Remarks on effect-tribes

Pulmannová, Sylvia, and Vinceková, Elena. "Remarks on effect-tribes." Kybernetika 51.5 (2015): 739-746. <http://eudml.org/doc/276219>.

@article{Pulmannová2015,
abstract = {We show that an effect tribe of fuzzy sets $\{\mathcal \{T\}\}\subseteq [0,1]^X$ with the property that every $f\in \{\mathcal \{T\}\}$ is $\{\mathcal \{B\}\}_0(\{\mathcal \{T\}\})$-measurable, where $\{\mathcal \{B\}\}_0(\{\mathcal \{T\}\})$ is the family of subsets of $X$ whose characteristic functions are central elements in $\{\mathcal \{T\}\}$, is a tribe. Moreover, a monotone $\sigma $-complete effect algebra with RDP with a Loomis-Sikorski representation $(X, \{\mathcal \{T\}\},h)$, where the tribe $\{\mathcal \{T\}\}$ has the property that every $f\in \{\mathcal \{T\}\}$ is $\{\mathcal \{B\}\}_0(\{\mathcal \{T\}\})$-measurable, is a $\sigma $-MV-algebra.},
author = {Pulmannová, Sylvia, Vinceková, Elena},
journal = {Kybernetika},
keywords = {effect-tribe; tribe; monotone $\sigma $-complete effect algebra; Riesz decomposition property; MV-algebra},
language = {eng},
number = {5},
pages = {739-746},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Remarks on effect-tribes},
url = {http://eudml.org/doc/276219},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Pulmannová, Sylvia
AU - Vinceková, Elena
TI - Remarks on effect-tribes
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 5
SP - 739
EP - 746
AB - We show that an effect tribe of fuzzy sets ${\mathcal {T}}\subseteq [0,1]^X$ with the property that every $f\in {\mathcal {T}}$ is ${\mathcal {B}}_0({\mathcal {T}})$-measurable, where ${\mathcal {B}}_0({\mathcal {T}})$ is the family of subsets of $X$ whose characteristic functions are central elements in ${\mathcal {T}}$, is a tribe. Moreover, a monotone $\sigma $-complete effect algebra with RDP with a Loomis-Sikorski representation $(X, {\mathcal {T}},h)$, where the tribe ${\mathcal {T}}$ has the property that every $f\in {\mathcal {T}}$ is ${\mathcal {B}}_0({\mathcal {T}})$-measurable, is a $\sigma $-MV-algebra.
LA - eng
KW - effect-tribe; tribe; monotone $\sigma $-complete effect algebra; Riesz decomposition property; MV-algebra
UR - http://eudml.org/doc/276219
ER -