Preaggregation Functions: Construction and an Application

• Published in: IEEE transactions on fuzzy systems Vol. 24; no. 2; pp. 260 - 272
• Main Authors: Lucca, Giancarlo, Sanz, Jose Antonio, Dimuro, Gracaliz Pereira, Bedregal, Benjamin, Mesiar, Radko, Kolesarova, Anna, Bustince, Humberto
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-04-2016; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additives; Aggregation functions; Boundary conditions; Choquet integral; Cities and towns; directional monotonicity; Electronic mail; Fuzzy reasoning; Indexes; Open wireless architecture; Aggregation functions; directional monotonicity; fuzzy reasoning method (FRM); fuzzy measures; Choquet integral; fuzzy rule-based classification systems (FRBCSs)
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2015.2453020

In this paper, we introduce the notion of preaggregation function. Such a function satisfies the same boundary conditions as an aggregation function, but, instead of requiring monotonicity, only monotonicity along some fixed direction (directional monotonicity) is required. We present some examples of such functions. We propose three different methods to build preaggregation functions. We experimentally show that in fuzzy rule-based classification systems, when we use one of these methods, namely, the one based on the use of the Choquet integral replacing the product by other aggregation functions, if we consider the minimum or the Hamacher product t-norms for such construction, we improve the results obtained when applying the fuzzy reasoning methods obtained using two classical averaging operators such as the maximum and the Choquet integral.