A (continuous) t-norm is called equationally definable when the corresponding standard BL-algebra [0, 1]∗ defined by ∗ and its residuum is the only (up to isomorphism) standard BL-algebra that generates the same variety Var([0, 1]∗). In this chapter we check that a continuous t-norm ∗ is equationally definable if and only if the t-norm is a finite ordinal sum of copies of the three basic contin...

Pearson’s statistic is investigated for nominal-ordinal two-way contingency tables in which we wish to test for identical rows. The statistic is expressed as a sum, the first summand of which is a statistic given by Yates (1948), and examines location effects for the nominal category. The second and subsequent summands reflect the corresponding moments: for example, dispersion, skewness, kurtos...

Dominance is a relation on operations which are defined on a common poset. We treat the dominance relation on the set of ordinal sum t-norms which involve either exclusively the Lukasiewicz t-norm or exclusively the product t-norm as summand operations. We show that in both cases, the question of dominance can be reduced to a simple property of the idempotent elements of the dominating t-norm. ...

Arguments have been provided against the use of the eigenvector as the operator that derives priorities. A highlight of the arguments is that the eigenvector solution does not always respect the condition of ordinal preference (COP) based on the decision maker’s judgments. While this condition may be reasonable when dealing with measurable concepts (such as distance or time) that lead to consis...

We prove two theorems of the type of Dieudonné for the classes of p-torsion n-Σ-groups and weakly n-summable groups, respectively. These claims extend the classical Dieudonné criterion (Portugal. Math., 1952) and Honda criterion (Comment. Math. Univ. St. Pauli, 1964) as well as generalize recent results of ours in (Acta Math. Univ. Ostrav., 2006; 2007) and (Alg. Colloq., 2008). Introduction and...

Support vector ordinal regression (SVOR) is a popular method to tackle ordinal regression problems. However, until now there were no effective algorithms proposed to address incremental SVOR learning due to the complicated formulations of SVOR. Recently, an interesting accurate on-line algorithm was proposed for training ν-support vector classification (ν-SVC), which can handle a quadratic form...

Rank sum scoring is a popular manner by which to obtain group rankings from events that are individual in nature. For example, rank sum scoring is employed in cross country team competition, the Putnam Mathematics Team Competition, snowboard cross team competition, snowboard half-pipe team competition, and snowboard slopestyle team competition. It also forms the basis for a non-parametric stati...

In this paper we summarize our results obtained recently on continuous triangular norms that are migrative with respect to an arbitrary continuous triangular norm. We start with the original notion of migrativity and completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent t-norm classes, the characterization and construc...