In this paper we will introduce a measure of interactivity between marginal distributions of a joint possibility distribution as the expected value of the interactivity relation between the -level sets of its marginal distributions

Given a lattice (; ⊑), we define to be the fuzzy sets such that their cuts are crisp closed intervals of (; ⊑). We show that: given a complete lattice (; ⊑) the collection of its fuzzy intervals is a complete lattice. Furthermore we show that: if (; ⊑) is completely distributive then the...

An inequality for a normalised isotonic linear functional of Grüss type and particular cases for integrals and norms are established. Applications in obtaining a counterpart for the Cauchy-Buniakowski-Schwartz inequality for functionals and Jessen's inequality for convex functions are also given

Strong lattice martingale arrays over Z are considered under the form of set-indexed processes and a central limit theorem is established under conditional Lindeberg condition, after having extended the limit theorem in Tjostheim (1983) to spatial processes that are nearly lattice martingales

The detection of insufficiently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the which allows inferences approaching the theoretical 100% rate of success, under error estimate...

We propose a new spatially adaptive smoothing procedure which is based on bagging algorithm and hybrid adaptive splines. Extensive simulation studies demonstrate its advantages in spatial adaptability and competitive performance with other existing well known methods. Furthermore, this method...

We prove that a tournament with vertices has more than 013(1 + (1)) edge-disjoint transitive triples. We also prove some results on the existence of large packings of -vertex transitive tournaments in an -vertex tournament. Our proofs combine probabilistic arguments and some powerful packing...

We present a method based on degree one extensions of Lie algebras by a derivation to compute the Casimir operator of perfect Lie algebras having only one invariant for the coadjoint representation and an abelian radical. In particular, the Casimir operator of the special affine Lie algebras...

Non-Hermitian matrix Schrödinger equation obtained by the Bäcklund- Darboux transformation (BDT) is treated. The potentials, fundamental solutions, and Weyl functions are constructed explicitly. Λ symmetric reduction of the BDT is introduced and this case is studied in greater detail:...