On the convergence of fuzzy sets and the completeness of the space of fuzzy sets (Q2367742)

The authors introduce several convergence concepts of fuzzy sets such as convergent in measure, convergent uniformly, \(\mu\)-uniform convergence and \(L^ p\)-convergent. After defining these concepts, the authors construct an embedding of the space of fuzzy sets in a normed linear space. Then based on this embedding of the space of fuzzy sets in a normed linear space, the authors define the \(L^ p\)-convergence concept. With the help of these, the authors have proved the very interesting property which states that the space of fuzzy sets under the embedding is a complete metric space.