A New Kind of Generalized Pythagorean Fuzzy Soft Set and Its Application in Decision-Making

The aim of this paper is to introduce the concept of a generalized Pythagorean fuzzy soft set(GPFSS),which is a combination of the generalized fuzzy soft sets and Pythagorean fuzzy sets.Several of important operations of GPFSS including complement,restricted union,and extended intersection are discussed.The basic properties of GPFSS are presented.Further,an algorithm of GPFSSs is given to solve the fuzzy soft decision-making.Finally,a comparative analysis between the GPFSS approach and some existing approaches is provided to show their reliability over them.

考虑对称交互熵的对偶犹豫模糊企业环境行为决策模型分析

顺应绿色新发展理念,建设高质量生态文明,提升企业环境治理能力现代化水平,企业环境行为指标已逐渐被纳入投资者考量范围。本文针对第三方国际环境审计平台对企业环境行为评价的问题,研究面向对偶犹豫模糊评价信息的聚类方法。首先,定义对偶犹豫模糊相对熵与对称交互熵,并基于信息论角度提出一个新的对偶犹豫模糊相似度公式;然后,构造相似系数矩阵,并基于编网聚类方法对对偶犹豫模糊集进行聚类。最后,以不同指标权重下评价企业环境行为优劣程度为例进行计算,并与使用传统相关系数聚类方法所得结果进行对比,说明在考虑决策者提供的信息量较大的情况下,本文方法概念清晰、计算简单、分辨率高,是一种更加灵活、全面的多层次评价方法,为完善企业环境评价系统的构建提供了一种新思路。

计及群体压力和群体极化的PDHFSs-TODIM多属性群体决策算法

在概率对偶犹豫模糊环境下的多属性决策中,针对决策过程一般未考虑决策专家在讨论中所受的群体压力和群体极化的问题,提出了一种计及群体压力和群体极化的概率对偶犹豫模糊集-拓扑判别目标间方法(probabilistic discriminative heterogeneous fuzzy sets-topological discriminative inter-objective method,PDHFSsTODIM)的多属性群体决策算法。首先,定义了考虑群体压力的决策信息修正公式,有效削弱群体压力对专家决策信息的影响;然后,搭建了一种考虑群体极化现象的决策模型,该模型充分考虑了专家的主观性,为专家讨论和修正决策提供了机会,通过分配动态决策权重提高决策的置信度,并通过群体极化阈值约束群体的极化效应;进一步,将计算得到的决策数据输入改进的TODIM算法,得到最终决策结果。将算法运用于储能电池综合性能评估分析,通过与其他先进决策算法做对比,验证了所提算法的可靠性与准确性。

集对 Fuzzy 格及其在格表示论中的应用

用幂集格构造了集对 Ｆｕｚｚｙ 格（这与用整数对构造有理数集有相似之处），并用它证明了完整的软代数表示定理，即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Ｆｕｚｚｙ 格的子格同构．这样，与分配格在幂集 Ｂｏｏｌｅ 格中表示相对应，软代数在集对 Ｆｕｚｚｙ 格中有表示。

A Novel Multi-Attribute Decision-Making Method Based on Probabilistic Hesitant Fuzzy Soft Set and Its Application

The probabilistic hesitant fuzzy multi-attribute group decision-making method introduces probability and hesitation into decision-making problems at the same time,which can improve the reliability and accuracy of decision-making results,and has become a research hotspots in recent years.However,there are still many problems,such as overly complex calculations and difficulty in obtaining probability data.Based on these,the paper proposes a multi-attribute group decision-making model based on probability hesitant fuzzy soft sets.Firstly,the definition of probabilistic hesitant fuzzy soft set is given.Then,based on soft set theory and probabilistic hesitant fuzzy set,the similarity measure of probabilistic hesitant fuzzy soft set is proposed,and the two measures are further combined.Finally,it is applied to the construction of multi-attribute group decision-making model,and the effectiveness and rationality of the model are verified by an example.The example shows that the new similarity calculation formula and algorithm model in this paper have higher accuracy,and the calculation process is more simple,it provides a feasible method for multi-attribute group decision making problems.

