Solutions of fuzzy correspondence inequations with sup-conjunctor composition

This paper investigates the solutions of fuzzy correspondence inequations with sup-conjunctor composition, i.e., it discusses those solutions for the input and output fuzzy sets which are unknown while a fuzzy correspondence is fixed. First, it proves that the solutions of the fuzzy correspondence inequations can be analyzed and formulated by solving the corresponding cut set problems. It then shows that the space of solutions of the fuzzy correspondence inequation is a complete distributive lattice and the same holds for the space of solutions of the fuzzy correspondence equation. Moreover, it describes the solution set of the fuzzy correspondence inequation partly.