| Abstract: | 在模糊理論中，模糊計算及其應用為眾多學者所探討，其中Alpha截集法(Alpha-cuts)是經常被利用來進行模糊運算的一種方式，然而根據Zadeh的延伸法則(Extension principle)所定義之運算三角形基準 (t-norm)，並未被深入探討於運算中且兩種類型之模糊計算於複雜系統中邊界擴張及合理性並未被探討。因此，本研究將著重於下列方向，探討模糊計算t-norm並擴展模糊計算應用性、模糊計算導入系統動態實際模型及解決模糊系統中模糊量不可控制累積問題。首先提出延伸法則所定義出之模糊計算除法，在t-norm 準則下加法、減法、乘法於近年此類型模糊計算已經應用在許多領域中，本研究證明推導t-norm 準則下之模糊計算除法，此計算除法包含Yager’s t-norm準則及the weakest t-norm準則，這些方法將會擴展模糊計算之應用性。 其次本研究將模糊計算導入系統動態學實際模型，傳統系統動態學已經廣泛的被應用於許多領域上，於傳統系統動態可以觀察出某些變數屬於模糊因子，因此有些系統動態之變數或參數可以擴展成模糊變數，此模糊計算之系統動態評估可以提供決策者在不確定環境下系統行為之資訊，於本研究將以α截集、Yager’s t-norm及the weakest t-norm等模糊計算方式導入系統動態傳染病模式，觀察不同模糊計算對於系統動態模式之變化，模糊計算以the weakest t-norm準則下可獲得模式變數最小模糊間距，而α截集獲得模式變數最大模糊間距，而Yager’s t-norm 可控制參數介於兩者計算之間，但於系統動態模式中可發現，變數模糊量隨著時間累積變成不可控制，因此最後本研究提出累積系統在每個時間區間結束時可以將其變數解模糊，這解模糊值代表系統可能預期值，再將此解模糊值模糊化帶入下一個時間點，此方法可以避免模糊量隨著時間累積而造成無法控制的情形，同時本研究以顧客-生產者-勞工模式為實例觀察結合模糊計算之系統動態模式及利用解模糊技巧控制模糊量累積且測試最大(α截集)及最小間距(the weakest t-norm)計算準則，並測試觀察三角模糊數不同大小之模糊間距以及非對稱之三角模糊數於系統模式，可得到模糊計算之系統動態皆可得到穩定之結果，並可依據決策環境下不確定性之程度選擇模糊計算方式及不同之三角模糊數。
In fuzzy theory the fuzzy arithmetic has been widely studied. Among them, α-cut arithmetic is a popular method in fuzzy arithmetic. However, based on the Zadeh’s extension principle, the t-norm operators have not widely been investigated. Moreover, in fuzzy system the problem, which the fuzzy accumulations become uncontrollable, has not been investigated. Therefore, this research thoroughly investigates the division of fuzzy arithmetic and system dynamics with fuzzy arithmetic, and solving uncontrollable accumulations in fuzzy system. First of all this research provides division of fuzzy arithmetic based on extension principle. In recent years, the operations of fuzzy arithmetic have been developed and applied to many fields in addition, subtraction, and multiplication based on ?-cut or t-norm. This research shows the division of fuzzy arithmetic based on Yager’s t-norm and the weakest t-norm. These operations of division will extend application of fuzzy arithmetic.In the second place this research applies fuzzy arithmetic to system dynamics analysis. Traditional crisp system dynamics can be observed that some variables/parameters may belong to the uncertain factors. It is necessary to extend the system dynamics to treating the vague variables/parameters too. The evaluation of fuzzy system dynamics may provide the decision maker information regarding the system’s behavior uncertainties. In this research the epidemics model is examined with the fuzzy system dynamics in three types of fuzzy arithmetic, ?-cut fuzzy arithmetic, Tp Yager’s t-norm, and T? weakest t-norm operator. In this model we can observe that the ?-cut fuzzy arithmetic variables get larger fuzzy spreads in epidemics model, and the weakest t-norm operator variables get smaller fuzzy spreads in epidemics model. Based on the Yager’s t-norm operator variable of model can get intermediate fuzzy spreads with tuning parameter p. However, we can find that accumulations become uncontrollable with dynamic time in this model. Finally, this research uses defuzzification method to solve uncontrollable accumulations in fuzzy system. The fuzzy variables of the system at the end of each interval can be defuzzified to obtain the representative value similar to the expected values or interval-end defuzzification is performed. The representative values of the variables may be supplied to the next time interval with fuzzy inputs again. The purpose of defuzzification is obvious that it avoids the fuzziness from continually accumulating in the model and by time possibly becoming very uncontrollable. Moreover, in this research, the customer-producer-employment model is also examined with the fuzzy system dynamics in two types of fuzzy arithmetic, ?-cut fuzzy arithmetic and the T? weakest t-norm operator, and this model uses defuzzification method to control fuzzy accumulations. Symmetrical and non-symmetrical triangular-fuzzy-number, varied amount of fuzzy inputs’ fuzziness, and length of the system time delay are examined with useful results provided. |
