A Generalized Definition of Fuzzy Subrings

In this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L-fuzzy subring measures are presented. The properties of L-fuzzy subring m...

Full description

Saved in:
Bibliographic Details
Published inJournal of mathematics (Hidawi) Vol. 2022; no. 1
Main Authors An, Ying-Ying, Shi, Fu-Gui, Wang, Lan
Format Journal Article
LanguageEnglish
Published Cairo Hindawi 01.01.2022
Hindawi Limited
Wiley
Subjects
Convexity
Fuzzy sets
Homomorphisms
Mapping
Mathematics
Quotients
Online AccessGet full text

Cover

More Information
Summary:In this study, under the condition that L is a completely distributive lattice, a generalized definition of fuzzy subrings is introduced. By means of four kinds of cut sets of fuzzy subset, the equivalent characterization of L-fuzzy subring measures are presented. The properties of L-fuzzy subring measures under these two kinds of product operations are further studied. In addition, an L-fuzzy convexity is directly induced by L-fuzzy subring measure, and it is pointed out that ring homomorphism can be regarded as L-fuzzy convex preserving mapping and L-fuzzy convex-to-convex mapping. Next, we give the definition and related properties of the measure of L-fuzzy quotient ring and give a new characterization of L-fuzzy quotient ring when the measure of L-fuzzy quotient ring is 1.
ISSN:2314-4629
2314-4785
DOI:10.1155/2022/5341207