The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between  $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is  bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.

A bimonotone linear inequality is a linear inequality with at most two nonzero coefficients that are of opposite signs (if both different from zero). A linear inequality defines a halfspace that is a sublattice of Rn (a subset closed with respect to componentwise maximum and minimum) if and only if it is bimonotone. Veinott has shown that a polyhedron is a sublattice if and only if it can be de...

We discuss some interesting sublattices of interval-valued fuzzy subgroups. In our main result, we consider the set of all interval-valued fuzzy normal subgroups with finite range that attain the same value at the identity element of the group. We then prove that this set forms a modular sublattice of the lattice of interval-valued fuzzy subgroups. In fact, this is an interval-valued fuzzy vers...

In this paper, a characterization of convex fuzzy mappings is obtained. SupposeF C : ® F is a fuzzy mapping, whereC is a non-empty convex subset ofR andF is the set of all fuzzy numbers. With respect to the fuzzy-max order, F is convex if and only if it is both quasi-convex and intermediate-point convex. In this paper, a characterization of convex fuzzy mappings will be given. Specifically, it ...

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...

The problem of finding the digital convex fuzzy hull of a digital fuzzy set, whose support is made of some digital points (centroids) in Z, is considered here. A region is DL−convex if, for any two pixels belonging to it, there exists a digital straight line between them, all of whose pixels belong to the region. An algorithm how to compute the DL−convex hull of a digital region is described. A...

In many scientific and engineering applications, the fuzzy set concept plays an important role. The fuzziness appears when we need to perform, on manifold, calculations with imprecision variables. The fuzzy set theory was introduced initially by Zadeh [1] in 1965. In the theory and applications of fuzzy sets, convexity is a most useful concept. In fact, in the basic and classical paper [1], Zad...

K e y w o r d s F u z z y convexity; Fuzzy criterion sets, Pareto-optimal decision, Multiple objective optimization. 1. I N T R O D U C T I O N Since most of practical decision problems are fuzzy and approximate, fuzzy decision making becomes one of the most impor tan t practical approaches. However, the result ing problems are frequently complicated and difficult to solve. One effective way to...

Keywords--Fuzzy numbers, Convexity, Preinvexity, Generalized convexity, Fuzzy mappings. 1. I N T R O D U C T I O N Let R n deno te t he n -d imens iona l Euc l idean space. T h e suppor t , supp (p), of a fuzzy set # : R n ~ I = [0, 1] is def ined as s u p p ( # ) = { x e R n ] # ( x ) > 0} . A fuzzy set # : R n ~ I is cal led fuzzy convex if i t is quas i concave in c o m m o n sense on its su...

Generalized concept lattices have been recently proposed to deal with uncertainty or incomplete information as a non-symmetric generalization of the theory of fuzzy formal concept analysis. On the other hand, concept lattices have been defined as well in the framework of fuzzy logics with non-commutative conjunctors. The contribution of this paper is to prove that any concept lattice for noncom...