On the Correspondence between Approximations and Similarity
Linköping University, Department of Computer and Information Science, KPLAB - Knowledge Processing Lab
Linköping University, The Institute of Technology
Conference paper (Refereed)
Proceedings of the International Conference on Rough Sets and Current Trends in Computing (RSCTC)
Shusaku Tsumoto, Roman Slowinski, Jan Komorowski and Jerzy W. Grzymala-Busse
Lecture Notes in Computer Science, ISSN 0302-9743; 3066
This paper focuses on the use and interpretation of approximate databases where both rough sets and indiscernibility partitions are generalized and replaced by approximate relations and similarity spaces. Similarity spaces are used to define neighborhoods around individuals and these in turn are used to define approximate sets and relations. There is a wide spectrum of choice as to what properties the similarity relation should have and how this affects the properties of approximate relations in the database. In order to make this interaction precise, we propose a technique which permits specification of both approximation and similarity constraints on approximate databases and automatic translation between them. This technique provides great insight into the relation between similarity and approximation and is similar to that used in modal correspondence theory. In order to automate the translations, quantifier elimination techniques are used.