Algebraic Properties of Intuitionistic Fuzzy Residuated Lattices

Abstract

In this paper, we investigate more relations between the symmetric residuated lattices $L$ with their corresponding intuitionistic fuzzy residuated lattice $tilde{L}$. It is shown that some algebraic structures of $L$ such as Heyting algebra, Glivenko residuated lattice and strict residuated lattice are preserved for $tilde{L}$. Examples are given for those structures that do not remain the same. Also some special subsets of $tilde{L}$ such as regular elements $Rg(tilde{L})$, dense elements $D(tilde{L})$, infinitesimal elements $Inf(tilde{L})$, boolean elements $B(tilde{L})$ and $Rad_{BL}(tilde{L})$ are characterized. The relations between these and corresponding sets in $L$ will be investigated.