Two-Sided Matching Decision Making with Multi-Attribute Probabilistic Hesitant Fuzzy Sets

In previous research on two-sided matching(TSM)decision,agents’preferences were often given in the form of exact values of ordinal numbers and linguistic phrase term sets.Nowdays,the matching agent cannot perform the exact evaluation in the TSM situations due to the great fuzziness of human thought and the complexity of reality.Probability hesitant fuzzy sets,however,have grown in popularity due to their advantages in communicating complex information.Therefore,this paper develops a TSM decision-making approach with multi-attribute probability hesitant fuzzy sets and unknown attribute weight information.The agent attribute weight vector should be obtained by using the maximum deviation method and Hamming distance.The probabilistic hesitancy fuzzy information matrix of each agent is then arranged to determine the comprehensive evaluation of two matching agent sets.The agent satisfaction degree is calculated using the technique for order preference by similarity to ideal solution(TOPSIS).Additionally,the multi-object programming technique is used to establish a TSM method with the objective of maximizing the agent satisfaction of two-sided agents,and the matching schemes are then established by solving the built model.The study concludes by providing a real-world supply-demand scenario to illustrate the effectiveness of the proposed method.The proposed method is more flexible than prior research since it expresses evaluation information using probability hesitating fuzzy sets and can be used in scenarios when attribute weight information is unclear.

Pythagorean probabilistic hesitant triangular fuzzy aggregation operators with applications in multiple attribute decision making

As a generalization of fuzzy set,hesitant probabilistic fuzzy set and pythagorean triangular fuzzy set have their own unique advantages in describing decision information.As modern socioeconomic decision-making problems are becoming more and more complex,it also becomes more and more difficult to appropriately depict decision makers’cognitive information in decision-making process.In order to describe the decision information more comprehensively,we define a pythagorean probabilistic hesitant triangular fuzzy set(PPHTFS)by combining the pythagorean triangular fuzzy set and the probabilistic hesitant fuzzy set.Firstly,the basic operation and scoring function of the pythagorean probabilistic hesitant triangular fuzzy element(PPHTFE)are proposed,and the comparison rule of two PPHTFEs is given.Then,some pythagorean probabilistic hesitant triangular fuzzy aggregation operators are developed,and their properties are also studied.Finally,a multi-attribute decision-making(MADM)model is constructed based on the proposed operators under the pythagorean probabilistic hesitant triangular fuzzy information,and an illustration example is given to demonstrate the practicability and validity of the proposed decision-making method.

Novel Decision Making Methodology under Pythagorean Probabilistic Hesitant Fuzzy Einstein Aggregation Information

This research proposes multicriteria decision-making(MCDM)-based real-time Mesenchymal stem cells(MSC)transfusion framework.The testing phase of the methodology denotes the ability to stick to plastic surfaces,the upregulation and downregulation of certain surface protein markers,and lastly,the ability to differentiate into various cell types.First,two scenarios of an enhanced dataset based on a medical perspective were created in the development phase to produce varying levels of emergency.Second,for real-timemonitoring ofCOVID-19 patients with different emergency levels(i.e.,mild,moderate,severe,and critical),an automated triage algorithmbased on a formal medical guideline is proposed,taking into account the improvement and deterioration procedures fromone level to the next.For this strategy,Einstein aggregation information under the Pythagorean probabilistic hesitant fuzzy environment(PyPHFE)is developed.Einstein operations on PyPHFE such as Einstein sum,product,scalar multiplication,and their properties are investigated.Then,several Pythagorean probabilistic hesitant fuzzy Einstein aggregation operators,namely the Pythagorean probabilistic hesitant fuzzy weighted average(PyPHFWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein weighted geometric(PyPHFEWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted average(PyPHFEOWA)operator,Pythagorean probabilistic hesitant fuzzy Einstein ordered weighted geometric(PyPHFEOWG)operator,Pythagorean probabilistic hesitant fuzzy Einstein hybrid average(PyPHFEHA)operator and Pythagorean probabilistic hesitant fuzzy Einstein hybrid geometric(PyPHFEHG)operator are investigated.All the above-mentioned operators are helpful in design the algorithm to tackle uncertainty in decision making problems.In last,a numerical case study of decision making is presented to demonstrate the applicability and validity of the proposed technique.Besides,the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

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.

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.

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.

