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Nonparametric recursive aggregation process

Elena Tsiporkova, Veselka Boeva (2004)

Kybernetika

In this work we introduce a nonparametric recursive aggregation process called Multilayer Aggregation (MLA). The name refers to the fact that at each step the results from the previous one are aggregated and thus, before the final result is derived, the initial values are subjected to several layers of aggregation. Most of the conventional aggregation operators, as for instance weighted mean, combine numerical values according to a vector of weights (parameters). Alternatively, the MLA operators...

Non-perfect rings and a theorem of Eklof and Shelah

Jan Trlifaj (1991)

Commentationes Mathematicae Universitatis Carolinae

We prove a stronger form, A + , of a consistency result, A , due to Eklof and Shelah. A + concerns extension properties of modules over non-left perfect rings. We also show (in ZFC) that A does not hold for left perfect rings.

Nonreflecting stationary subsets of P κ λ

Yoshihiro Abe (2000)

Fundamenta Mathematicae

We explore the possibility of forcing nonreflecting stationary sets of P κ λ . We also present a P κ λ generalization of Kanamori’s weakly normal filters, which induces stationary reflection.

Non-separable Banach spaces with non-meager Hamel basis

Taras Banakh, Mirna Džamonja, Lorenz Halbeisen (2008)

Studia Mathematica

We show that an infinite-dimensional complete linear space X has: ∙ a dense hereditarily Baire Hamel basis if |X| ≤ ⁺; ∙ a dense non-meager Hamel basis if | X | = κ ω = 2 κ for some cardinal κ.

Non-stochastic uncertainty quantification of a multi-model response

Chleboun, Jan (2025)

Programs and Algorithms of Numerical Mathematics

The focus is put on the application of fuzzy sets and Dempster-Shafer theory in assessing the nature and extent of uncertainty in the response of M models that model the same phenomenon and depend on fuzzy input data. Dempster-Shafer theory uses a weighted family of fixed sets called the focal elements to evaluate the relationship between an arbitrarily chosen set and the focal elements. It is proposed to create at least M weighted focal elements on the basis of 1) the responses to fuzzy inputs...

Normal numbers and subsets of N with given densities

Haseo Ki, Tom Linton (1994)

Fundamenta Mathematicae

For X ⊆ [0,1], let D X denote the collection of subsets of ℕ whose densities lie in X. Given the exact location of X in the Borel or difference hierarchy, we exhibit the exact location of D X . For α ≥ 3, X is properly D ξ ( Π α 0 ) iff D X is properly D ξ ( Π 1 + α 0 ) . We also show that for every nonempty set X ⊆[0,1], D X is Π 3 0 -hard. For each nonempty Π 2 0 set X ⊆ [0,1], in particular for X = x, D X is Π 3 0 -complete. For each n ≥ 2, the collection of real numbers that are normal or simply normal to base n is Π 3 0 -complete. Moreover, D ℚ , the...

Normal numbers and the Borel hierarchy

Verónica Becher, Pablo Ariel Heiber, Theodore A. Slaman (2014)

Fundamenta Mathematicae

We show that the set of absolutely normal numbers is Π⁰₃-complete in the Borel hierarchy of subsets of real numbers. Similarly, the set of absolutely normal numbers is Π⁰₃-complete in the effective Borel hierarchy.

Note on "construction of uninorms on bounded lattices"

Xiu-Juan Hua, Hua-Peng Zhang, Yao Ouyang (2021)

Kybernetika

In this note, we point out that Theorem 3.1 as well as Theorem 3.5 in G. D. Çaylı and F. Karaçal (Kybernetika 53 (2017), 394-417) contains a superfluous condition. We have also generalized them by using closure (interior, resp.) operators.

Notes on locally internal uninorm on bounded lattices

Gül Deniz Çaylı, Ümit Ertuğrul, Tuncay Köroğlu, Funda Karaçal (2017)

Kybernetika

In the study, we introduce the definition of a locally internal uninorm on an arbitrary bounded lattice L . We examine some properties of an idempotent and locally internal uninorm on an arbitrary bounded latice L , and investigate relationship between these operators. Moreover, some illustrative examples are added to show the connection between idempotent and locally internal uninorm.

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