In this paper, a new definition of fuzzy bounded sets and totallyfuzzy bounded sets is introduced and properties of such sets are studied. Thena relation between totally fuzzy bounded sets and N-compactness is discussed.Finally, a geometric characterization for fuzzy totally bounded sets in I- topologicalvector spaces is derived.

The C-structurally stable diffeomorphims of a compact manifold are those that satisfy Axiom A and the strong transversality condition (AS). We generalize the concept of AS from diffeomorphisms to invariant compact subsets. Among other properties, we show the structural stability of the AS invariant compact sets K of surface diffeomorphisms f . Moreover if f̂ is the dynamics of a compact manifold...

Continuous set-valued functions with convex images can be approximated by known positive operators of approximation, such as the Bernstein polynomial operators and the Schoenberg spline operators, with the usual sum between numbers replaced by the Minkowski sum of sets. Yet these operators fail to approximate set-valued functions with general sets as images. The Bernstein operators with growing...

In this paper, we show that the Chvátal-Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver [17] for irrational polytopes1, and generalizes the same result for the case of rational polytopes [17], rational ellipsoids [8] and strictly convex bodies [7].

Here we consider the problem of providing near optimal performance for a large set of possible models. We adopt the H∞ framework in the single-input single-output (SISO) setting with structured uncertainty: a compact set of controllable and observable plant models of a fixed order; we consider the control problem of designing a controller to minimize the worst case performance. We consider two ...

Comparative genomic studies are often conducted by reconciliation analyses comparing gene and species trees. One of the issues with reconciliation approaches is that an exponential number of optimal scenarios is possible. The resulting complexity is masked by the fact that a majority of reconciliation software pick up a random optimal solution that is returned to the end-user. However, the alte...

Most published ATPG methods cannot handle three-state primitives, generate too large test sets, or require excessive CPU time. An eecient ATPG system was introduced in 1]]2], which can handle non-Boolean prim-itives, generates compact test sets, within aaordable CPU time. In this paper, the system is extended to handle pulled and wired buses, in addition to pure three-state buses. These bus typ...

In this note we consider the set of metric spaces which are the limits with respect to Lipschitz distance dL of compact connected C°°-Riemannian manifolds of curvature uniformly bounded above and below. We call this set "bounded curvature closure" (BCC). It is well known that the limit spaces need not be C-Riemannian manifolds [P, Example 1.8]. Hence, the problem arising is to give a geometrica...

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

We present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure. We then extend it to the non-compact case by describing a metric on the set of rooted complete locally compact length spaces endowed with a locally finite measure. We prove that this space with the ex...