Going off from the importance of combining fuzzy set theory and the fuzzy logic in many ways with several models of artificial intelligent which named as "Intelligent modeling", fuzzy logic like other paradigms such as ;Expert Systems ,Neural Networks,…,etc ,which were used as intelligent techniques that offer some advantages in real world applications(Jain L.& Jain R.,1997).These techniques are fusing together by Fusion Technology. These fusing be susceptible with mistakes and risks .To avoid these all in this work we need to study the topology of fuzzy logic which is based fuzzy set theory.
Most ways that in majority exploit fuzzy logic such in domain of control ,domains of science from biology to particle physics(Thuillard,2000).Since a fuzzy logic extend values from two values to many values, there are a subtle questions to be answered : (i)What is(are) result(s) gotten on if we invert a view of fuzzy logic from multiplicity by filtering sets of points(members) ,or in other words ;Are the results for filtering results of fuzzy logic(sets) by executables be acceptably?(ii)Is the fuzzy version image of image is equal original?(iii)Is filtering fuzzy get on the original(restricted solves)? (iv)Do the operations on fuzzy sets that satisfies for classical sets be true under theorems of filters topology? .
Such questions are needed in practical applications such signal processing .
In that context the theorems in topology of filters were proven for crisp(classical) proves of topology and several proves occurred for some theorems by fuzzy logic , fuzzy set theory that to explain what caused the need for this all .