Remarks on the uncertainty expansion problem in calculations of models of relational fuzzy cognitive maps

During the modeling of uncertain and imprecise systems, the intelligent approach, based on the use of so-called Fuzzy Cognitive Maps (FCM) is often used. Constructors of the FCM models usually use a technique, in which fuzzy quantities are converted to their crisp equivalents (e.g. in a model learning phase). Such a procedure converts the fuzzy model in a crisp model, which may be a problem in systems with uncertainty. This risk can be avoided by building a model based on fuzzy numbers, fuzzy relations and fuzzy arithmetic operations, but then the new problem - of technical nature - arises, related to the specifics of operations on fuzzy numbers - manifested in the support deformations. The paper proposes a solution to this problem, consisting in a new look at the interpretation of the results of arithmetic operations on fuzzy numbers. New mechanism, that allows overcoming the negative effects of such deformations, is presented. The use of the proposed approach enables maintaining the fuzzy nature of the model at each stage of its operation. The results of simulations for different variants of the proposed method are also shown.