@INPROCEEDINGS { Rsds2589,
title = {Granular Computing with Shadowed Sets}, 
booktitle = {Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing, Part I}, 
series =  = {Lecture Notes in Artificial Intelligence}, 
volume = 3641, 
pages = {23--32}, 
publisher = {Springer-Verlag}, 
address = {Heidelberg - Berlin, Germany}, 
month = {August}, 
year = 2005, 
editor = {Slezak, Dominik and Wang, Guoying and Szczuka, Marcin and Duntsch, Ivo and Yao, Yiyu}, 
issn = {0302-9743}, 
isbn = {3-540-28653-5}, 
abstract = {In this study, we discuss a concept of shadowed sets and elaborate on their applications. To establish some sound compromise between the qualitative Boolean (two-valued) description of data and quantitative membership grades, we introduce an interpretation framework of shadowed sets. Shadowed sets are discussed as three-valued constructs induced by fuzzy sets assuming three values (that could be interpreted as full membership, full exclusion, and uncertain). The algorithm of converting membership functions into this quantification is a result of a certain optimization problem guided by the principle of uncertainty localization. With the shadowed sets of clusters in place, discussed are various ideas of relational calculus on such constructs. We demonstrate how shadowed sets help in problems in data interpretation in fuzzy clustering by leading to the three-valued quantification of data structure that consists of core, shadowed, and uncertain structure.}, 
keywords = {shadowed sets, three-valued logic, fuzzy sets, principle of uncertainty localization, relational equations, data interpretation, fuzzy clustering, outliers, cores of clusters, }, 
}