Interactive fuzzy numbers arithmetic in financial analyses

Fuzzy arithmetic seems to be a well-developed and well-formalized branch of fuzzy sets theory. Nevertheless, there are some problems with its practical implementation. In practice, one can very often encounter the question of how to calculate the value of an arithmetic expression when its arguments are presented as linked fuzzy numbers. This article presents the generalization of Zadeh’s extension principle for arithmetic operations on fuzzy linked variables. Typical kinds of interaction between financial analyses parameters in industrial enterprises are discussed later. These interactions make use of nonlinear programming methods necessary to calculate the values of selected financial indices expressed by the fuzzy numbers. The article presents the problem of nonlinear programming applied to the calculation of the values of these indices. Additionally, the paper proposes the use of computer simulations in arithmetic operations on fuzzy linked variables. Furthermore, the example of gross profit calculations for two metallurgical companies is presented. The calculations done show that the interaction between the arguments of the arithmetic expression influences the final result significantly.