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.

knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. due to properly converting the task of optimization to an equivalent...

‎In this paper‎, ‎we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings‎. ‎Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived‎. ‎Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate...

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,...

We introduce a new measure for planar point sets S that captures a combinatorial distance that S is from being a convex set: The reflexivity ρ(S) of S is given by the smallest number of reflex vertices in a simple polygonalization of S. We prove various combinatorial bounds and provide efficient algorithms to compute reflexivity, both exactly (in special cases) and approximately (in general). O...

in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

In this paper, we have focused to study convex $L$-subgroups of an $L$-ordered group. First, we introduce the concept of a convex $L$-subgroup and a convex $L$-lattice subgroup of an $L$-ordered group and give some examples. Then we find some properties and use them to construct convex $L$-subgroup generated by a subset $S$ of an $L$-ordered group $G$ . Also, we generalize a well known result a...