Fuzzy Positional Function

In this book, the concept of the fuzzy positional function is introduced based on the fuzzy filter. Certain properties are obtained and they are clarified examples were provided these properties. Also, we presented the types of fuzzy positional function by utilizing the q-neighborhood. we found that the value of the fuzzy positional function is an empty set when the fuzzy set does not belong to fuzzy filter. The types of the fuzzy positional function are based on the fuzzy filter and the concepts of the bounded-product, intersection, algebraic product, and drastic product between the fuzzy sets . The relations between them are also, studied . And we noticed a correlation between the four types of the fuzzy positional function, where the second type is more general than the first type, and the first type is more general than the third and the fourth types. Finally, we presented types of fuzzy ?_i- operators whose definitions are depending of the fuzzy positional function. We provided the relationship between them and most important characteristics and supported with examples that clarify those properties .