臺灣博碩士論文加值系統

近來許多類型模糊數的逼近問題已經被研究過，包含三角、梯形與半梯形模糊數的逼近問題，也提出計算公式與演算法。接著針對模糊數的特性，提出了保持特定性質的逼近問題，包含保持區間，保持模糊度，保持模糊寬度的模糊數的逼近問題，在本論文中，我們提出另一個解法處理保持x 重心的逼近問題，包含對稱三角形與對稱梯形模糊數。最後提出實例具體呈現理論的結果。

Recently, we study more general approximations of fuzzy numbers which will generalize many approximations including interval, triangular, trapezoidal, semi-trapezoidal approximations. For properties of fuzzy numbers, the approximation-preserving the specific property
problem, including preserving interval, ambiguity or width, are proposed. In this paper, we propose translation method to solve approximation preserving its x-coordinate of the centroid point of a fuzzy number, including symmetric triangular and trapezoidal approximation, in
Hilbert space. In the end, numerical results show that the presented method is valid.

中文摘要i
英文摘要ii
誌　　謝iii
目　　錄iv
1 Preliminaries 1
1.1 The definition of fuzzy numbers . . . . . . . . . . . . . . . . . . . . . 1
1.2 Symmetric trapezoidal approximation of a fuzzy number . . . . . . . . . . 5
2 Embedding fuzzy numbers into a Hilbert space 6
2.1 Hilbert space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Embedding fuzzy numbers into a Hilbert space . . . . . . . . . . . . . . 7
3 The symmetric trapezoidal approximation-preserving its x-coordinate
of the centroid point of a fuzzy number 9
3.1 The symmetric trapezoidal approximation-preserving its x-coordinate of the
centroid point of a fuzzy number A~ with x (A~) = 0 . . . . . . . . . . . . 9
3.2 The symmetric triangular approximation-preserving its x-coordinate of the
centroid point of a fuzzy number A~ with x (A~) = 0 . . . . . . . . . . . . 13
3.3 The symmetric trapezoidal approximation-preserving its x-coordinate of the
centroid point of a fuzzy number . . . . . . . . . . . . . . . . . . . . . 14
3.4 A numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Reference 20

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