非线性中智集的集结算法及其在多属性群决策中的应用研究

Research on Aggregation Algorithm of Nonlinear Intelligent Sets and Its Application in Multi-Attribute Group Decision Making

摘要: 本文针对偏好信息由中智集(NS)表示的多属性群决策问题(MAGDM)进行研究，将静态决策环境下的中智集扩展为动态决策环境下的非线性中智集，并开发了相应的投影模型和集结算法。首先，本文给出了非线性中智集的定义及运算法则。然后，将非线性中智数投影为三维空间中的曲线，用曲线之间所围成曲面的面积大小来描述决策者偏好之间的差异，从而完成非线性中智集空间投影模型的建立。最后，开发基于模拟植物生长算法(PGSA)的空间曲线集结算法，通过寻找与所有偏好曲线围成曲面面积之和最小的最优集结曲线来完成非线性中智集的集结，并结合TOPSIS算法完成多属性群决策问题中的方案排序工作。文章的实验部分通过一个具体案例来说明本文所提出方法的有效性。

Abstract: This paper investigates the problem of multi-attribute group decision making (MAGDM) where preference information is represented by a neutrosophic set (NS). It extends the concept of neutral set from static decision environments to nonlinear neutrosophic set in dynamic decision environments, and develops a corresponding projection model and aggregation algorithm. Firstly, we provide the definition and algorithm for nonlinear neutrosophic sets. Then, we project the nonlinear neutral set onto a curve in three-dimensional space, describing differences in decision makers’ preferences through the surface area between curves. This allows us to establish a projection model for the space of nonlinear neutral sets. Finally, we develop a space curve aggregation algorithm based on the plant growth simulation algorithm (PGSA). By identifying an optimal aggregation curve with minimal sum of surface areas between all preference curves, we assemble the nonlinear neutral set and combine it with TOPSIS algorithm to sort schemes in multi-attribute group decision making problems. The experimental section demonstrates the effectiveness of our proposed method through a specific case.