The ordinal sum construction provides a very effective way to generate new triangular norm on the real unit interval from existing ones. One of most prominent theorems concerning norms states that is continuous if and only it uniquely representable as an Archimedean norms. However, subintervals bounded lattice not always (even one summand involved), just extends in naïve way. In present paper, ...

Several observations suggest that overlearned ordinal categories (e.g., letters, numbers, weekdays, months) are processed differently than non-ordinal categories in the brain. In synesthesia, for example, anomalous perceptual experiences are most often triggered by members of ordinal categories (Rich et al., 2005; Eagleman, 2009). In semantic dementia (SD), the processing of ordinal stimuli app...

The most popular unidimensional psychological test evaluation rule is the trivial scoring function: To the answers of each item of a test item scores of 0,1,...m points are awarded and the unweighted or simple or total sum of the item scores gives the test score (also: Likert score). This total score has desirable stochastic ordering properties like monotone likelihood ratio (MLR), stochastic o...

Composition theorems are tools which reduce reasoning about compound data structures to reasoning about their parts. For example, the truth value of a sentence about the Cartesian product of two structures can be reduced to the truth values of sentences on the components of the product. A seminal example of a compositional theorem is the Feferman-Vaught Theorem [2]. Feferman and Vaught introduc...

Many applied studies collect one or more ordered categorical predictors, which do not fit neatly within classic regression frameworks. In most cases, ordinal predictors are treated as either nominal (unordered) variables or metric (continuous) variables in regression models, which is theoretically and/or computationally undesirable. In this paper, we discuss the benefit of taking a smoothing sp...

The National Eye Institute developed a visual functioning questionnaire (NEI-VFQ) designed to assess health-related quality of life of patients with visual impairments. The developers of the NEI-VFQ distributed the original 52 items into 13 different domains. The recommended method for scoring the NEI-VFQ is to linearly transform the sum of the ordinal ratings to each item within each domain to...

We develop an alternative approach to well-ordering proofs beyond the Bachmann-Howard ordinal using transsnite sequences of ordinal notations and use it in order to carry out well-ordering proofs for-ordinal systems. We extend the approach of ordinal systems as an alternative way of presenting ordinal notation systems started in Set98b] and develop ordinal systems, which have in the limit exact...

We show that classification rules used in ordinal regression are equivalent to a certain class of linear multi-class classifiers. This observation not only allows to design new learning algorithms for ordinal regression using existing methods for multi-class classification but it also allows to derive new models for ordinal regression. For example, one can convert learning of ordinal classifier...

A finite poset X carries a natural structure of a topological space. Fix a field k, and denote by D(X) the bounded derived category of sheaves of finite dimensional k-vector spaces over X. Two posets X and Y are said to be derived equivalent if D(X) and D(Y ) are equivalent as triangulated categories. We give explicit combinatorial properties of X which are invariant under derived equivalence, ...