## Nonparametric recursive aggregation process.(English)Zbl 1249.62004

Summary: We introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine the numerical values according to a vector of weights (parameters). Alternatively, the MLA operators apply recursively over the input values a vector of aggregation operators. Consequently, a sort of unsupervised self-tuning aggregation process is induced combining the individual values in a certain fashion determined by the choice of aggregation operators.

### MSC:

 62G99 Nonparametric inference 47N30 Applications of operator theory in probability theory and statistics 62P99 Applications of statistics 68T10 Pattern recognition, speech recognition

### Keywords:

multilayer aggregation operators; power means; monotonicity
Full Text:

### References:

 [1] Fodor J. C., Roubens M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer, Dordrecht 1994 · Zbl 0827.90002 [2] Matkowski J.: Iterations of mean-type mappings and invariant means. Ann. Math. Sil. 13 (1999), 211-226 · Zbl 0954.26015 [3] Matkowski J.: On iteration semi-groups of mean-type mappings and invariant means. Aequationes Math. 64 (2002), 297-303 · Zbl 1020.39011 · doi:10.1007/PL00013194 [4] Mesiar R.: Aggregation operators: some classes and construction methods. Proceedings of IPMU’2000, Madrid, 2000, pp. 707-711 [5] Mizumoto M.: Pictorial representations of fuzzy connectives. Part 2: Cases of compensatory and self-dual operators. Fuzzy Sets and Systems 32 (1989), 245-252 · Zbl 0709.03524 · doi:10.1016/0165-0114(89)90087-0 [6] Moser B., Tsiporkova, E., Klement K. P.: Convex combinations in terms of triangular norms: A characterization of idempotent, bisymmetrical and self-dual compensatory operators. Fuzzy Sets and Systems 104 (1999), 97-108 · Zbl 0928.03063 · doi:10.1016/S0165-0114(98)00262-0 [7] Páles Z.: Nonconvex function and separation by power means. Mathematical Inequalities & Applications 3 (2000), 169-176 · Zbl 0947.26010 · doi:10.7153/mia-03-20 [8] Tsiporkova E., Boeva V.: Multilayer aggregation operators. Proc. Summer School on Aggregation Operators 2003 (AGOP’2003), Alcalá de Henares, Spain, pp. 165-170 [9] Turksen I. B.: Interval-valued fuzzy sets and ‘compensatory AND’. Fuzzy Sets and Systems 51 (1992), 295-307 · doi:10.1016/0165-0114(92)90020-5 [10] Yager R. R.: MAM and MOM opereators for aggregation. Inform. Sci. 69 (1993), 259-273 · Zbl 0783.04007 · doi:10.1016/0020-0255(93)90124-5 [11] Yager R. R.: Noncommutative self-identity aggregation. Fuzzy Sets and Systems 85 (1997), 73-82 · Zbl 0903.04005 · doi:10.1016/0165-0114(95)00325-8 [12] Zimmermann H.-J., Zysno P.: Latent connectives in human decision making. Fuzzy Sets and Systems 4 (1980), 37-51 · Zbl 0435.90009 · doi:10.1016/0165-0114(80)90062-7
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.