We introduce the principle of robust ordinal regression to group decision. We consider the main multiple criteria decision methods to which robust ordinal regression has been applied, i.e., UTA and GRIP methods, dealing with choice and ranking problems, UTADIS , dealing with sorting (ordinal classification) problems, and ELECTRE , being an outranking method applying robust ordinal regression to...

Recently, ordinal regression, which predicts categories of ordinal scale, has received considerable attention. In this paper, we propose a new approach to solve ordinal regression problems within the learning vector quantization framework. It extends the previous approach termed ordinal generalized matrix learning vector quantization with a more suitable and natural cost function, leading to mo...

In this paper, we address the Multi-Instance-Learning (MIL) problem when bag labels are naturally represented as ordinal variables (Multi–Instance–Ordinal Regression). Moreover, we consider the case where bags are temporal sequences of ordinal instances. To model this, we propose the novel Multi-Instance Dynamic Ordinal Random Fields (MI-DORF). In this model, we treat instance-labels inside the...

We study the complexity of automatic structures via well-established concepts from both logic and model theory, including ordinal heights (of well-founded relations), Scott ranks of structures, and Cantor-Bendixson ranks (of trees). We prove the following results: 1) The ordinal height of any automatic wellfounded partial order is bounded by ω; 2) The ordinal heights of automatic well-founded r...

§0. The ordinal numbers were Georg Cantor’s deepest contribution to mathematics. After the natural numbers 0, 1, . . . , n, . . . comes the first infinite ordinal number ù, followed by ù + 1, ù + 2, . . . , ù + ù, . . . and so forth. ù is the first limit ordinal as it is neither 0 nor a successor ordinal. We follow the von Neumann convention, according to which each ordinal number α is identifi...

The objective of this paper is to introduce an ordinal representation system which has been employed in the determination of the proof{theoretic strength of 1 2 comprehension and related systems.

We show that in the presence of large cardinals proper forcings do not change the theory of L(R) with real and ordinal parameters and do not code any set of ordinals into the reals unless that set has already been so coded in the ground model.

A well known argument of James yields that if a Banach space X contains `1 ’s uniformly, then X contains `1 ’s almost isometrically. In the first half of the paper we extend this idea to the ordinal `1-indices of Bourgain. In the second half we use our results to calculate the `1-index of certain Banach spaces. Furthermore we show that the `1-index of a separable Banach space not containing `1 ...