σ优劣关系熵及其在多属性决策的应用
σ superior-inferior relation entropy and its application in multi-attribute decision making
吴家明 1黄哲煌 1李进金 2刘丹玥1
作者信息
- 1. 华侨大学数学科学学院,福建泉州 362021
- 2. 华侨大学数学科学学院,福建泉州 362021;闽南师范大学数学与统计学院,福建漳州 363000
- 折叠
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.
Abstract
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 with σ superior-inferior relation.On this basis,a new σ superior-inferior relation entropy are proposed,and some of its derived entropy,such as σ superior-inferior relation conditional entropy,σ superior-inferior relation joint entropy and σ superior-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 with σ superior-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Key words
dominance relation/rough sets/fuzzy sets/information entropy/multi-attribute decision making引用本文复制引用
基金项目
国家自然科学基金项目(12271191)
国家自然科学基金项目(11871259)
福建省自然科学基金项目(2017J01114)
福建省自然科学基金项目(2022J01306)
华侨大学高层次人才项目(16BS814)
出版年
2024
NETL
NSTL
万方数据