Weighted expected value operators on fuzzy numbers

The expected value operator is a widely used defuzzifier on fuzzy numbers. It treats each $\alpha$-cut equally. In theory and applications, it is often necessary to reflect the differences of the importance of the $\alpha$-cuts. To this aim, we introduce the weighted expected value operators from fuzzy numbers to □, which allow weighting the $\alpha$-cuts. It’s shown that the weighted expected value operators are defuzzifiers and that they are additive and scale invariant. Furthermore, we investigate the continuity of the weighted expected value operators according to two types of hyperspace metrics: the sendograph metric and the endograph metric, respectively.