Complete subobjects of fuzzy sets over $MV$-algebras

Močkoř, Jiří. "Complete subobjects of fuzzy sets over $MV$-algebras." Czechoslovak Mathematical Journal 54.2 (2004): 379-392. <http://eudml.org/doc/30867>.

@article{Močkoř2004,
abstract = {A subobjects structure of the category $\Omega $- of $\Omega $-fuzzy sets over a complete $MV$-algebra $\Omega =(L,\wedge ,\vee ,\otimes ,\rightarrow )$ is investigated, where an $\Omega $-fuzzy set is a pair $\{\mathbf \{A\}\}=(A,\delta )$ such that $A$ is a set and $\delta \:A\times A\rightarrow \Omega $ is a special map. Special subobjects (called complete) of an $\Omega $-fuzzy set $\{\mathbf \{A\}\}$ which can be identified with some characteristic morphisms $\{\mathbf \{A\}\}\rightarrow \Omega ^*=(L\times L,\mu )$ are then investigated. It is proved that some truth-valued morphisms $\lnot _\{\Omega \}\:\Omega ^*\rightarrow \Omega ^*,\cap _\{\Omega \}$, $\cup _\{\Omega \} \:\Omega ^*\times \Omega ^*\rightarrow \Omega ^*$ are characteristic morphisms of complete subobjects.},
author = {Močkoř, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {fuzzy set over $MV$-lagebra; complete subobjects; subobjects classification; fuzzy set over MV-algebra; complete subobjects; subobjects classification},
language = {eng},
number = {2},
pages = {379-392},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Complete subobjects of fuzzy sets over $MV$-algebras},
url = {http://eudml.org/doc/30867},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Močkoř, Jiří
TI - Complete subobjects of fuzzy sets over $MV$-algebras
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 2
SP - 379
EP - 392
AB - A subobjects structure of the category $\Omega $- of $\Omega $-fuzzy sets over a complete $MV$-algebra $\Omega =(L,\wedge ,\vee ,\otimes ,\rightarrow )$ is investigated, where an $\Omega $-fuzzy set is a pair ${\mathbf {A}}=(A,\delta )$ such that $A$ is a set and $\delta \:A\times A\rightarrow \Omega $ is a special map. Special subobjects (called complete) of an $\Omega $-fuzzy set ${\mathbf {A}}$ which can be identified with some characteristic morphisms ${\mathbf {A}}\rightarrow \Omega ^*=(L\times L,\mu )$ are then investigated. It is proved that some truth-valued morphisms $\lnot _{\Omega }\:\Omega ^*\rightarrow \Omega ^*,\cap _{\Omega }$, $\cup _{\Omega } \:\Omega ^*\times \Omega ^*\rightarrow \Omega ^*$ are characteristic morphisms of complete subobjects.
LA - eng
KW - fuzzy set over $MV$-lagebra; complete subobjects; subobjects classification; fuzzy set over MV-algebra; complete subobjects; subobjects classification
UR - http://eudml.org/doc/30867
ER -