Fundamentals of pattern recognition (2nd revised and expanded ed.)
Fundamentals of pattern recognition (2nd revised and expanded ed.)
Tolerance approximation spaces
Fundamenta Informaticae - Special issue: rough sets
Near Sets. Special Theory about Nearness of Objects
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Rough Granular Computing in Knowledge Discovery and Data Mining
Rough Granular Computing in Knowledge Discovery and Data Mining
Information Sciences: an International Journal
Rough sets and near sets in medical imaging: a review
IEEE Transactions on Information Technology in Biomedicine - Special section on body sensor networks
Rough Fuzzy Image Analysis: Foundations and Methodologies
Rough Fuzzy Image Analysis: Foundations and Methodologies
Perceptual tolerance intersection
RSCTC'10 Proceedings of the 7th international conference on Rough sets and current trends in computing
Perceptual tolerance intersection
Transactions on rough sets XIII
Rough matroids based on relations
Information Sciences: an International Journal
Nearness of subtly different digital images
Transactions on Rough Sets XVI
Maximal clique enumeration in finding near neighbourhoods
Transactions on Rough Sets XVI
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This article considers the origins, theoretical aspects and applications of tolerance spaces. In terms of the origin of tolerance spaces, this article calls attention to the seminal work by J.H. Poincare (1854-1912) and E.C. Zeeman (1925-) on establishing the foundations for tolerance spaces. During the period from 1895 to 1912, Poincare introduced sets of sensations and sequences of almost the same sensations as a means of characterizing the physical spectrum. The perception of physical objects that are almost the same leads to a tolerance space view of visual perception as well as other forms of perception such as touch and sound. Roughly 60years later (in 1962), Zeeman formally introduced the notion of a tolerance space as a useful means of investigating a geometry of visual perception. In addition to the general theory of tolerance spaces, this article also carries forward earlier work on perceptual tolerance relations and considers the resemblance (nearness) between tolerance spaces. From an information systems point of view, it can be observed that tolerance spaces have proved to be fruitful in a number of research areas. Evidence of the utility of tolerance spaces in information systems can be seen in the introduction of tolerance rough sets, tolerance approximation spaces, and tolerance near sets. The contribution of this article is an overview of tolerance spaces considered in the context of visual perception and a presentation of a formal basis for the study of perceptual tolerance spaces.