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Characterization of fuzzy order relation by fuzzy cone

Masamichi Kon (2022)

Kybernetika

In the present paper, fuzzy order relations on a real vector space are characterized by fuzzy cones. It is well-known that there is one-to-one correspondence between order relations, that a real vector space with the order relation is an ordered vector space, and pointed convex cones. We show that there is one-to-one correspondence between fuzzy order relations with some properties, which are fuzzification of the order relations, and fuzzy pointed convex cones, which are fuzzification of the pointed...

Characterizing the powerset by a complete (Scott) sentence

Ioannis Souldatos (2013)

Fundamenta Mathematicae

This paper is part II of a study on cardinals that are characterizable by a Scott sentence, continuing previous work of the author. A cardinal κ is characterized by a Scott sentence ϕ ℳ if ϕ ℳ has a model of size κ, but no model of size κ⁺. The main question in this paper is the following: Are the characterizable cardinals closed under the powerset operation? We prove that if ℵ β is characterized by a Scott sentence, then 2 ℵ β + β ₁ is (homogeneously) characterized by a Scott sentence, for all 0 < β₁ < ω₁....

Characterizing tolerance trivial finite algebras

Ivan Chajda (1994)

Archivum Mathematicum

An algebra A is tolerance trivial if A ̰ = A where A ̰ is the lattice of all tolerances on A . If A contains a Mal’cev function compatible with each T A ̰ , then A is tolerance trivial. We investigate finite algebras satisfying also the converse statement.

Choice principles in elementary topology and analysis

Horst Herrlich (1997)

Commentationes Mathematicae Universitatis Carolinae

Many fundamental mathematical results fail in ZF, i.e., in Zermelo-Fraenkel set theory without the Axiom of Choice. This article surveys results — old and new — that specify how much “choice” is needed precisely to validate each of certain basic analytical and topological results.

Choice principles in Węglorz’ models

N. Brunner, Paul Howard, Jean Rubin (1997)

Fundamenta Mathematicae

Węglorz' models are models for set theory without the axiom of choice. Each one is determined by an atomic Boolean algebra. Here the algebraic properties of the Boolean algebra are compared to the set theoretic properties of the model.

Chromatic number of the product of graphs, graph homomorphisms, antichains and cofinal subsets of posets without AC

Amitayu Banerjee, Zalán Gyenis (2021)

Commentationes Mathematicae Universitatis Carolinae

In set theory without the axiom of choice (AC), we observe new relations of the following statements with weak choice principles. ∘ If in a partially ordered set, all chains are finite and all antichains are countable, then the set is countable. ∘ If in a partially ordered set, all chains are finite and all antichains have size ℵ α , then the set has size ℵ α for any regular ℵ α . ∘ Every partially ordered set without a maximal element has two disjoint cofinal sub sets – CS. ∘ Every partially ordered set...

Class preserving mappings of equivalence systems

Ivan Chajda (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

By an equivalence system is meant a couple 𝒜 = ( A , θ ) where A is a non-void set and θ is an equivalence on A . A mapping h of an equivalence system 𝒜 into ℬ is called a class preserving mapping if h ( [ a ] θ ) = [ h ( a ) ] θ ' for each a ∈ A . We will characterize class preserving mappings by means of permutability of θ with the equivalence Φ h induced by h .

Classes de Wadge potentielles et théorèmes d'uniformisation partielle

Dominique Lecomte (1993)

Fundamenta Mathematicae

On cherche à donner une construction aussi simple que possible d'un borélien donné d'un produit de deux espaces polonais. D'où l'introduction de la notion de classe de Wadge potentielle. On étudie notamment ce que signifie "ne pas être potentiellement fermé", en montrant des résultats de type Hurewicz. Ceci nous amène naturellement à des théorèmes d'uniformisation partielle, sur des parties "grosses", au sens du cardinal ou de la catégorie.

Classes of fuzzy measures and distortion

Ľubica Valášková, Peter Struk (2005)

Kybernetika

Distortion of fuzzy measures is discussed. A special attention is paid to the preservation of submodularity and supermodularity, belief and plausibility. Full characterization of distortion functions preserving the mentioned properties of fuzzy measures is given.

Currently displaying 381 – 400 of 2138