Equality and identity of fuzzy numbers and fuzzy arithmetic with equality constraints

The difference between equality and identity of two fuzzy numbers is discussed in this paper. According to fuzzy arithmetic with requisite constraints put forward by Klir, the fuzzy arithmetic with equality constraints and its expression based on structured element are put forward, and then the irreversible problem in traditional fuzzy arithmetic is solved. From the expression based on structured element, the fuzzy arithmetic with equality constraints is turned into the operation of two monotone functions with the same monotonic form. From this transition we get the operation method of equality constraint arithmetic and the calculation method of fuzzy equation.