$L$-fuzzy strongest postcondition predicate transformers as $L$-idempotent linear or affine operators between semimodules of monotonic predicates

For a completely distributive quantale $L$, $L$-fuzzy strongest postcondition predicate transformers are introduced, and it is shown that, under reasonable assumptions, they are linear or affine continuous mappings between continuous $L$-idempotent semimodules of $L$-fuzzy monotonic predicates.