区间值q阶犹豫模糊Frank集成算子及其决策应用

doi:10.6040/j.issn.1671-9352.4.2020.238

摘要/Abstract

摘要： 将q阶犹豫模糊集进行了拓展,提出了区间值q阶犹豫模糊集;并将Frank算子与区间值q阶犹豫模糊集相结合,提出了区间值q阶犹豫模糊Frank集成算子。首先,基于Frank算子定义了区间值q阶犹豫模糊元的运算性质,提出了区间值q阶犹豫模糊元的得分函数、精确函数及其排序方法;其次,定义了区间值q阶犹豫模糊Frank算术平均算子、几何平均算子、有序加权平均算子以及混合平均算子,分别给出了算子的计算公式,研究了其相关性质并讨论了算子的特殊形式;最后,给出一种基于区间值q阶犹豫模糊Frank集成算子的多属性决策方法,通过算例和比较分析说明了方法的可行性与有效性。该方法可以根据决策者的风险偏好态度灵活地选择参数以满足不同决策情况的要求。

关键词: 区间值q阶犹豫模糊集, Frank算子, 算术平均算子, 几何平均算子, 混合平均算子, 多属性决策

Abstract: In this article, the q-rung hesitant fuzzy set is extended, and interval-valued q-rung hesitant fuzzy set is proposed. Combining Frank operator with interval-valued q-rung hesitant fuzzy set, the interval-valued q-rung hesitant fuzzy Frank aggregation operators are proposed. Firstly, based on the Frank operator, the operation properties of interval-valued q-rung hesitant fuzzy elements are defined, and the score function, accuracy function and ranking method of interval-valued q-rung hesitant fuzzy elements are proposed. Secondly, the interval-valued q-rung hesitant fuzzy Frank arithmetic average operator, geometric average operator, ordered weighted average operator and hybrid average operator are defined. The calculation formulas of the operators are given respectively, the related properties are studied, and the special forms of the operators are discussed. Finally, a multi-attribute decision-making method based on interval-valued q-rung hesitant fuzzy Frank aggregation operator is given, and the feasibility and effectiveness of the method are demonstrated through calculation examples and comparative analysis. This method can flexibly choose parameters according to the risk preference attitude of the decision maker to meet the requirements of different decision-making situations.

Key words: interval-valued q-rung hesitant fuzzy set, Frank operator, arithmetic average operator, geometric average operator, hybrid average operator, multiple-attribute decision making

中图分类号:

O159

黄林,袁修久,索中英,庞梦洋,包壮壮,李智伟. 区间值q阶犹豫模糊Frank集成算子及其决策应用[J]. 《山东大学学报(理学版)》, 2021, 56(3): 54-66.

HUANG Lin, YUAN Xiu-jiu, SUO Zhong-ying, PANG Meng-yang, BAO Zhuang-zhuang, LI Zhi-wei. Interval-valued q-rung hesitant fuzzy frank aggregation operators and their application in multi-attribute decision making[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(3): 54-66.

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