Fuzzy arithmetic with product t-norm

The focus of this thesis is fuzzy arithmetic operations under the product t-norm. A review of the literature shows that the results of the studies on the product t-norm demonstrate even in the best approach now available an algorithm that can only compute results for discrete points, requiring high computing costs only be able to find approximations of the results. In this study, explicit formulas are obtained for addition with the product t-norm and multiplication with the product t-norm for triangular fuzzy numbers. Contrary to the calculation methods proposed so far, these formulas can easily replace the previous studies with their low computational cost and precise results for all points. The lack of shape preservation in these processes creates problems for repetitive operations. However, this problem is solved by the presentation of appropriate approximations leading to notable results for performing repetitive operations. Briefly, the aim of this study is to present a new method that produces the exact result of the arithmetic operations to be performed with the product t-norm in a continuous form.