Lebesgue measure of \(\alpha\)-cuts approach for finding the height of the membership function (Q1973347)

The maximum of a membership function \(\mu_A\) is found by the help of the function \(H:[0,1]\to [0,\infty]\) defined by the equality \(H(\alpha)= \lambda(\{x\in\mathbb{R}^N; \mu_A(x)\geq \alpha\})\), where \(\lambda\) is the \(n\)-dimensional Lebesgue measure. A statistical approach is considered, too, and an algorithm is given for finding the height of \(\mu_A\).