犹豫模糊非概率熵测度及其应用研究

不同的犹豫模糊元包含的隶属度个数往往不同,且犹豫模糊集的不确定性包括模糊不确定性与犹豫不确定性两个方面,这直接导致犹豫模糊熵计算的复杂性。针对此问题,将犹豫模糊元置于欧式空间进行分析,任意一个犹豫模糊元看作欧式空间中的点,而隶属度值则是相应点的坐标,欧式空间的多维性与犹豫模糊元的多值性刚好契合。基于此种思路,首先,基于空间分析,给出了犹豫模糊非概率熵的公理化定义。然后,基于空间距离提出犹豫模糊非概率熵测度公式,即为距离之比,犹豫模糊元分别与最近的(最远的)两个非模糊点之间的距离之比,该犹豫模糊非概率熵能够有效融合犹豫不确定性与模糊不确定性,同时解决了犹豫模糊元中隶属度个数不同带来的计算问题。最后,结合TOPSIS思想,提出了一种基于熵权法的犹豫模糊多属性群决策途径,并用实例分析验证其科学性和有效性。

加权概率犹豫模糊集多属性群决策算法及应用

对于概率犹豫模糊集中的不同隶属度值赋予了决策专家的综合权重,由此构造出一种蕴含信息量更大、更方便解决决策问题的概率犹豫模糊集合——加权概率犹豫模糊集.针对加权概率犹豫模糊集中的加权概率犹豫模糊元,在使用三维点坐标进行描述的基础上建立加权概率犹豫模糊元的三维得分值模型、三维离差值模型、2个加权概率犹豫模糊元的几何距离模型以及大小判别准则.结合决策专家的综合权重与属性的综合权重提出一种确定正理想方案与负理想方案的方法,基于TOPSIS思想给出一种新的贴近度公式,并利用新的贴近度公式来鉴别各方案优劣.最后,通过一个数值算例说明文中理论与方法的可行性.

概率区间值犹豫模糊集多属性群决策模型及其应用

目的:研究概率区间值犹豫模糊集及应用。方法:将概率区间值犹豫模糊数,用区间值隶属度的中位数、区间值隶属度的清晰度以及概率构成的三维点坐标进行刻画,在此基础上提出了概率区间值犹豫模糊元的相关运算。根据概率区间值犹豫模糊元的相关运算采用熵值法计算属性权重。最后基于TOPSIS思想给出了一个新的贴近度公式,并利用新的贴近度公式对方案排序。结果:建立的概率区间值犹豫模糊集多属性群决策模型可以有效排序方案。结论:将概率区间值犹豫模糊集采用区间值隶属度的中位数、区间值隶属度的清晰度以及概率来表示不仅可行,而且可以用来解决多属性群决策问题。

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。

基于决策场理论的多阶段动态应急决策方法

针对应急决策过程中决策主体的微观偏好波动,多阶段权重变化问题,并考虑决策主体认知偏差对方案的选择影响,提出一种基于决策场理论的多阶段动态决策模型。首先在微观视角下结合概率犹豫模糊集,构建以思考时间为自变量的动态偏好计算方法;然后依据应急决策的多阶段过程,提出以属性权重均值的转移来代替单一权重;其次为分析有限理性下决策主体认知偏差对方案选择的影响,通过设定不同顺序效应值来获取选择过程的差异;最后以实验室应急事件来验证方法的合理性。结果表明:在应急决策中随着决策主体思考时间的增加,方案偏好存在波动与反转,特别是在不同顺序效应影响下,决策过程存在明显的差别,并且在不同阶段其决策最低时间阈值也不一样。

基于改进TOPSIS方法的武装直升机空地火力打击能力量化评估研究

武装直升机空地火力打击能力量化评估研究是联合作战背景下武器装备运用的重要决策依据。基于武装直升机在低空作战中的特殊优势,建立了武装直升机空地火力打击能力量化评估指标体系。针对实际战场和装备使用的复杂性,考虑到各指标属性信息的不确定性,引入概率犹豫模糊集的概念来刻画评估过程中专家偏好信息的模糊性和不确定性,结合后悔理论在刻画决策者心理状态和TOPSIS决策方法在多属性决策中的优势,实现了信息不确定条件下武装直升机空地火力打击能力的量化评估。

