Search results for " set"
showing 10 items of 2095 documents
L -valued bornologies on powersets
2016
In M. Abel and A. ostak (2011) [1], the concept of an L-fuzzy bornology was introduced. Actually, an L-fuzzy bornology on a set X is a certain ideal in the family LX of L-fuzzy subsets of a set X. Here we propose an alternative approach to fuzzification of the concept of bornology. We define an L-valued bornology on a set X as an L-fuzzy subset B of the powerset 2X satisfying L-valued analogues of the axioms of a bornology. Basic properties of L-valued bornological spaces are studied. Our special interest concerns L-valued bornologies induced by fuzzy metrics and relative compactness-type L-valued bornologies in ChangGoguen L-topological spaces.
Extensions and intentions in the rough set theory
1998
Abstract The approach to rough set theory proposed in this paper is based on the mutual correspondence of the concepts of extension and intension. It is different from the well-known approaches in the literature in that the upper approximations and the lower approximations of ‘unknown’ sets are considered as certain families of ‘known’ sets. This approach makes it possible to formulate necessary and sufficient conditions for the existence of operations on rough sets, which are analogous to classical operations on sets. The basic results presented in this paper, based on certain ideas of the second author, were formulated by the first author in his doctoral dissertation prepared under the su…
On Rough Sets in Topological Boolean Algebras
1994
We have focused on rough sets in topological Boolean algebras. Our main ideas on rough sets are taken from concepts of Pawlak [4] and certain generalizations of his constructions which were offered by Wiweger [7]. One of the most important results of this note is a characterization of the rough sets determined by regular open and regular closed elements.
Collection Principles in Dependent Type Theory
2002
We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation interpretation.
Perturbations of surjective convolution operators
2002
Let μ 1 and μ 2 be (ultra)distributions with compact support which have disjoint singular supports. We assume that the convolution operator f → μ 1 *f is surjective when it acts on a space of functions or (ultra)distributions, and we investigate whether the perturbed convolution operator f→ (μ 1 + μ 2 ) * f is surjective. In particular we solve in the negative a question asked by Abramczuk in 1984.
Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation
2013
We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
On the points realizing the distance to a definable set
2011
Abstract We prove a definable/subanalytic version of a useful lemma, presumably due to John Nash, concerning the points realizing the Euclidean distance to an analytic submanifold of R n . We present a parameter version of the main result and we discuss the properties of the multifunction obtained.
Spatial reasoning withRCC8and connectedness constraints in Euclidean spaces
2014
The language RCC 8 is a widely-studied formalism for describing topological arrangements of spatial regions. The variables of this language range over the collection of non-empty, regular closed sets of n-dimensional Euclidean space, here denoted RC + ( R n ) , and its non-logical primitives allow us to specify how the interiors, exteriors and boundaries of these sets intersect. The key question is the satisfiability problem: given a finite set of atomic RCC 8 -constraints in m variables, determine whether there exists an m-tuple of elements of RC + ( R n ) satisfying them. These problems are known to coincide for all n � 1 , so that RCC 8 -satisfiability is independent of dimension. This c…
The small-world of 'Le Petit Prince': Revisiting the word frequency distribution
2016
[EN] Many complex systems are naturally described through graph theory, and different kinds of systems described as networks present certain important characteristics in common. One of these features is the so-called scale-free distribution for its node s connectivity, which means that the degree distribution for the network s nodes follows a power law. Scale-free networks are usually referred to as small-world because the average distance between their nodes do not scale linearly with the size of the network, but logarithmically. Here we present a mathematical analysis on linguistics: the word frequency effect for different translations of the Le Petit Prince in different languages. Compar…
Heyting-valued interpretations for Constructive Set Theory
2006
AbstractWe define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory (CZF). These interpretations provide models for CZF that are analogous to Boolean-valued models for ZF and to Heyting-valued models for IZF. Heyting-valued interpretations are defined here using set-generated frames and formal topologies. As applications of Heyting-valued interpretations, we present a relative consistency result and an independence proof.