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
Shadowed Clustering for Speech Data and Medical Image Segmentation
RSCTC '08 Proceedings of the 6th International Conference on Rough Sets and Current Trends in Computing
Shadowed c-means: Integrating fuzzy and rough clustering
Pattern Recognition
Soft clustering -- Fuzzy and rough approaches and their extensions and derivatives
International Journal of Approximate Reasoning
Building the fundamentals of granular computing: A principle of justifiable granularity
Applied Soft Computing
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Given the rapidly growing diversity of techniques and applications of fuzzy clustering, an interpretation of grouping results becomes of paramount relevance. Fuzzy clusters offer a lot of detailed information about the structure in data by allocating patterns to clusters with numeric degrees of membership. While this information could be highly beneficial, its level of detail could be too overwhelming and in some sense somewhat detrimental to the formation of the global view of the structure. 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 is a taxonomy of patterns leading to the three-valued quantification of data structure that consists of core, shadowed, and uncertain structure.