These data suggest that facial emotion processing can be impaired in MCI prior to the more marked cognitive deficits seen with clinically diagnosed Alzheimer disease.

The existence of a Richter-Peleg multi-utility representation of a preorder by means of upper semicontinuous or continuous functions is discussed in connection with the existence of a Richter-Peleg utility representation.\ud We give several applications that include the analysis of countable Richter-Peleg multi-utility representations

In the framework of the representability of ordinal qualitative data by means of interval-valued correspondences, we study interval orders defined on a nonempty set X. We analyse the continuous case, that corresponds to a set endowed with a topology that furnishes an idea of continuity, so that it becomes natural to ask for the existence of quantifications based on interval-valued mappings from the set of data into the real numbers under preservation of order and topology. In the present paper we solve a continuous representability problem for interval orders. We furnish a characterization of the representability of an interval order through a pair of continuous real-valued functions so that each element in X has associated in a continuous manner a characteristic interval or equivalently a symmetric triangular fuzzy number.

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total preorders, continuous utility representations, separating scales, decreasing scales, C 60, D 11, 54 F 05, 06 A 06,

Let X be an arbitrary set. Then a topology t on X is completely useful if every upper semicontinuous linear preorder on X can be represented by an upper semicontinuous order preserving  real-valued function. In this paper we characterize in ZFC (<span style="text-decoration: underline;">Z</span>ermelo-<span style="text-decoration: underline;">F</span>raenkel + Axiom of <span style="text-decoration: underline;">C</span>hoice) and ZFC+SH (ZFC + <span style="text-decoration: underline;">S</span>ouslin <span style="text-decoration: underline;">H</span>ypothesis) completely useful topologies on X. This means, in the terminology of mathematical utility theory, that we clarify the topological structure of any type of semicontinuous utility representation problem.

On the basis of the classical continuous multi-utility representation theorem of\ud Levin on locally compact and $\sigma$-compact Hausdorff spaces, we present necessary and sufficient conditions on a topological space $(X,t)$ under which every semi-closed and closed\ud preorder respectively admits a continuous multi-utility representation. This discussion provides the fundaments of a mainly topological\ud theory that systematically combines topological and order theoretic aspects of the\ud continuous multi-utility representation problem