The aim of the contribution is the discussion of some types and classes of means on ordinal scales, especially kernel and shift invariant ordinal means, weighted ordinal means based on weighted divisible t–conorms (t–norms) and dissimilarity based ordinal means. Moreover, several types of ordinal arithmetic means are introduced.

Feature Pattern Analysis (FPA), as a part of the theory of data (Coombs, 1964), can be interpreted as a formal model of some procedures frequently applied in the behavioral and social sciences, e.g., for Guttman scaling, Parallelogram Analysis, Likert scaling, the Semantic Differential, and the Kelly Grid. FPA may also be used as a scaling procedure for nominal and ordinal data with qualitative...

There exists a family {Bα}α<ω1 of sets of countable ordinals such that (1) maxBα = α, (2) if α ∈ Bβ then Bα ⊆ Bβ , (3) if λ ≤ α and λ is a limit ordinal then Bα ∩ λ is not in the ideal generated by the Bβ , β < α, and by the bounded subsets of λ, (4) there is a partition {An}n=0 of ω1 such that for every α and every n, Bα∩An is finite.

Many classi®cation tasks can be viewed as ordinal. Use of numeric information usually provides possibilities for more powerful analysis than ordinal data. On the other hand, ordinal data allows more powerful analysis when compared to nominal data. It is therefore important not to overlook knowledge about ordinal dependencies in data sets used in data mining. This paper investigates data mining ...

The cricket is one of the model animals used to investigate neuronal mechanisms underlying adaptive locomotion. An intact walks mostly with a tripod gait, similar other insects. motor control center leg movements located in thoracic ganglia. In this study, we investigated walking gait patterns crickets whose ventral nerve cords were surgically cut gain an understanding how descending signals fr...

The performance of medical image classification has been enhanced by deep convolutional neural networks (CNNs), which are typically trained with cross-entropy (CE) loss. However, when the label presents an intrinsic ordinal property in nature, e.g., development from benign to malignant tumor, CE loss cannot take into account such information allow for better generalization. To improve model gen...

Combinatorics coding is a new data coding method based on combinatorics. Ordinal computing is the core technology of in the combinatorics coding. Ordinal properties of combinatorics coding is studied in this paper. Firstly, the combinatorics coding theory and the correlative basic concepts are described. Then, the properties of the ordinal are revealed. The study indicates that the value of ord...