Jia Zihang, Qiao Junsheng
College of Mathematics and Statistics, Northwest Normal University, No. 967, Anning East Road, Lanzhou, 730070 Gansu People's Republic of China.
School of Mathematical Sciences, Dalian University of Technology, No. 2, Linggong Road, Dalian, 116024 Liaoning People's Republic of China.
Artif Intell Rev. 2023;56(7):5881-5927. doi: 10.1007/s10462-022-10316-z. Epub 2022 Nov 13.
In 2014, Hu introduced the concept of three-way decision spaces and axiomatic definition of decision evaluation functions. In three-way decision spaces, decision evaluation function satisfies minimum element axiom, monotonicity axiom and complement axiom. Since then, the research on construction method of decision evaluation functions from commonly used binary aggregation functions becomes a research hotspot. Meanwhile, uninorms, as one class of binary aggregation functions, have been successfully applied in various application problems, such as in decision making, image processing, data mining, etc. This paper continues to consider this research topic and mainly explores the new construction methods of decision evaluation functions based on uninorms. Firstly, we show two novel transformation methods from semi-decision evaluation functions to decision evaluation functions based on uninorms. Secondly, using known semi-decision evaluation functions, we give some new construction methods of semi-decision evaluation functions. Thirdly, we give some novel construction methods of decision evaluation functions and semi-decision evaluation functions related to fuzzy sets, interval-valued fuzzy sets, fuzzy relations and hesitant fuzzy sets. Based on them, decision maker can obtain more useful decision evaluation functions, thereby more choices can be used for realistic decision-making problems. Finally, we consider two real evaluation problems to illustrate the results obtained in this paper. The three-way decisions results of evaluation problem show that the construction method proposed in this paper is superior to some existing construction methods under some conditions.
2014年，胡提出了三方决策空间的概念以及决策评估函数的公理定义。在三方决策空间中，决策评估函数满足最小元公理、单调性公理和补公理。从那时起，从常用二元聚合函数构建决策评估函数的方法研究成为一个研究热点。同时，幺模作为一类二元聚合函数，已成功应用于各种应用问题，如决策、图像处理、数据挖掘等。本文继续探讨这一研究课题，主要探索基于幺模的决策评估函数的新构建方法。首先，我们展示了两种从半决策评估函数到基于幺模的决策评估函数的新颖变换方法。其次，利用已知的半决策评估函数，我们给出了一些半决策评估函数的新构建方法。第三，我们给出了一些与模糊集、区间值模糊集、模糊关系和犹豫模糊集相关的决策评估函数和半决策评估函数的新颖构建方法。基于这些方法，决策者可以获得更有用的决策评估函数，从而为实际决策问题提供更多选择。最后，我们考虑两个实际评估问题来说明本文得到的结果。评估问题的三方决策结果表明，本文提出的构建方法在某些条件下优于一些现有构建方法。
