Comparison of Formulations of Applied Tasks With Interval, Fuzzy Set and Probability Approaches

The focus of this paper is to clarify the concepts of solutions in linear equations in interval, probabilistic and fuzzy sets setting for real word tasks. There is a fundamental difference between formal definitions of the solutions and physically meaningful concept of solution in applied tasks when equations have uncertain components. For instance, a formal definition of the solution in terms of Moore interval analysis can be completely irrelevant for solving a real world task. We show that formal definitions must follow meaningful concept of the solution in the real world. The paper proposed several formalized definitions of the concept of solution for the linear equations with uncertain components in the interval, probability and fuzzy sets terms