Categorical Analysis of Logic Operators on Fuzzy Sets

Although the concept of Topos can lead naturally to the logic operations of the class of sets, SetH cannot be connected to the logic operations of fuzzy sets due to the fact that Sell-I has no subobject classifier. In thsi work, from category Fuz we introduce several concepts such as middle object, WSC and WTopos. It is shown that by the use of category Fuz which is a WTopos, the fuzzy logic operations can be obtained both logically and naturally.