基于概率犹豫模糊集的麻醉设备安全运行风险评估模型构建与应用价值研究

目的:基于概率犹豫模糊集(HPFS)构建麻醉设备安全运行风险评估模型,探讨其在麻醉设备安全运行风险控制管理中的应用价值。方法:以全生命周期安全和管理安全为重要风险评估维度,构建麻醉设备安全运行风险指标体系,采用HPFS和层次-优劣解距离法进行风险量化分析,制定安全自查和风险控制处理策略。选取2020年7月至2023年6月北京市通州区妇幼保健院收治的150例外科手术患者,按照麻醉设备管理模式不同,将其分为对照组和观察组,每组75例。在手术治疗中共使用16台麻醉设备,对照组患者手术治疗期间使用的10台麻醉机采用常规风险控制模式,观察组使用的12台麻醉机(含对照组中使用的6台和新增6台)采用风险评估控制模式。对比两组患者围术期内麻醉设备相关风险事件发生率、麻醉医护人员对潜在安全风险知晓率和麻醉设备故障率。结果:观察组患者围术期发生麻醉设备操作不当、麻醉用量不合理、相关感染和记录缺失风险事件例数分别为4例(占5.3%)、0例(占0%)、1例(占1.3%)和1例(占1.3%),发生率低于对照组,差异有统计学意义(x^(2)=4.478、4.110、6.857、4.754;P<0.05);观察组麻醉设备操作的医护人员安全管理理论知识、安全使用、管理意识和故障判定能力平均评分分别为(96.27±3.93)分、(94.31±2.69)分、(91.82±1.94)分和(84.97±4.36)分,均高于对照组,差异有统计学意义(t=5.176、5.322、5.541、5.942;P<0.05);两组设备操作设置、麻醉气路、麻深监测、阈值报警及其他故障的总次数分别为90、37、25、316和125次,观察组的故障发生率分别为30%(27/90)、35%(13/37)、28%(7/25)、22%(69/316)和39%(49/125),低于对照组,差异有统计学差异(x^(2)=28.800、6.541、9.680、200.532、11.664;P<0.05)。结论:基于HPFS的风险评估模式,能够降低麻醉设备相关风险事件发生率,提升麻醉医护人员安全风险控制意识,改善麻醉设备临床运行质量。

加权概率区间值犹豫模糊集及决策应用

对概率区间值犹豫模糊集中的不同区间值隶属度赋予了决策专家权重,定义了加权概率区间值犹豫模糊集(WPIVHFS).针对WPIVHFS中的加权概率区间值犹豫模糊数,采用区间值隶属度的中位数、区间值隶属度的清晰度、概率以及相对应的决策专家权重构成四维点坐标进行刻画,在此基础上建立了加权概率区间值犹豫模糊元(WPIVHFE)的外部固定函数模型、内部稳定函数模型、2个WPIVHFE的大小比较准则与距离测度模型.利用熵值法分别计算属性的外部权重与内部权重,并依据属性的外部权重与内部权重相离程度值来确定属性的综合权重.考虑方案的外部固定函数值、内部稳定函数值来计算各个方案的综合属性值.方案的排序结果表明:在采用四维点坐标来描述WPIVHFS的基础上建立的决策算法不但科学有效,而且提供了一种多角度观察方案排序结果的方法.

基于融合专家综合权重的WPHFS多属性群决策模型

目的:研究加权概率犹豫模糊集及应用。方法:根据每个属性上的绝对权威专家评分数据,利用离差最大化来计算其余专家的综合权重。将评审专家的综合权重注入概率犹豫模糊集,进而定义了加权概率犹豫模糊集,在三维向量描述加权概率犹豫模糊数的基础上提出了加权概率犹豫模糊元的相关运算。基于提出的运算来计算属性的综合权重。最后建立了用参数调整方案的属性整体得分值与内部评价信息差异值的比例来计算方案综合决策值的模型。结果:建立的加权概率犹豫模糊集多属性群决策模型可以有效对备选方案进行排序。结论:相较于概率犹豫模糊集,加权概率犹豫模糊集储存更多的决策信息,能更好的解决群决策问题。

