On the foundations of weak fuzzy complex-real functions

This paper aims to create a strong background of many algebraic structures dealing with Weak Fuzzy Complex (WFC) elements. So, we build a special transformation function that has an important role in working with variables from a Real number set instead of a WFC set. We study its algebraic properties and models. Also, we define the WFC function, its canonical formula, and its main establishments. Therefore, we show some famous functions and relations formulas in WFC variables. On the other hand, differentiability, integrability, and continuity of WFC functions in one variable will be presented in terms of theorems, and many related examples will be illustrated to clarify the validity of our work.