犹豫模糊元的质心与犹豫模糊PROMETHEE群决策方法  

The Centroid of Hesitant Fuzzy Element and the Approach PROMETHEE of Group Decision Making Based on Hesitant Fuzzy Set

作　　者：王兆浩[1] 张凤 WANG Zhao-hao;ZHANG Feng(School of Mathematics and Computer Science,Shanri Normal University,Taiyuan 030000,China)

机构地区：[1]山西师范大学数学与计算机科学学院,山西太原030000

出　　处：《模糊系统与数学》2024年第3期120-130,共11页Fuzzy Systems and Mathematics

基　　金：山西省自然科学基金面上项目(202103021224261)。

摘　　要：许多实际的数据集都可转化为决策表,对决策表的一个重要的研究主题就是探讨相应的决策方法.当决策表的数据是犹豫模糊元时,称该决策表为犹豫模糊决策表。本文主要探讨犹豫模糊决策表的群决策问题。首先,本文提出了一种新的聚合犹豫模糊元的思路,即从犹豫模糊元的数据特点出发聚合犹豫模糊元,给出犹豫模糊元的质心的概念,并研究了相关性质;其次,本文借用质心概念,建立了犹豫模糊元效用值的概念。最后,借助于质心、效用值,本文将群决策方法PROMETHEE引入到犹豫模糊决策表的研究,提出了犹豫模糊PROMETHEE群决策方法,并举例说明该方法的有效性与实用性。Many data sets from practical problems can be transformed into decision tables.Exploring the decisionmaking methods of decision tables is one of the fundamental topics.If the data set of a decision table consists of hesitant fuzzy elements,the decision table is referred to as a hesitant fuzzy decision table.This paper focuses on investigating the group decision-making problems for the hesitant fuzzy decision table.First,a new design idea for integrating a hesitant fuzzy element is given,that is,integrating the hesitant fuzzy element by considering its characteristics.As a result,this paper defines the concept of centroid of hesitant fuzzy elements,and investigates its properties.Second,by using centroid,the definition of utility score of a hesitant fuzzy element is proposed.Finally,by means of centroid and utility score,this paper introduces the method PROMETHEE of group decision making into the research on the hesitant fuzzy decision table,and establishes the approach PROMETHEE of group decision making based on hesitant fuzzy sets,Furthermore,an example illustrates the practicability and the effectiveness of the proposed method.

关 键 词：决策表 犹豫模糊集 质心 效用值 群决策 

分 类 号：O159[理学—数学] O225[理学—基础数学]