Abbreviation: IInFL

An \emph{integral involutive FL-algebra} or \emph{integral involutive residuated lattice} is an involutive residuated lattice that is

integral: $x\vee 1 = 1$

Let $\mathbf{A}$ and $\mathbf{B}$ be involutive residuated lattices. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism: $h(x \vee y)=h(x) \vee h(y)$, $h(x \cdot y)=h(x) \cdot h(y)$, $h({\sim}x)={\sim}h(x)$ and $h(1)=1$.

Example 1:

$\begin{array}{lr}

f(1)= &1\\
f(2)= &1\\
f(3)= &1\\
f(4)= &3\\
f(5)= &3\\

\end{array}\begin{array}{lr}

f(6)= &12\\
f(7)= &17\\
f(8)= &78\\
f(9)= &\\
f(10)= &\\

\end{array}$

Cyclic integral involutive FL-algebras subvariety

Involutive FL-algebras supervariety