3 research outputs found
Pseudo-polynomial functions over finite distributive lattices
In this paper we consider an aggregation model f: X1 x ... x Xn --> Y for
arbitrary sets X1, ..., Xn and a finite distributive lattice Y, factorizable as
f(x1, ..., xn) = p(u1(x1), ..., un(xn)), where p is an n-variable lattice
polynomial function over Y, and each uk is a map from Xk to Y. The resulting
functions are referred to as pseudo-polynomial functions. We present an
axiomatization for this class of pseudo-polynomial functions which differs from
the previous ones both in flavour and nature, and develop general tools which
are then used to obtain all possible such factorizations of a given
pseudo-polynomial function.Comment: 16 pages, 2 figure
Decision-making with Sugeno integrals: Bridging the gap between multicriteria evaluation and decision under uncertainty
International audienceThis paper clarifies the connection between multiple criteria decision-making and decision under uncertainty in a qualitative setting relying on a finite value scale. While their mathematical formulations are very similar, the underlying assumptions differ and the latter problem turns out to be a special case of the former. Sugeno integrals are very general aggregation operations that can represent preference relations between uncertain acts or between multifactorial alternatives where attributes share the same totally ordered domain. This paper proposes a generalized form of the Sugeno integral that can cope with attributes which have distinct domains via the use of qualitative utility functions. It is shown that in the case of decision under uncertainty, this model corresponds to state-dependent preferences on act consequences. Axiomatizations of the corresponding preference functionals are proposed in the cases where uncertainty is represented by possibility measures, by necessity measures, and by general order-preserving set-functions, respectively. This is achieved by weakening previously proposed axiom systems for Sugeno integrals
Axiomatizations and factorizations of sugeno utility functions
In this paper we consider a multicriteria aggregation model
where local utility functions of different sorts are aggregated
using Sugeno integrals, and which we refer to as Sugeno utility
functions. We propose a general approach to study such functions
via the notion of pseudo-Sugeno integral (or, equivalently,
pseudo-polynomial function), which naturally generalizes that of
Sugeno integral, and provide several axiomatizations for this
class of functions. Moreover, we address and solve the problem
of factorizing a Sugeno utility function as a composition
q(phi(1)(x(1)), ... ,phi(n)(x(n))) of a Sugeno integral q with
local utility functions phi(i), if such a factorization exists