subset are studied. Finally, we obtai...

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ord...

 The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generate...

In this paper, we propose a new method for fuzzy numbers. In this method, we assume that Ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. So, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. Then, Mic and Mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. Finally,...