A new algorithm for minimizing a linear objective function with fuzzy relation equation constraints

In this paper, we study the problem of minimizing a linear objective function subject to a fuzzy system constraint. By utilizing the fuzzy system's compact system, we define k-form chained solutions and spaces of k-form chained solutions. Then we prove that any minimal solution of the fuzzy system is a k-form chained solution. By using an operation method expressed in tables, we sieve out basic solutions from the spaces of k-form chained solutions. Finally, we obtain optimal solutions of the studied problem from the obtained basic solutions. Examples are provided to show that our algorithm is simple and convenient.