By using parameterized representation of fuzzy numbers, criteria for a lower semicontinuous fuzzy mapping defined on a non-empty convex subset of Rn to be a convex fuzzy mapping are obtained. c © 2007 Elsevier Ltd. All rights reserved.

Despite convex mathematical optimization methods be applied to general linear optimization problems it can also be applied in a special class of nonlinear optimization. As ambiguity and vagueness are natural and ever-present in real-life situations requiring solutions, it makes perfect sense to attempt to address them using fuzzy convex optimization. In this work, two fuzzy convex approaches ba...

In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several...

and Applied Analysis 3 2.1. Fuzzy Numbers In this section, we give certain essential concepts of fuzzy numbers and their basic properties. For further information see 2, 3 . A fuzzy set à on a set X is a function à : X → 0, 1 . Generally, the symbol μà is used for the function à and it is said that the fuzzy set à is characterized by itsmembership function μà : X → 0, 1 which associates with ea...

This paper characterizes those finite lattices which are a maximal sublattice of an infinite lattice. There are 145 minimal lattices with this property, and a finite lattice has an infinite minimal extension if and only if it contains one of these 145 as a sublattice. In [12], I. Rival showed that if L is a maximal sublattice of a distributive lattice K with |K| > 2, then |K| ≤ (3/2)|L|. In [1]...

Let σ be a permutation of the set {1,2, — -, n} and let Π(N) denote the lattice of partitions of {1,2, •••,%}. There is an obvious induced action of σ on Π(N); let Π(N)σ — L denote the lattice of partitions fixed by σ. The structure of L is analyzed with particular attention paid to ^f, the meet sublattice of L consisting of 1 together with all elements of L which are meets of coatoms of L. It ...