Couceiro, Miguel[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

Marichal, Jean-Luc[University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]

2009

Proc. of 2009 Int. Fuzzy Systems Assoc. World Congress and 2009 Int. Conf. of the Eur. Soc. for Fuzzy Logic and Technology (IFSA-EUSFLAT 2009 Joint Conference)

Carvalho, J. P.

Dubois, D.

Kaymak, U.

Sousa, J. M. C.

531-536

Yes

No

International

978-989-95079-6-8

2009 Int. Fuzzy Systems Assoc. World Congress and 2009 Int. Conf. of the Eur. Soc. for Fuzzy Logic and Technology (IFSA-EUSFLAT 2009 Joint Conference)

from 20-07-2009 to 24-07-2009

Lisbon

Portugal

[en] Discrete Sugeno integral ; quasi-polynomial function ; horizontal maxitivity and minitivity ; comonotonic maxitivity and minitivity ; functional equation

[en] Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We present complete descriptions of the function classes axiomatized by each of these properties, up to weak versions of monotonicity, in the cases of horizontal maxitivity and minitivity. While studying the classes axiomatized by combinations of these properties, we introduce the concept of quasipolynomial function which appears as a natural extension of the well-established notion of polynomial function. We present further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and present characterizations accordingly.