基于改进的区间值对偶犹豫模糊集的绿色建筑方案决策

根据《绿色建筑评价标准》,绿色建筑需要从安全耐久、健康舒适、生活便利、环境宜居、资源节约、社会效益和创新与提高7个指标评价和指导北京市绿色建筑的设计工作。在“一带一路”背景下,该指标体系对古建筑更新和沿线新建筑兴建都具有重要指导意义。依据北京市绿色建筑评价标准所提出的指标,提出利用改进的区间值对偶犹豫模糊集对绿色建筑的设计方案进行评价与排序,从而帮助选择最优设计方案。最后根据实例计算,验证该决策方法在绿色建筑方案决策领域的可行性。

A New Hesitant Fuzzy Multiple Attribute Decision Making Method with Unknown Weight Information

In this paper, we focus on a new approach based on new generalized hesitant fuzzy hybrid weighted aggregation operators, in which the evaluation information provided by decision makers is expressed in hesitant fuzzy elements (HFEs) and the information about attribute weights and aggregation-associated vector is unknown. More explicitly, some new generalized hesitant fuzzy hybrid weighted aggregation operators are proposed, such as the new generalized hesitant fuzzy hybrid weighted averaging (NGHFHWA) operator and the new generalized hesitant fuzzy hybrid weighted geometric (NGHFHWG) operator. Some desirable properties and the relationships between them are discussed. Then, a new algorithm for hesitant fuzzy multi-attribute decision making (HF-MADM) problems with unknown weight information is introduced. Further, a practical example is used to illustrate the detailed implementation process of the proposed approach. A sensitivity analysis of the decision results is analyzed with different parameters. Finally, comparative studies are given to verify the advantages of our method.

概率对偶犹豫模糊集的距离测度及其在疾病诊断中的应用

概率对偶犹豫模糊集由于能够同时表达随机性与模糊性而被广为关注,而距离测度在模式识别、医疗诊断、多属性决策等诸多可以使用概率对偶犹豫模糊集进行建模的研究领域中起着至关重要的作用。但目前已有的概率对偶犹豫模糊集的距离依然存在一定的缺陷,因此,首先定义了概率对偶犹豫模糊元隶属度和非隶属度的上界、下界、均值、标准差与犹豫度,从不同侧面来反映其隶属度与非隶属度的取值信息;其次,基于以上所定义的5个指标提出了两个概率对偶犹豫模糊元之间的标准汉明距离、标准欧氏距离、标准广义距离及其加权形式,并且证明了所提出的新的概率对偶犹豫模糊距离及其加权形式均满足三角不等式;同时我们还研究了两个概率犹豫模糊集之间的标准汉明距离、标准欧氏距离、标准广义距离及其加权形式。最后,通过一个医疗诊断的例子说明提出的距离测度的有效性与实用性。

新型对偶犹豫模糊集距离测度及其多属性决策方法

对偶犹豫模糊集为处理复杂问题的不确定性提供了有效手段,其距离测度是一重要衡量指标。针对现有距离测度的局限性,本文定义了对偶犹豫模糊集的犹豫度,给出了基于犹豫度偏差以及隶属度与非隶属度完全偏差的对偶犹豫模糊集距离测度。新距离测度从3个信息维度来衡量距离偏差,更全面客观地体现出数据信息,弥补了传统距离测度可能无法识别的不足。最后结合TOPSIS决策思想给出决策步骤,并应用于航空公司服务质量评价,验证了新距离测度的有效性和合理性。

基于直觉支持度的对偶犹豫模糊粗糙集模型

支持直觉模糊集多属性决策虽考虑了备选方案的固有属性值评价,也关注如经济能力等决策方的自身支持程度,有效避免了多属性决策中模糊元被均值化的情形,然而面向解决更复杂的现实决策问题时仍显不足。论文将支持度扩展为直觉模糊形式表示,为此提出了直觉支持度对偶犹豫模糊集模型,给出其定义和得分函数。后将粗糙集引入到直觉支持度对偶犹豫模糊环境,构造直觉支持度的对偶犹豫模糊粗糙集模型,定义集合及其上下近似,后讨论该模型的一些性质,并对上下近似集合进行函数拟合,由得分结果排序进行决策。通过对舰船动力系统供应商选择的实例验证了该模型有效性。

