This article considers the problem of how approach spaces can be used in the study of near filters, in general, and descriptively near filters, in particular. The solution to the problem stems from recent work on approach spaces, approach merotopies, near filters, descriptively near sets, and a specialised form of merotopy defined in terms of a variation of the C̆ech gap functional in measuring ...

Abstract This article considers the problem of how to formulate a framework for the study of the nearness of tolerance rough sets (TRS). The solution to the problem stems from recent work on near sets and approach spaces as well as from the realisation that disjoint TRSs can be viewed in the context of approach merotopic spaces. A set of TRSs equipped with a distance function satisfying certain...

The problem considered in this paper is the approximation of sets of perceptual objects that are qualitatively near each other. A perceptual object is either something presented to the senses or knowable by the mind. Objects that have the same appearance are considered qualitatively near each other, i.e., objects with matching descriptions. The term approximate means very near, in position or i...

Fitness landscapes are a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space that is equipped with some notion of adjacency, nearness, distance or accessibility, into the real numbers. Landscape theory has emerged as an attempt to devise suitable mathematical structures for descr...

The performance of interval estimates in a uniform-beta mixture model is evaluated using three computational strategies. Such a model has found use when modeling a distribution of P -values from multiple testing applications. The number of P -values and the closeness of a parameter to the boundary of its space both play a role in the precision of parameter estimates as does the “nearness” of th...

Suppose that the matrix equation AXB = C with unknown matrix X is given, where A, B, and C are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of the matrix equation AXB = C when the equation is consistent and inconsistent, respectively. The implicit form of the best approximate solutions of the problems over the set of sy...

We consider a curve reconstruction problem from unorganized point clouds with noise. In general, the result of curve reconstruction depends on how to select and order the representative points to resemble the shape of the clouds. We exploit a natural distance based on a property of onedimensional Brownian motion to order sample points, which simultaneously reflect smoothness and nearness of poi...

Fitness landscapes have proven to be a valuable concept in evolutionary biology, combinatorial optimization, and the physics of disordered systems. A fitness landscape is a mapping from a configuration space into the real numbers. The configuration space is equipped with some notion of adjacency, nearness, distance or accessibility. Landscape theory has emerged as an attempt to devise suitable ...