It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and complete n-lattices,...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations ...

Purpose. The purpose of this study is to retrospectively evaluate the efficacy and safety of the Prostar XL device for percutaneous large access site closure in an unselected patient and operator collective. Materials and Methods. All patients (n = 50) who had received percutaneous vascular closing with the Prostar XL device in our institution with follow-up data of at least 6 months were retro...

We provide a semantical reconstruction of rational closure. We first consider rational closure as defined by Lehman and Magidor for propositional logic, and we provide a semantical characterization based on minimal models mechanism on rational models. Then, we extend the whole formalism and semantics to Description Logics focusing our attention to the standard ALC: we first naturally adapt to D...

BACKGROUND We describe a vascular closure technique, convenient in practice, that permits effective femoral artery closure after CoreValve (Medtronic) implantation during transcatheter aortic valve implantation (TAVI). Vascular complications of transfemoral access implantation have been associated with significantly increased patient morbidity and mortality, as well as with increased hospitaliz...

There has been a great eeort in giving machine independent, algebraic characterizations of complexity classes, especially of functions. Astonishingly, no satisfactory characterization of the prominent class # P has been known up to now. Here, we characterize # P as the closure of a set of simple arithmetical functions under summation and weak product. Building on that result, the hierarchy of c...

The closure ordinal of a formula of modal μ-calculus μXφ is the least ordinal κ, if it exists, such that the denotation of the formula and the κ-th iteration of the monotone operator induced by φ coincide across all transition systems (finite and infinite). It is known that for every α < ω2 there is a formula φ of modal logic such that μXφ has closure ordinal α [3]. We prove that the closure or...

We study the compactness of composition operators on Bergman spaces certain bounded convex domains in $\mathbb{C}^n$ with non-trivial analytic discs contained boundary. As a consequence we characterize that operator continuous symbol (up to closure) space polydisc.

Rough set theory is an excellent mathematical tool for the analysis of a vague description actions in decision problems. Now, this paper by considering notion equality algebra, lower and upper approximations are introduced some properties them given. Moreover, it proved that define interior operator closure operator, respectively. Also, using D-lower D-upper approximation, conditions nonempty s...