Notes on anti \(L\)-fuzzy subfield of a field (Q2856599)

Let \((F,+,.)\) be a field. An L-fuzzy subset \(A\) of \(F\) is said to be an anti-L-fuzzy subfield of \(F\) if the following conditions are satisfied: {\parindent=6mm \begin{itemize}\item[(1)] \(A(x + y) \leq A(x) \vee A(y)\), for all \(x, y \in F\), \item[(2)] \(A(-x) \leq A(x)\), for all \(x \in F\), \item[(3)] \(A(x . y) \leq A(x) \vee A(y)\), for all \(x, y \in F\), \item[(4)] \(A(x^{-1}) \leq A(x)\), for all \(x \in F - \{ 0 \}\), where 0 is the additive identity element of \(F\). NEWLINENEWLINE\end{itemize}} Some properties of the anti-L-fuzzy subfield are discussed.