Fully hesitant fuzzy linear programming with hesitant fuzzy numbers

In this paper, we introduce a new approach to solve a fully hesitant fuzzy linear programming (FHFLP) problem with hesitant fuzzy numbers (HFNs) as parameters. Using an (alpha, k)-cut for the HFNs, we convert this problem into some interval linear programming (ILP) problems, and solve these problems through one of the available algorithms to solve the ILP problems. Then through statistical regression analysis, we get k fuzzy numbers as the final approximate solutions, and we have proved that they are well defined. Finally, using the hesitant fuzzy arithmetic, we obtain a hesitant fuzzy value of the objective function. An example is introduced to clarify the solution process of this method, and a comparison between the optimal solutions through the proposed method to an FHFLP problem and its converted form to a fully fuzzy linear programming problem has been done. The outcomes indicate that the obtained solutions for decision variables and objective function are reasonable.

Automated summary

This paper introduces a new approach to solve fully hesitant fuzzy linear programming problems with hesitant fuzzy numbers as parameters. By converting the problem into interval linear programming problems and using statistical regression analysis, approximate solutions are obtained. The method is validated through an example, showing that the solutions for decision variables and objective function are reasonable.