We prove that any standard parabolic subgroup of any Artin group is convex with respect to the standard generating set.

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (∈,∈ ∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investiga...

A measure of nonspecificity is proposed for fuzzy sets with continuous membership functions defined, in general, on the n-dimensional Euclidean space R". The proposed measure is restricted to fuzzy sets that are convex. The measure is justified in terms of the usual axiomatic requirements.

Recently, Gasimov and Yenilmez proposed an approach for solving two kinds of fuzzy linear programming (FLP) problems. Through the approach, each FLP problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. Then, the crisp problem is solved by the use of the modified subgradient method. In this paper we will have another look at the earlier defuzzifi...

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued (∈,∈ ∨q)fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend t...

This contribution, rstly, motivates the need for a new, indistin-guishability-based approach to fuzzy orderings 1]. The main part is devoted to the basic theory, especially constructions, representations, and properties of hulls. Moreover, a general approach to orderings of fuzzy sets is presented. The current work, however, already concentrates on applications in fuzzy control and decision mak...

The purpose of this article is two-fold. In the first place, we prove that a set is the image of a non empty closed convex subset of a real Banach space under an onto Fredholm operator of positive index if and only if it can be written as the union of {Dn : n ∈ N}, a non-decreasing family of non empty, closed, convex and bounded sets such that Dn + Dn+2 ⊆ 2Dn+1 for every n ∈ N. The second part ...

Let X be a metrizable compact convex subset of a locally convex space. Using Choquet's Theorem, wc determine the structure of the support point set of X when X has countably many extreme points. We also characterize the support points of certain families of analytic functions.

If X is a convex surface in a Euclidean space, then the squared (intrinsic) distance function dist(x, y) is d.c. (DC, delta-convex) on X×X in the only natural extrinsic sense. For the proof we use semiconcavity (in an intrinsic sense) of dist(x, y) on X × X if X is an Alexandrov space with nonnegative curvature. Applications concerning r-boundaries (distance spheres) and the ambiguous locus (ex...