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.

868 NOTICES OF THE AMS VOLUME 46, NUMBER 8 I n his pivotal 1916 paper [P], Georg Pick begins somewhat provocatively with the phrase, “The so-called Schwarz Lemma says...”, followed by a reference to a 1912 paper of Carathéodory. Pursuing that lead, one finds a reference to the original source in the expanded notes from a lecture course at the Eidgenössische Polytechnische Schule in Zürich given...

The approximation-solvability of the following class of nonlinear variational inequality (NVI) problems, based on a new generalized auxiliary problem principle, is discussed. Find an element x∗ ∈K such that 〈(S − T ) (x∗) , x− x∗〉+ f(x)− f (x∗) ≥ 0 for all x ∈ K, where S, T : K → H are mappings from a nonempty closed convex subset K of a real Hilbert space H into H , and f : K → R is a continuo...

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...

the intuitionistic fuzzy set has been applied to game theory very rarely since it was introduced by atanassov in 1983. the aim of this paper is to develop an effective methodology for solving matrix games with payoffs of atanassov’s triangular intuitionistic fuzzy numbers (tifns). in this methodology, the concepts and ranking order relations of atanassov’s tifns are defined. a pair of bi-object...

Deconvolution filtering where the system and noise dynamics are obtained by parametric system identification is considered. Consistent with standard identification methods, ellipsoidal uncertainty in the estimated parameters is considered. Three problems are considered: 1) Computation of the worst case H2 performance of a given deconvolution filter in this uncertainty set. 2) Design of a filter...

Statistical model validation is treated for a general class of nonparamet-ric uncertainty models. This problem is shown to reduce, in many cases of interest, to computing the limit of a sequence (V k) 1 1 of relative weighted volumes of convex sets in R k. An associated decision problem is shown to reduce to a pair of likelihood ratio tests. The notion of testability is introduced to describe u...