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Median‐based aggregation operators for prototype construction in ordinal scales
Author(s) -
DomingoFerrer Josep,
Torra Vicenç
Publication year - 2003
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.10107
Subject(s) - ordinal optimization , ordinal scale , operator (biology) , monotonic function , ordinal data , computer science , property (philosophy) , ordinal regression , cluster analysis , process (computing) , mathematics , theoretical computer science , data mining , artificial intelligence , statistics , machine learning , operating system , mathematical analysis , biochemistry , chemistry , philosophy , epistemology , repressor , transcription factor , gene
This article studies aggregation operators in ordinal scales for their application to clustering (more specifically, to microaggregation for statistical disclosure risk). In particular, we consider these operators in the process of prototype construction. This study analyzes main aggregation operators for ordinal scales [plurality rule, medians, Sugeno integrals (SI), and ordinal weighted means (OWM), among others] and shows the difficulties for their application in this particular setting. Then, we propose two approaches to solve the drawbacks and we study their properties. Special emphasis is given to the study of monotonicity because the operator is proven nonsatisfactory for this property. Exhaustive empirical work shows that in most practical situations, this cannot be considered a problem. © 2003 Wiley Periodicals, Inc.