加权犹豫模糊集的群决策方法

对于犹豫模糊元中的不同隶属度值赋予不同的权重,由此构造出一种应用范围更广、更符合实际需要的犹豫模糊集合 ----- 加权犹豫模糊集合.针对加权犹豫模糊集中的加权犹豫模糊元,定义了加权犹豫模糊集合和加权犹豫模糊元的并、交、余、数乘和幂等运算及其运算法则,并讨论它们的运算性质;同时,给出加权犹豫模糊元的得分函数和离散函数,进而给出一种比较加权犹豫模糊元的排序法则.在此基础上,提出两类集成算子:加权犹豫模糊元的加权算术平均算子和加权犹豫模糊元的加权几何平均算子,并针对专家权重(已知和未知)的两种情形,将加权犹豫模糊集合应用于群决策,给出两种基于加权犹豫模糊集合的群决策方法.最后,通过一个应用实例表明所提出的群决策方法的有效性和实用性.

Group decision making approach of weighted hesitant fuzzy sets

In this paper, we introduce the concept of weighted hesitant fuzzy set, in which different weights are designed to these possible membership values, and the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. Then we define some basic operations such as union, intersection, complement, multiplication and power operation of weighted hesitant fuzzy elements and weighted hesitant fuzzy sets, discuss their operation properties, and propose the score function and variance function of the weighted hesitant fuzzy element to compare two weighted hesitant fuzzy elements. Furthermore, we present two aggregation operators such as the weighted hesitant fuzzy element weighted averaging(WHFWA) operator and the weighted hesitant fuzzy element weighted geometric(WHFWG) operator to aggregate weighted hesitant fuzzy information, and build the mathematical model of group decision making based on the expert weights(known and unknown). Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed method.