It is known that a fuzzy set $\bar A$ on $S$ $(S\neq\emptyset)$, as a mapping from $S$ onto a complete lattice $L$, determines a family $\{A_p;\ p\in L\}$ of subsets of $S$ indexed by the elements of $L$ (i.e. $\bar A=\cup_{p\in L}p\cdot A_p$, see for example [1]).