L -fuzzy ideal degrees in effect algebras

Xiaowei Wei; Fu Gui Shi

Kybernetika (2022)

  • Volume: 58, Issue: 6, page 996-1015
  • ISSN: 0023-5954

Abstract

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In this paper, considering L being a completely distributive lattice, we first introduce the concept of L -fuzzy ideal degrees in an effect algebra E , in symbol 𝔇 e i . Further, we characterize L -fuzzy ideal degrees by cut sets. Then it is shown that an L -fuzzy subset A in E is an L -fuzzy ideal if and only if 𝔇 e i ( A ) = ⊤ , which can be seen as a generalization of fuzzy ideals. Later, we discuss the relations between L -fuzzy ideals and cut sets ( L β -nested sets and L α -nested sets). Finally, we obtain that the L -fuzzy ideal degree is an ( L , L ) -fuzzy convexity. The morphism between two effect algebras is an ( L , L ) -fuzzy convexity-preserving mapping.

How to cite

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Wei, Xiaowei, and Shi, Fu Gui. "$L$-fuzzy ideal degrees in effect algebras." Kybernetika 58.6 (2022): 996-1015. <http://eudml.org/doc/299488>.

@article{Wei2022,
abstract = {In this paper, considering $L$ being a completely distributive lattice, we first introduce the concept of $L$-fuzzy ideal degrees in an effect algebra $E$, in symbol $\mathfrak \{D\}_\{ei\}$. Further, we characterize $L$-fuzzy ideal degrees by cut sets. Then it is shown that an $L$-fuzzy subset $A$ in $E$ is an $L$-fuzzy ideal if and only if $\mathfrak \{D\}_\{ei\}(A)=\top ,$ which can be seen as a generalization of fuzzy ideals. Later, we discuss the relations between $L$-fuzzy ideals and cut sets ($L_\{\beta \}$-nested sets and $L_\{\alpha \}$-nested sets). Finally, we obtain that the $L$-fuzzy ideal degree is an $(L,L)$-fuzzy convexity. The morphism between two effect algebras is an $(L,L)$-fuzzy convexity-preserving mapping.},
author = {Wei, Xiaowei, Shi, Fu Gui},
journal = {Kybernetika},
keywords = {effect algebra; $L$-fuzzy ideal degree; cut set; $(L,L)$-fuzzy convexity},
language = {eng},
number = {6},
pages = {996-1015},
publisher = {Institute of Information Theory and Automation AS CR},
title = {$L$-fuzzy ideal degrees in effect algebras},
url = {http://eudml.org/doc/299488},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Wei, Xiaowei
AU - Shi, Fu Gui
TI - $L$-fuzzy ideal degrees in effect algebras
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 6
SP - 996
EP - 1015
AB - In this paper, considering $L$ being a completely distributive lattice, we first introduce the concept of $L$-fuzzy ideal degrees in an effect algebra $E$, in symbol $\mathfrak {D}_{ei}$. Further, we characterize $L$-fuzzy ideal degrees by cut sets. Then it is shown that an $L$-fuzzy subset $A$ in $E$ is an $L$-fuzzy ideal if and only if $\mathfrak {D}_{ei}(A)=\top ,$ which can be seen as a generalization of fuzzy ideals. Later, we discuss the relations between $L$-fuzzy ideals and cut sets ($L_{\beta }$-nested sets and $L_{\alpha }$-nested sets). Finally, we obtain that the $L$-fuzzy ideal degree is an $(L,L)$-fuzzy convexity. The morphism between two effect algebras is an $(L,L)$-fuzzy convexity-preserving mapping.
LA - eng
KW - effect algebra; $L$-fuzzy ideal degree; cut set; $(L,L)$-fuzzy convexity
UR - http://eudml.org/doc/299488
ER -

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