Weighted semi-trapezoidal approximations of fuzzy numbers

作者：Yeh Chi Tsuen^*

来源：Fuzzy Sets and Systems, 2011, 165(1): 61-80.

DOI：10.1016/j.fss.2010.11.001

• Fuzzy numbers
• Approximation
• Hilbert space

Recently, many scholars investigated interval, triangular, and trapezoidal approximations of fuzzy numbers. These publications can be grouped into two classes: Euclidean distance class and non-Euclidean distance class. Most approximations in Euclidean distance class can be calculated by formulas, but calculating approximations in the other class is more complicated. In the present paper, we study a special class of non-linear approximations with respect to a weighted Euclidean distance. We call it "weighted semi-trapezoidal approximations". The proposed approximations generalize all recent approximations in Euclidean distance class. First, we embed fuzzy numbers into a Hilbert space. Then compute weighted semi-trapezoidal approximations by means of best approximations in a closed convex subset of the Hilbert space. Finally, we propose formulas of matrix type, which is more clear than the previous contributions.

• 出版日期2011-2-16