Sums of fuzzy topological spaces

In classical logic, which is purely a mathematical modeling based on binary evaluation, there are only two cases for each value, the first case where the symbol 1 is given and means true, and the second case where the symbol 0 is given and means false. But the truth is broader than that and may not depend solely on two states 0 and 1. Therefore, a new logic was needed that provides the general framework to solve the problem of representing approximate or nonspecific information. This logic, called fuzzy logic, was first put forward by Iranian scientist Lutfi Zadeh in 1965. Fuzzy logic is based on deduction through idioms such as hot, cold, warm, less, more, and indefinite expressions. Throughout the study, it is concluded that fuzzy logic is an extension of classical logic. Classical logic is a special case of fuzzy logic, when the membership degree is {0,1} set, Fuzzy logic has great importance not only in set theory, but also in artificial intelligence, advanced electronic devices, industrial controllers and even in our daily life. In this thesis, fuzzy set, fuzzy set types and important algebraic operations related to them will be explained. Then, by giving the definition of fuzzy topological space, we will define open sets, covered sets, interior, closure, base, neighborhoods and continuity on the sums of fuzzy topological spaces. Some of the results obtained for these topological sums will be mentioned.