We investigate the numbers dk of all (isomorphism classes of) distributive lattices with k elements, or, equivalently, of (unlabeled) posets with k antichains. Closely related and useful for combinatorial identities and inequalities are the numbers vk of vertically indecomposable distributive lattices of size k. We present the explicit values of the numbers dk and vk for k < 50 and prove the fo...

Two basic aggregation methods of reals are idempotent ones (min, max, arithmetic mean) and Archimedean ones (sum, bounded sum). Under some additional requirements, these methods can be shown to be the only possible up to isomorphic transformation and composition of operators (e. g. ordinal sum), see for example Isemigroups of Mostert and Shields [15], compare also [9], or quasi-arithmetic means...

Free algebras with an arbitrary number of free generators in varieties of BL-algebras generated by one BL-chain that is an ordinal sum of a finite MV-chain Ln and a generalized BL-chain B are described in terms of weak Boolean products of BL-algebras that are ordinal sums of subalgebras of Ln and free algebras in the variety of basic hoops generated by B. The Boolean products are taken over the...

The univariate conditioning of copulas is studied, yielding a construction method for copulas based on an a priori given copula. Based on the gluing method, g-ordinal sum of copulas is introduced and a representation of copulas by means of g-ordinal sums is given. Though different right conditionings commute, this is not the case of right and left conditioning, with a special exception of Archi...

We present a method for motion estimation using ordinal measures. Ordinal measures are based on relative ordering of intensity values in a image region called rank permutation. While popular measures like the sum-of squared-difference ( S S D ) and normalized correlation (NCC) rely on linearity between corresponding intensity values, ordinal measures only require them to be monotonically relate...

Canine hip dysplasia (CHD) is a serious and common musculoskeletal disease of pedigree dogs and therefore represents both an important welfare concern and an imperative breeding priority. The typical heritability estimates for radiographic CHD traits suggest that the accuracy of breeding dog selection could be substantially improved by the use of estimated breeding values (EBVs) in place of sel...

We present a method for motion estimation using ordinal measures. Ordinal measures are based on relative ordering of intensity values in a image region called rank permutation. While popular measures like the sum-of-squared-diierence (SSD) and normalized correlation (NCC) rely on linearity between corresponding intensity values, ordinal measures only require them to be monon-tonically related s...

The class of componentwise concave copulas is considered, with particular emphasis on its closure under some constructions of copulas (e. g., ordinal sum) and its relations with other classes of copulas characterized by some notions of concavity and/or convexity. Then, a sharp upper bound is given for the L ∞-measure of non-exchangeability for copulas belonging to this class.

The present contribution deals with domination in the framework of continuous t-norms. Basic properties and recent results for continuous Archimedean and continuous ordinal sum t-norms are presented and discussed. The domination property within several families of t-norms is mentioned.

Suppose A is an Abelian p-group and α is an ordinal such that A/pA is a direct sum of countable groups. It is shown that A has a nice basis if, and only if, pA has a nice basis. This strengthens an earlier result of ours in Bull. Allah. Math. Soc. (2011) proved when α < ω.