Some representable De Morgan algebras (Q1057296)

For a set X, let \(R=\{R_ x: x\in X\}\) be a family of bounded lattices \((R_ x,\bigwedge_ x,\bigvee_ x,1_ x,0_ x)\). A fuzzy subset of X is defined as a mapping \(A: X\to \cup_{x\in X}R_ x\). The set of fuzzy subsets of X is denoted by \(P_ R(X)\) and operations \(\cup\) and \(\cap\) are defined by \((A\cup B)(x)=A(x)\vee_ xB(x)\) and \((A\cap B)(x)=A(x)\wedge_ xB(x)\). The author studies representations of De Morgan algebras by bounded lattices of fuzzy sets \((P_ R(X),\cup,\cap)\) on which some kind of involution can be defined.