# ON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET

Document Type: Research Paper

Authors

Department of Mathematics, Ocean University of China, Qing Dao 266071, PR China

Abstract

This paper focuses on the relationship between an \$L\$-subset and the system of level-elements induced by it, where the underlying lattice \$L\$ is a complete residuated lattice and the domain set of \$L\$-subset is an \$L\$-partially ordered set \$(X,P)\$. Firstly, we obtain the sufficient and necessary condition that an \$L\$-subset is represented by its system of level-elements. Then, a new representation theorem of intersection-preserving \$L\$-subsets is shown by using union-preserving system of elements. At last, another representation theorem of compatible intersection-preserving \$L\$-subsets is obtained by means of compatible union-preserving system of elements.

Keywords

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