Fuzzy Set and Fuzzy Local Function

In this book we have reexamined the concept of fuzzy local functions presented by Sarkar. It is possible to present several different concepts of fuzzy local functions based on the fuzzy ideal. The properties and characteristics of each type and its relation to Sakar''s definition are studied. Also the relation with each other and the possibility of employing each type on the results and predictions reached by researchers in the field the fuzzy topological spaces are investigated. A created definition wider than the definition of Sakar is found in this book. Also introduces a definition which is different from the definition of Sakar by utilizing the q-neighborhood. The case only depends on the neighborhood we found that the value of the fuzzy local function is zero or one for all points. We also preseted different types of fuzzy ψ i -operators whose definitions are based on fuzzy local functions.