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This paper deals with the uniqueness of L-fuzzy sets in the representation of a given family of subsets of a nonempty set. It first shows a formula of the number of L-fuzzy sets whose collection of cuts coincides with a given family of subsets of a nonempty set, and then provides a necessary and sufficient condition under which such L-fuzzy set is unique.
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...
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...
This paper deals with a fuzzy relational equation with sup-conjunctor composition in a complete lattice. We investigate its properties and describe its solution set. In particular, we give a sufficient and necessary condition that the solution set is nonempty, and a sufficient condition that there exist minimal elements in the solution set.
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