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A Generalized Definition of Fuzzy Subrings

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  • Ying-Ying An
  • Fu-Gui Shi
  • Lan Wang
  • Jun Ye

Abstract

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.

Suggested Citation

  • Ying-Ying An & Fu-Gui Shi & Lan Wang & Jun Ye, 2022. "A Generalized Definition of Fuzzy Subrings," Journal of Mathematics, Hindawi, vol. 2022, pages 1-11, September.
    • Handle: RePEc:hin:jjmath:5341207
    DOI: 10.1155/2022/5341207
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