On the new solutions for a fully fuzzy linear system
After defining fully interval linear systems and fully fuzzy linear systems, the authors restrict themselves to such systems with trapezoidal fuzzy numbers and propose a solution of such problems by solving two programming problems the objective function of which is linear but the restrictions contain nonlinear equations as well. In case the programming problem does not possess a suitable solution, they define a fuzzy surrounding solution and a fuzzy peripheral solution. These solutions, which are contained in a tolerable fuzzy solution set, respectively in a controllable fuzzy solution set, are shown to be obtainable by solving corresponding nonlinear programming problems. If a fully fuzzy linear systems possesses both a fuzzy surrounding and a fuzzy peripheral solution which coincide, the authors show that then that solution is solving the fully fuzzy linear system. The paper concludes by exhibiting three academic examples and one example with economic background.
scientific article; zbMATH DE number 6506250
scientific article