The present paper investigates approximation spaces in the context of topological structures which axiomatise the notion of nearness. Starting with the framework of information quanta which distinguishes two levels of information structures, namely property systems (the first level) and information quantum relational systems (the second level), we shall introduce the notion of Pawlak’s property...

J. Dobrakovová and the author in [7] introduced the relation of nearness in Banach space. In this paper we will go on investigating the nearness relation in a linear space with a countable vector base, focusing the results to topological properties of such relations.

Let S be a closed convex set of matrices and C be a given matrix. The matrix nearness problem considered in this paper is to find a matrix X in the set S at which max {|xij − cij |} reaches its minimum value. In order to solve the matrix nearness problem, the problem is reformulated to a min-max problem firstly, then the relationship between the min-max problem and a monotone linear variational...

The development of cognitively plausible models of human spatial reasoning may ultimately result in computational systems that are better equipped to meet human needs. This paper explores how human subjects perceive the qualitative spatial relation nearness within an environmental space. Based on experimental data, a three-valued nearness relation is analysed in two stages. First, the results a...

An important step in the solution of a matrix nearness problem that arises in certain machine learning 3 applications is finding the zero of f(α) = z exp(logX + αzz )z − b. The matrix valued exponential and logarithm 4 in f(α) arises from the use of the von Neumann matrix divergence tr(X logX − X log Y − X + Y ) to measure the 5 nearness between the positive definite matrices X and Y . A key st...

To avoid the false results of deterministic identification methods induced by uncertainties, a fuzzy nearness-based method is proposed for the damage identification of bridge. An improved index based on ratios of modal shape components is used as identification measurements. The knowledge base for damage identification is established through corresponding relationship between fuzzified measurem...

This article gives a brief overview of near sets. The proposed approach in introducing near sets is to consider a set theory-based form of nearness (proximity) called discrete proximity. There are two basic types of near sets, namely, spatially near sets and descriptively near sets. By endowing a nonempty set with some form of a nearness (proximity) relation, we obtain a structured set called a...