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 point out that the proof of Theorem 2.4(5), Proposition 2.6(1) and 2.8(1) in paper titled ?On (L,M)-fuzzy convex structures? (Filomat 33(13): 4151-4163, 2019) are not true general. Then, give three correct proofs these results

This paper presents the concepts of (L,M)-remotehood spaces and (L,M)-convergence in framework (L,M)-fuzzy convex spaces. Firstly, it is shown that category isomorphic to Secondly, proved can be embedded as a reflective subcategory. Finally, preconvex (L,M)- convergence are introduced

Properties of several sorts of lattices of convex subsets of Rn are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of Rn and the lattice of all convex subsets of R. The lattices of arbitrary, of open bounded, and of compact convex sets in Rn all satisfy the same identitie...

We introduce the concept of Mσ-approachability for a semicontinuous function (i.e. a nonadditive measure) on a σ-complete sublattice of a locally complete σ-continuous lattice L and using it we extend a nonadditive measure from a sublattice of L to a σ-complete sublattice of L. AMS Mathematics Subject Classification (2000): 28A12, 28C15, 28B10

Whaley’s Theorem on the existence of large proper sublattices of infinite lattices is extended to ordered sets and finite lattices. As a corollary it is shown that every finite lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 3 . It is also shown that that every finite modular lattice L with |L| ≥ 3 contains a proper sublattice S with |S| ≥ |L| 2 , and every finite distribut...

g e y w o r d s F u z z y numbers, Convexity, Continuity, Convex fuzzy mappings, Linear ordering, Fuzzy Weirstrass theorem, Fuzzy optimization. 1. I N T R O D U C T I O N Let R n denote the n-dimensional Eucl idean space. The suppor t , supp(#) , of a fuzzy set # : R ~ I = [0, 1] is defined as supp(/~) = {x • R n I #(x) > 0}. A fuzzy set # : R n --~ I is called fuzzy convex if #(Ax + (1 A)y) _>...

The Carathéodory, Helly, and Radon numbers are three main invariants in convexity theory. They relate, respectively, to minimal representations of points in a convex hull; to the size of minimal infeasible inequality systems; and to VC-dimensions and the existence of centerpoints (generalized medians). These invariants have been determined, exactly or approximately, for a number of different co...

the aim of this paper is to introduce and study set- valued homomorphism on lattices and t-rough lattice with respect to a sublattice. this paper deals with t-rough set approach on the lattice theory. the result of this study contributes to, t-rough fuzzy set and approximation theory and proved in several papers. keywords: approximation space; lattice; prime ideal; rough ideal; t-rough set; set...

 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...