σ优劣关系熵及其在多属性决策的应用  

σsuperior-inferior relation entropy and its application in multi-attribute decision making

作　　者：吴家明 黄哲煌[1] 李进金 刘丹玥 WU Jia-ming;HUANG Zhe-huang;LI Jin-jin;LIU Dan-yue(College of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China;College of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,China)

机构地区：[1]华侨大学数学科学学院,福建泉州362021 [2]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《控制与决策》2024年第2期613-624,共12页Control and Decision

基　　金：国家自然科学基金项目(12271191,11871259);福建省自然科学基金项目(2017J01114,2022J01306);华侨大学高层次人才项目(16BS814)。

摘　　要：目前大多数的模糊关系熵是由一般的模糊二元关系构造,无法有效地对具有优劣顺序的模糊关系族进行评估,这限制了它们在多属性决策的应用.为此,提出一种新的优劣关系熵.首先,研究一种参数化的模糊优劣关系用于表征样本间的差异,进而探讨几种σ优劣关系的模糊类;然后,在此基础上提出一种新的σ优劣关系熵,并介绍其一些衍生熵,如σ优劣关系条件熵、σ优劣关系联合熵和σ优劣关系互信息,探讨它们间的关系以及一些重要性质;最后,给出2种基于σ优劣关系熵的多属性决策方法,并通过数据实例验证所提出方法的有效性和可行性.比较和敏感性分析表明,所提出方法与一些经典多属性决策方法的排序结果具有高度一致性.特别地,在多专家评判环境下,所提出方法具有更广泛的适用性.At present,most fuzzy relation entropies are constructed by means of general fuzzy binary relations,which cannot effectively evaluate the fuzzy relation families with order attributes.This limits their application in multi-attribute decision-making.For this reason,a new superior-inferior relationship entropy is presented in this paper.First,a parameterized fuzzy superior-inferior relation is studied to characterize the differences between samples,and some fuzzy classes are then proposed withσsuperior-inferior relation.On this basis,a newσsuperior-inferior relation entropy are proposed,and some of its derived entropy,such asσsuperior-inferior relation conditional entropy,σsuperior-inferior relation joint entropy andσsuperior-inferior relation mutual information,are then introduced.We discuss the relationship between them and some important properties are explored.Finally,two multi-attribute decision-making methods withσsuperior-inferior relation entropy are developed,and the effectiveness and feasibility of the presented method are verified by data examples.Comparison and sensitivity analysis show that the ranking results of the proposed model and some classical methods are highly consistent.In particular,the proposed method has wider applicability in the multiple expert evaluation environment.

关 键 词：优势关系 粗糙集 模糊集 信息熵 多属性决策 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]