基于灰色关联分析的概率对偶犹豫模糊多目标决策模型及算法

研究概率对偶犹豫模糊环境下权重未知的多目标决策问题。首先,定义标准概率对偶犹豫模糊Hamming距离;其次,根据距离测度及最大偏差法确定权重,通过灰色关联系数和加权关联度进行多目标择优,提出基于灰色关联分析的概率对偶犹豫模糊多目标决策模型及算法;最后,通过实例验证模型及算法的有效性。

Conceptual design and configurations selection of S/H-UAVs based on Q-rung dual hesitant double layer FQFD

For the conceptual design phase of Unmanned Aerial Vehicles(UAVs),a process for conceptual design and configuration selection of Solar/Hydrogen powered UAVs(S/H-UAVs)is proposed.The design requirements of S/H-UAVs were analyzed firstly.The proposed process used Fuzzy Quality Function Deployment(FQFD)to establish logical and quantitative standards.Moreover,in order to appropriately describe the hesitancy of experts while making decision,it used Q-Rung Dual Hesitant Fuzzy Sets(QRDHFS)to score the correlationships.In addition,a decision-making framework is proposed to perform a logical selection of typical layouts based on defuzzi-fication method and Technique for Order Preference by Similarity to the Ideal Solution(TOPSIS).The present process has been applied for S/H-UAVs.The resulting set of design requirements con-sists of three categories:Mission Requirements(MRs),Engineering Characteristics(ECs)and Tech-nical Indicators(TIs).Four typical layouts of S/H-UAVs were sorted and determined.The performance of four typical layouts were evaluated and the Strut-Braced Wing(SBW)with external hydrogen storage was selected as the best layout for S/H-UAVs.

Maclaurin Symmetric Mean Aggregation Operators and Their Application to Hesitant Q-Rung Orthopair Fuzzy Multiple Attribute Decision Making

The Maclaurin symmetric mean(MSM)operator exhibits a desirable characteristic by effectively capturing the correlations among multiple input parameters,and it serves as an extension of certain existing aggregation operators through adjustments to the parameter k.The hesitant q-rung orthopair set(Hq-ROFSs)can serve as an extension of the existing orthopair fuzzy sets,which provides decision makers more freedom in describing their true opinions.The objective of this paper is to present an MSM operator to aggregate hesitant q-rung orthopair numbers and solve the multiple attribute decision making(MADM)problems in which the attribute values take the form of hesitant q-rung orthopair fuzzy sets(H-qROFSs).Firstly,the definition of H-qROFSs and some operational laws of H-qROFSs are proposed.Then we develop a family of hesitant q-rung orthopair fuzzy maclaurin symmetric mean aggregation operators,such as the hesitant q-rung orthopair fuzzy maclaurin symmetric mean(Hq-ROFMSM)operator,the hesitant q-rung orthopair fuzzy weighted maclaurin symmetric mean(Hq-ROFWMSM)operator,the hesitant q-rung orthopair fuzzy dual maclaurin symmetric mean(Hq-ROFDMSM)operator,the hesitant q-rung orthopair fuzzy weighted dual maclaurin symmetric mean(Hq-ROFWDMSM)operator.And the properties and special cases of these proposed operators are studied.Furthermore,an approach based on the Hq-ROFWMSM operator is proposed for multiple attribute decision making problems under hesitant q-rung orthopair fuzzy environment.Finally,a numerical example and comparative analysis is given to illustrate the application of the proposed approach.

