@ARTICLE { Rsds4692,
author = {Cyran, Krzysztof A.}, 
title = {Modified Indiscernibility Relation in the Theory of Rough Sets with Real-Valued Attributes: Application to Recognition of Fraunhofer Diffraction Patterns}, 
journal = {Transactions on Rough Sets}, 
number = 	{(no. IX)}, 
volume = 5390, 
pages = {14--34}, 
publisher = {Springer-Verlag}, 
address = {Heidelberg - Berlin, Germany}, 
year = 2008, 
issn = {0302-9743}, 
isbn = {978-3-540-89875-7}, 
abstract = {The goal of the paper is to present the modification of classical indiscernibility relation, dedicated for rough set theory in a real-valued attributes space. Contrary to some other known generalizations, indiscernibility relation modified here, remains an equivalence relation and it is obtained by introducing a structure into collection of attributes. It defines real-valued subspaces, used in a multidimensional cluster analysis, partitioning the universe in a more natural way, as compared to one-dimensional discretization, iterated in classical model. Since the classical model is a special, extreme case of our modification, the modified version can be considered as more general. But more importantly, it allows for natural processing of real-valued attributes in a rough-set theory, broadening the scope of applications of classical, as well as variable precision rough set model, since the latter can utilize the proposed modification, equally well. In a case study, we show a real application of modified relation, a hybrid, opto-electronic recognizer of Fraunhofer diffraction patterns. Modified rough sets are used in an evolutionary optimization of the optical feature extractor implemented as a holographic ring-wedge detector. The classification is performed by a probabilistic neural network, whose error, assessed in an unbiased way is compared to earlier works.}, 
keywords = {rough sets, indiscernibility relation, holographic ring-wedge detector, evolutionary optimization, probabilistic neural network, hybrid pattern recognition, }, 
}