Wu, Hsien-Chung The fuzzy Riemann integral and its numerical integration. (English) Zbl 0941.26014 Fuzzy Sets Syst. 110, No. 1, 1-25 (2000). Summary: The fuzzy Riemann integral and its numerical integration are proposed in this paper. The \(\alpha\)-level set of this fuzzy Riemann integral is a closed interval whose end points are the classical Riemann integrals, thus we provide a numerical method to approximate the fuzzy Riemann integral by invoking the Simpson’s rule. We fit the end points (closed interval) of the \(\alpha\)-level set of the fuzzy Riemann integral as polynomials with variable \(\alpha\) in a least-squares sense. Finally, the membership function of the fuzzy Riemann integral can be transformed into a nonlinear programming problem and can be solved by any current optimizer. Cited in 36 Documents MSC: 26E50 Fuzzy real analysis 65D30 Numerical integration 90C30 Nonlinear programming Keywords:fuzzy Riemann integral; numerical integration; Simpson’s rule; least-squares; nonlinear programming PDFBibTeX XMLCite \textit{H.-C. Wu}, Fuzzy Sets Syst. 110, No. 1, 1--25 (2000; Zbl 0941.26014) Full Text: DOI