Pythagorean犹豫模糊熵及其多属性群决策方法  

An Approach to Multiple Attribute Group Decision Making Based on the Pythagorean Hesitant Fuzzy Entropy

作　　者：张俊芳 吴澎[1] 周礼刚[1] 肖箭[1] 薛明香[1] ZHANG Jun-fang;WU Peng;ZHOU Li-gang;XIAO Jian;XUE Ming-xiang(School of Mathematical Science,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《重庆工商大学学报（自然科学版）》2020年第6期62-70,共9页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：国家自然科学基金(71771001,71701001,71501002,71871001,71901001,71901088);安徽省自然科学基金杰出青年基金(1908085J03);安徽省学术和技术带头人及后备人选资助项目(2018H179);安徽省自然科学基金(1808085QG211);高校优秀青年人才支持计划项目(GXYQ2019236);安徽省教育厅人文社科重大项目(SK2019ZD55);安徽省高校人文社科基金重点项目(SK2019A0013,SK2018A0605);全国统计科学研究项目(2017LZ11).

摘　　要：针对模糊信息下的群决策问题,提出了一种基于Pythagorean犹豫模糊熵的多属性群决策方法;给出了Pythagorean犹豫模糊熵的公理化定义及计算公式;为克服传统Pythagorean犹豫模糊集规范化方法导致原始决策信息流失的不足,完善了基于Pythagorean犹豫模糊环境下的最小公倍数扩充方法,方法能有效地保持原始决策信息;又以Pythagorean犹豫模糊熵作为决策信息差异程度的度量,给出属性权重完全未知或部分已知情况下权重的确定方法,并定义了基于最小公倍数的Pythagorean犹豫模糊距离测度和Pythagorean犹豫模糊熵测度;构造了一种基于Pythagorean犹豫模糊熵的TOPSIS方法,并通过精准扶贫补贴项目案例说明了方法的可行性和有效性.For the decision-making problems with vague information,this paper presents a multiple attribute group decision making approach based on Pythagorean hesitant fuzzy entropy.Firstly,the axiomatic definition and calculation formula of Pythagorean hesitant fuzzy entropy are proposed.Classical normalization method may cause the loss of original information,in order to overcome the shortcoming,a least common multiple extended method is completed to normalize the Pythagorean hesitant fuzzy sets.This expansion method can effectively keep the original information.Then,taking Pythagorean hesitant fuzzy entropy as the difference degree of decision information,a multi-attribute group decision making method is given to determine the weight when the attribute weight is completely unknown or partially known.Meanwhile,the distance and entropy measures of Pythagorean hesitant fuzzy numbers are put forward.Finally,an approach of TOPSIS based on Pythagorean hesitant fuzzy entropy is developed.At the same time,a numerical example of precision poverty alleviation project is provided to illustrate the feasibility and effectiveness of the proposed method.

关 键 词：多属性群决策 Pythagorean犹豫模糊熵 属性权重 最小公倍数扩充方法 TOPSIS 

分 类 号：O221.6[理学—运筹学与控制论]