A Study of Fuzzy Arithmetic and Fuzziness Accumulation Controlling Method for System Dynamics with Fuzzy Arithmetic

• Main Authors: Kuo-Ping Lin, 林國平
• Other Authors: Ping-Teng Chang
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/66078284658984494340

博士 === 東海大學 === 工業工程與經營資訊學系 === 95 === 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.