EUDML

A method is presented making it possible to construct $p o$ -groups with a strong theory of quasi-divisors of finite character and with some prescribed properties as subgroups of restricted Hahn groups $H (Δ, ℤ)$ , where $Δ$ are finitely atomic root systems. Some examples of these constructions are presented.

Complete subobjects of fuzzy sets over $M V$ -algebras

Jiří Močkoř — 2004

Czechoslovak Mathematical Journal

A subobjects structure of the category $Ω$ - of $Ω$ -fuzzy sets over a complete $M V$ -algebra $Ω = (L, \land, \lor, \otimes, \to)$ is investigated, where an $Ω$ -fuzzy set is a pair $𝐀 = (A, δ)$ such that $A$ is a set and $δ A \times A \to Ω$ is a special map. Special subobjects (called complete) of an $Ω$ -fuzzy set $𝐀$ which can be identified with some characteristic morphisms $𝐀 \to Ω^{*} = (L \times L, μ)$ are then investigated. It is proved that some truth-valued morphisms $\neg_{Ω} Ω^{*} \to Ω^{*}, \cap_{Ω}$ , $\cup_{Ω} Ω^{*} \times Ω^{*} \to Ω^{*}$ are characteristic morphisms of complete subobjects.

Topological characterizations of ordered groups with quasi-divisor theory

Jiří Močkoř — 2002

Czechoslovak Mathematical Journal

For an order embedding $G \overset{h}{\to} \to Γ$ of a partly ordered group $G$ into an $l$ -group $Γ$ a topology $𝒯_{\hat{W}}$ is introduced on $Γ$ which is defined by a family of valuations $W$ on $G$ . Some density properties of sets $h (G)$ , $h (X_{t})$ and $(h (X_{t}) ∖ {h (g_{1}), \dots, h (g_{n})})$ ( $X_{t}$ being $t$ -ideals in $G$ ) in the topological space $(Γ, 𝒯_{\hat{W}})$ are then investigated, each of them being equivalent to the statement that $h$ is a strong theory of quasi-divisors.

Extensional subobjects in categories of $Ω$ -fuzzy sets

Jiří Močkoř — 2007

Czechoslovak Mathematical Journal

Two categories $𝕊𝕖𝕥 (Ω)$ and $𝕊𝕖𝕥𝔽 (Ω)$ of fuzzy sets over an $M V$ -algebra $Ω$ are investigated. Full subcategories of these categories are introduced consisting of objects $(s u b (A, δ)$ , $σ)$ , where $s u b (A, δ)$ is a subset of all extensional subobjects of an object $(A, δ)$ . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.

The group of divisibility of $\hat{𝐙}$

Jiří Močkoř — 1984

Archivum Mathematicum

A note on approximation theorems

Jiří Močkoř — 1979

Archivum Mathematicum

General fuzzy decision systems

Jiří Močkoř — 1997

Acta Mathematica et Informatica Universitatis Ostraviensis

Some remarks on Lorenzen $r$ -group of partly ordered groups

Jiří Močkoř; Angeliki Kontolatou — 1996

Czechoslovak Mathematical Journal

Divisor class groups of ordered subgroups

Jiří Močkoř; Angeliki Kontolatou — 1993

Acta Mathematica et Informatica Universitatis Ostraviensis

Output functions of fuzzy automata

Jiří Močkoř; Renata Smolíková — 1995

Acta Mathematica et Informatica Universitatis Ostraviensis

Category of extended fuzzy automata

Jiří Močkoř; Renata Smolíková — 1996

Acta Mathematica et Informatica Universitatis Ostraviensis

Some properties of Lorenzen ideal systems

Aleka Kalapodi; Angeliki Kontolatou; Jiří Močkoř — 2000

Archivum Mathematicum

Let $G$ be a partially ordered abelian group ( $p o$ -group). The construction of the Lorenzen ideal $r_{a}$ -system in $G$ is investigated and the functorial properties of this construction with respect to the semigroup $(R (G), \oplus, \leq)$ of all $r$ -ideal systems defined on $G$ are derived, where for $r, s \in R (G)$ and a lower bounded subset $X \subseteq G$ , $X_{r \oplus s} = X_{r} \cap X_{s}$ . It is proved that Lorenzen construction is the natural transformation between two functors from the category of $p o$ -groups with special morphisms into the category of abelian ordered semigroups.

Ordered groups with greatest common divisors theory.

Močkoř, Jiří — 2000

International Journal of Mathematics and Mathematical Sciences

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Topological groups of divisibility

An extension of approximation theorems

A realization of $d$ -groups

Prüfer $d$ -groups

Semivaluations and $d$ -groups

On $o$ -ideals of groups of divisibility

Families of almost finite character

Construction of $p o$ -groups with quasi-divisors theory

Complete subobjects of fuzzy sets over $M V$ -algebras

Topological characterizations of ordered groups with quasi-divisor theory

Extensional subobjects in categories of $Ω$ -fuzzy sets

The group of divisibility of $\hat{𝐙}$

A note on approximation theorems

General fuzzy decision systems

Some remarks on Lorenzen $r$ -group of partly ordered groups

Divisor class groups of ordered subgroups

Output functions of fuzzy automata

Category of extended fuzzy automata

Some properties of Lorenzen ideal systems

Ordered groups with greatest common divisors theory.