对偶犹豫模糊集的相关系数及其应用

对偶犹豫模糊集因其可以给决策者提供更多的决策信息成为模糊决策的热点研究问题,相关性指标可以用来度量两个模糊信息之间的相关关系,熵可以用来度量模糊信息的不确定程度。提出了一种基于对偶犹豫模糊集相关系数和熵的模糊多属性群决策方法。定义了对偶犹豫模糊集相关系数的概念,讨论了其基本性质;提出了两种对偶犹豫模糊集的熵,在此基础上,给出了模糊多属性群决策的权重确定方法;基于对偶犹豫模糊集相关系数和熵,提出了一种属性权重完全未知条件下的模糊多属性群决策方法;通过案例分析说明了该方法的有效性和可行性。

双犹豫模糊软集的研究

为对决策过程中犹豫模糊软集参数的非隶属度情况进行有效刻画,结合双犹豫模糊集的非隶属度与软集的参数化特性,提出双犹豫模糊软集的概念。基于双犹豫模糊软集的定义,描述双犹豫模糊软集的补、并、交、拓展交、限制并、且、或、差、平均及几何等运算方法,同时分析对应运算结果并论述相应性质。给出一个基于双犹豫模糊软集的相关性系数算法,解决了双犹豫模糊软集的非隶属度问题。

区间值对偶犹豫模糊集的相关系数及其应用

区间值对偶犹豫模糊集因其可能隶属度与可能非隶属度均采用区间的形式而更具有一般性,因而得到广泛的应用。相关系数可以用来度量两个模糊信息之间的相关关系。基于区间值对偶犹豫模糊集相关系数提出了一种新的多属性群决策方法。在对偶犹豫模糊集的基础上给出了区间值对偶犹豫模糊集的定义及其基本运算;给出了区间值对偶犹豫模糊集的相关系数的定义及相应的计算公式;构造了确定权重的优化模型;基于区间值对偶犹豫模糊集的相关系数和确定权重的优化模型,提出一种属性权重部分未知的模糊多属性群决策方法,并通过实例说明该方法的有效性和可行性。

基于双重犹豫模糊语言的多属性决策方法

结合语言术语集和双重犹豫模糊集给出了双重犹豫模糊语言集的定义,并给出双重犹豫模糊语言数的运算法则和比较方法。针对属性值为双重犹豫模糊语言数的多属性决策问题,提出集结双重犹豫模糊语言信息的双重犹豫模糊语言加权平均算子以及基于此算子的多属性决策方法,并将所提的决策方法应用于选址建厂问题以说明其可行性和有效性。

直觉对偶犹豫模糊集的集结算子及其应用

在对偶犹豫模糊集与直觉模糊集的基础上,提出了直觉对偶犹豫模糊集的概念和基本运算,构造了直觉对偶犹豫模糊集的算术加权平均集结算子和几何加权平均算子,并考虑有序和广义的情况,分别给出相对应的公式。同时针对某些算子的特殊性质,给出了详细描述和证明。针对模糊集的多属性群决策问题,提出了一种新的基于直觉对偶犹豫模糊集的集结算子的多属性群决策方法,通过一个实例说明了该方法的实用性和有效性。

基于犹豫模糊软集的专利质量评价模型

现有的专利质量评价方法以专家打分为主,需要专家对所评专利的全部指标给出一个评价值,并根据指标的相对重要程度分配权重值。但指标体系涉及不同领域的多个指标,专家对自己研究领域以外的指标难以做出准确评价,模糊性指标也使专家会在几个评价值之间犹豫。针对犹豫模糊软集可以更加准确的描述事物模糊本质,对可选对象没有限制,充分考虑专家决策的犹豫度得特性,本文提出一种基于犹豫模糊软集的专利质量评价模型,给出评价方法的具体步骤,并通过案例分析说明该方法的可行性与可靠性。

考虑优先级的广义犹豫模糊信息集成方法

研究了在属性之间存在优先级的情况下的广义犹豫模糊信息集成问题。考虑到属性优先级以及属性元素的统一程度的双重影响,首先给出了犹豫模糊信息下的熵值求法,并在其基础上提出了优先级混合赋权方法。之后,在该优先级混合赋权方法的基础上提出了广义犹豫模糊优先级混合几何(GHFPHG)算子,并给出了该类算子的优良特性。最后,利用案例验证了本文所提方法的实用性和有效性。