The aim of this paper is to completely classify all aggregation functions based on the notion of arity gap. We first establish explicit descriptions of the arity gap of the Lovász extensions of pseudo-Boolean functions and, in particular, of the Choquet integrals. Then we consider the wider class of order-preserving functions between arbitrary, possibly different, posets, and show that similar ...

EARLY DEVELOPMENT OF DICTYOSTELIUM DISCOIDEUM.................................................... 29 GENETIC ANALYSIS.................................................. 30 MUTANTS ALTERED IN AGGREGATION.................................................. 32 Numbers of Genes .................................................. 32 Selection Procedures.................................................. ...

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. Multidimensional database modelling with differentiated multiple aggregations. Many solutions have been defined for multidimensional database modelling. These propositions consider the same aggregation function to determine the values of an indicator accor...

Aggregation of intuitionistic fuzzy sets is studied from the point of view of preserving various kinds of convexity. We focus on aggregation functions for intuitionistic fuzzy sets. These functions correspond to simultaneous separate aggregations of the membership as well as of the nonmembership indicators. It is performed by means of the so-called representable functions. Sufficient and necess...

In this paper, we review the role of self-duality in the theory of aggregation functions, the dual decomposition of aggregation functions into a self-dual core and an anti-self-dual remainder, and some applications to welfare, inequality, and poverty measures. © 2015 Elsevier B.V. All rights reserved.

An aggregation operator [1, 5, 7, 8, 9, 12] is usually defined as a real function An such that, from n data items x1, . . . ,xn in [0,1], produces an aggregated value An(x1, . . . ,xn) in [0,1] [4]. This definition can be extended to consider the whole family of operators for any n instead of a single operator for an specific n. This has led to the current standard definition [4, 15] of a famil...

In wireless sensor networks, data aggregation protocols are used to prolong the network lifetime. However, the problem of how to perform data aggregation while preserving data privacy is challenging. This paper presents a polynomial regressionbased data aggregation protocol that preserves the privacy of sensor data. In the proposed protocol, sensor nodes represent their data as polynomial funct...