We consider cylindrical algebraic decompositions (CADs) as a tool for representing semi-algebraic subsets of <?TeX $\mathbb {R}^n$?> Math 1 . In this framework, a CAD <?TeX $\mathscr{C}$?> Math 2 is adapted to a given set S if S is a union of cells of <?TeX $\mathscr{C}$?> Math 3 . Different algorithms computing an adapted CAD may produce different outputs, usually with redundant cell divisions. In this paper we analyse the possibility to remove the superfluous data. More precisely we consider the set CAD(S) of CADs that are adapted to S, endowed with the refinement partial order and we study the existence of minimal and minimum elements in this poset.

This paper deals with the characterization of a class of aggregation operators. This class concerns operators that are symmetric, increasing, stable for the same positive linear transformations, and present a property close to the bisymmetry property: the ordered bisymmetry property. It is proved that the class investigated contains exactly the ordered weighted averaging operators introduced by Yager (1988).