概率犹豫模糊集的再定义及其在群决策中的应用

为了更好地解决概率犹豫模糊集多属性群决策问题,构建了一种在不同维度下比较各方案综合属性值大小的决策模型.首先,以二维坐标形式给出概率犹豫模糊集(PHFS)中的隶属度和概率,并在此基础上建立概率犹豫模糊元(PHFE)的二维几何距离模型和二维离差程度系数模型;其次,对PHFS中的隶属度赋予相应的评审专家权重,并用三维坐标刻画隶属度、概率和评审专家权重,以此建立PHFE的三维几何距离模型和三维离差程度系数模型;再次,在二维与三维条件下分别计算2种维度下PHFE的综合值,并利用Maclaurin对称平均算子对以上2种维度下各个PHFE的综合值进行集结并排序;最后,利用实例对在2种维度下建立的算法进行了验证分析.结果显示所建立的算法均可对各方案进行有效地排序,但由于在三维视角下建立的决策模型能够反映评审专家的偏好问题,因此该模型的决策效果相对更好.

二维变量信息视角下的概率犹豫模糊集决策方法研究

将概率犹豫模糊集中的隶属度与概率看作二维变量信息,在二维变量信息条件下研究概率犹豫模糊集多属性决策问题。首先,将概率犹豫模糊数书写形式改为点坐标形式,并在此形式下建立概率犹豫模糊元几何距离函数模型与离差程度系数模型;其次,属性的评价值为概率犹豫模糊元,在考虑其内部元素的离差程度与相互之间离差程度基础上,采用熵值法确定属性权重;再次,使用新定义的几何距离函数与离差程度系数函数计算由概率犹豫模糊元组成的属性值,得到属性的综合值,并利用Maclaurin对称平均算子对各方案属性的综合值进行集结,通过比较集结的方案属性综合值大小对各方案进行排序;最后用一个数值算例对本文方法进行验证分析,结果表明,该方法能够快速取得有效的排序结果。

加权的概率犹豫模糊集的三维向量测度法与决策应用

为了更加精细化地描述概率犹豫模糊集,将概率犹豫模糊元中的隶属度添加相应的决策专家权重,并由此提出了加权的概率犹豫模糊集概念.用三维向量表示加权的概率犹豫模糊数,在此基础上建立了加权的概率犹豫模糊元的三维向量得分函数模型、三维向量离差函数模型、2个加权的概率犹豫模糊元的大小比较规则与距离测度模型.分别给出了属性的外部权重、内部权重以及综合权重的计算方法.在属性的3种权重条件下,运用方案的整体得分值与内部决策专家评价差异值2个因素计算方案的综合属性值,进而对各个方案排序.决策结果表明,在利用三维向量刻画加权的概率犹豫模糊集的基础上建立的决策算法不但有效可行,而且提供了一种多元化的决策方法.

基于概率犹豫信息集成方法的群决策模型

现有犹豫模糊集在描述决策信息时会导致决策信息大量损失,因此文中基于概率犹豫模糊信息集成算子,构建多属性群决策模型.首先在概率犹豫模糊环境下引入Archimedean范数,定义概率犹豫模糊运算法则.基于该运算法则,提出广义概率犹豫模糊有序加权平均(GPHFOWA)算子和广义概率犹豫模糊有序加权几何(GPHFOWG)算子,并讨论它们的基本性质.然后分析GPHFOWA算子和GPHFOWG算子的常见形式和相互关系.最后运用提出的2类算子构建概率犹豫模糊多属性群决策模型,并且通过供应商的选择实例验证决策模型的可行性和有效性.

WPHFS多属性群决策模型与应用

对于概率犹豫模糊元中的不同隶属度值赋予了决策专家的综合权重,由此构造出一种蕴含信息量更大、更符合决策问题需要的概率犹豫模糊集合——加权的概率犹豫模糊集(WPHFS)。针对加权的概率犹豫模糊数(WPHFN),本文采用三维向量进行描述,并在此基础上建立了加权的概率犹豫模糊元(WPHFE)的三维向量得分函数模型、三维向量离差函数模型以及2个WPHFE的大小判别准则。首先,利用WPHFE的三维向量得分函数值与三维向量离差函数值分别计算属性的外部权重与内部权重,进而计算出属性的综合权重;其次,依据离差最大化思想给出了一种计算决策专家综合权重的方法;再次,结合决策专家的综合权重与属性的综合权重,利用0-1优先关系矩阵来直观地获取任意2个备选方案的总属性权重优势值与总属性权重劣势值,并根据二者的大小排序方案;最后,通过一个应用实例来说明文中理论与方法的实用价值。