本篇博士論文主要探討模糊數在一般條件下之對稱梯形逼近。Ban和Coroianu在2016年的《Soft Computing》期刊中提出模糊數在一般條件下之對稱三角形逼近的概念，本研究深入研究模糊數的對稱梯形逼近，特別在一般的條件下，這是前者未曾涵蓋的範疇。我們完整計算出對稱梯形逼近的解析解，並深入探討這種逼近方法的各項性質。同時，我們也研究了對稱梯形逼近退化為對稱三角逼近的條件。最後，論文提供了有關期望值和模糊性等關鍵參數的實例，以探討逼近過程中數值誤差的優勢。這份研究的貢獻在於針對模糊數的逼近提供更為實用、有效的逼近方式。

In their publication in Soft Computing [Soft Comput 20:1249–1261, 2016], Ban and Coroianu introduced the concept of symmetric triangular approximation under a general condition, along with extensive calculations and a computational formula. However, their conclusions did not support the derivation of the symmetric trapezoidal approximation. In this study, calculations for the symmetric trapezoidal approximations of fuzzy numbers are conducted under general conditions. Additionally, the properties of identity, translation, and scale invariance, as well as additivity of the derived approximation operators, are explored. The conditions that lead to the degeneration from the nearest symmetric trapezoidal approximation to the symmetric triangular approximation are also investigated. Furthermore, applications and numerical examples related to significant parameters such as value, expected value, and ambiguity are provided. Finally, quantitative improvements in the approximation process are examined using several illustrative examples.

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