Research And Application On Multi-Objective Group Decision-Making Based On Linguistic Preference Relations

Multi-objective Decision-making is a means to achieve the best options in a large number of possible options. In real life, we often have the need for Multi-objective Decision-making. Its core idea is to find a satisfactory solution, rather than the optimal solution. Because, under the complex decision making environments, multiple objectives are always conflicting and noncommensurable, which often result in inexistence of optimal solution.At present, Multi-objective Decision-making models based on Linguistic Preference Relations are rare, and the models related to Group Decision-making are extremely rare. However, faced with a major decision-making, a person's wisdom is far from sufficient. Therefore, we give a Multi-objective Group Decision-making Mode based on Linguistic Preference Relations.The model has four characteristics, as following:1. Based on Linguistic Preference Relations.In making decisions, it is difficult to give a precise numerical preference. Therefore, we introduce the Linguistic Preference Relations. decision-makers will be a very natural way to express the preferences of options.2. Based on Pareto Optimal Solution.Because the concept of Pareto Optimal Solution is in line with the problem of multi-objective decision-making , In the choice of optimization algorithm, we have adopted the algorithm with Pareto thinking.3. Based on Goal Satisfaction Degree.The goal that we introduce the Goal Satisfaction Degree is to reduce the Pareto optimal solutions, so that the remaining solutions are satisfactory solutions of decision-makers. This will reduce the burden of decision-making.4. Based on Group Decision-making.Multi-person decision is in line with the realistic needs, so we put forward the model based on Group Decision-making. Because aggregation operators can easily aggregate the views of decision-makers, we use the IULOWA operator to aggregate linguistic preferences of decision-makers in the model.In addition, we use the NSGA-Ⅱalgorithm to solve problems with discrete, to expand its scope of application and to enhance its practical value. We also develop a new application of induced variables. We not only use it to sort and calculate the weight, but also use it to calculate the language distance and deal with the tied OWA pairs. In order to reduce the burden of decision-making devices and improve decision-making speed, we have also found some properties of the model and have given a proof. At last, we apply the model to solve a complex problem of optimizing the allocation of resources in collaborative manufacturing.