linear fractional programming problem

In recent years, the hesitant fuzzy set as a proper generalization of the fuzzy set theory, which can imply in situations that the decision maker hesitates in determining the membership of parameters, has been introduced. Several applications of such sets have been revealed in the multi-criteria decision-making, graph theory and clustering methods, but there is little research on hesitant fuzzy programming problems and solving process for them in the literature. However, recently some research has been carried out in the field of linear programming under hesitant fuzzy information. However, less research can be found that has developed this perspective in nonlinear mode and especially for linear fractional programming under hesitant fuzzy data. Hence, our main focus is to propose the modeling of the linear fractional programming problem with hesitant fuzzy parameters along with the introduction of a method to solve this type of structure. For this aim, two kinds of linear fractional programming with hesitancy in different values are introduced. Then, a novel method is suggested to determine the optimal solutions for them. Some numerical examples show the reliability and validity of the models.

For the three last decades, the multi-objective fractional programming problem has attracted the attention of many researchers due to various applications in production planning, financial field, and inventory management, and so on. The main aim of this study is to introduce a new application of hesitant fuzzy sets in real-life modeling. We intend to model multi-objective linear fractional programming problems under a hesitant fuzzy environment and present a procedure to solve them. the increasing applications of multi-objective linear fractional programming problems and the lack of research papers in this field under a hesitant fuzzy environment are the main motivations of this study. In a hesitant fuzzy set, the membership degree of an element belongs to the set can be represented by several possible values in [0,1]. These values can be chosen by different experts that cannot reach a single opinion in determining a membership degree. so, in our model several evaluations for each of goals established by decision makers based on their attitudes. The generalization of the fuzzy decision-making principle and some new concepts provide an effective solution procedure for the problem. Finally, a practical example is extended to illustrate the applicability of the proposed method.