Abstract
The problem considered in this article stems from the observation that practical applications of near set theory require efficient determination of all the tolerance classes containing objects from the union of two disjoints sets. Near set theory consists in extracting perceptually relevant information from groups of objects based on their descriptions. Tolerance classes are sets where all the pairs of objects within a set must satisfy the tolerance relation and the set is maximal with respect to inclusion. Finding such classes is a computationally complex problem, especially in the case of large data sets or sets of objects with similar features. The contributions of this article are the observation that the problem of finding tolerance classes is equivalent to the MCE problem, empirical evidence verifying the conjecture from [15] that the extra perceptual information obtained by finding all tolerance classes on a set of objects obtained from a pair of images improves the CBIR results when using the tolerance nearness measure, and a new application of MCE to CBIR.
This research has been supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grants 194376 and 418413. Also, special thanks to Tariq Alusaifeer for recognizing the problem of finding tolerance classes is equivalent to maximal clique enumeration.
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Henry, C.J., Ramanna, S. (2013). Maximal Clique Enumeration in Finding Near Neighbourhoods. In: Peters, J.F., Skowron, A., Ramanna, S., Suraj, Z., Wang, X. (eds) Transactions on Rough Sets XVI. Lecture Notes in Computer Science, vol 7736. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36505-8_7
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