Granular computing with shadowed sets

Authors:
Witold Pedrycz
Affiliations:
,Department of Electrical & Computer Engineering, University of Alberta, Edmonton, AB, Canada
Venue:
RSFDGrC'05 Proceedings of the 10th international conference on Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing - Volume Part I
Year:
2005

Citing 7
Cited 1

On post-clustering evaluation and modification

Pattern Recognition Letters
Fuzzy Models and Algorithms for Pattern Recognition and Image Processing

Fuzzy Models and Algorithms for Pattern Recognition and Image Processing
Extreme physical information and objective function in fuzzy clustering

Fuzzy Sets and Systems - Clustering and modeling
Evolutionary semi-supervised fuzzy clustering

Pattern Recognition Letters
Fuzzy clustering with a knowledge-based guidance

Pattern Recognition Letters
Knowledge discovery by a neuro-fuzzy modeling framework

Fuzzy Sets and Systems
Shadowed sets: representing and processing fuzzy sets

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Orthopairs: A Simple and Widely UsedWay to Model Uncertainty

Fundamenta Informaticae - Advances in Rough Set Theory

Quantified Score

Hi-index	0.00

Visualization

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.