A pretopological approach for structuring data in non-metric spaces

doi:10.1016/S1571-0653(04)00011-3

Electronic Notes in Discrete Mathematics

Volume 2, April 1999, Pages 1-9

https://doi.org/10.1016/S1571-0653(04)00011-3 Get rights and content

Abstract

The aim of this paper is to bring out the structure of a space E which is not endowed with a metric. Indeed, there only is a family of binary relationships between points of E. The problem is to define a process to extract the structure E without building a distance between the elements of E. In this way, we've used a method based on pretopological notions.

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A pretopological approach for structural analysis
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Citation Excerpt :
For this reason, in pretopology [2], as in [7,8], it is not assumed that the pseudoclosure application is idempotent. This approach enabled us to develop a new algorithm for structural analysis [4,5,13]. The principle consists in constructing a pseudoclosure application a(·) from parts of E onto themselves based on the connection between the elements of population E.
The aim of this paper is to present a methodological approach for problems encountered in structural analysis. This approach is based upon the pretopological concepts of pseudoclosure and minimal closed subsets. The advantage of this approach is that it provides a framework which is general enough to model and formulate different types of connections that exist between the elements of a population. In addition, it has enabled us to develop a new structural analysis algorithm. An explanation of the definitions and properties of the pretopological concepts applied in this work is first shown and illustrated in sample settings. The structural analysis algorithm is then described and the results obtained in an economic study of the impact of geographic proximity on scientific collaborations are presented.
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ArticlesA pretopological approach for structuring data in non-metric spaces

Abstract

International Journal of Man-Machine Studies

Articles
A pretopological approach for structuring data in non-metric spaces