An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.

Novelty of Different Distance Approach for Multi-Criteria Decision-Making Challenges Using q-Rung Vague Sets

In this article,multiple attribute decision-making problems are solved using the vague normal set(VNS).It is possible to generalize the vague set(VS)and q-rung fuzzy set(FS)into the q-rung vague set(VS).A log q-rung normal vague weighted averaging(log q-rung NVWA),a log q-rung normal vague weighted geometric(log q-rung NVWG),a log generalized q-rung normal vague weighted averaging(log Gq-rung NVWA),and a log generalized q-rungnormal vagueweightedgeometric(logGq-rungNVWG)operator are discussed in this article.Adescription is provided of the scoring function,accuracy function and operational laws of the log q-rung VS.The algorithms underlying these functions are also described.A numerical example is provided to extend the Euclidean distance and the Humming distance.Additionally,idempotency,boundedness,commutativity,and monotonicity of the log q-rung VS are examined as they facilitate recognizing the optimal alternative more quickly and help clarify conceptualization.We chose five anemia patients with four types of symptoms including seizures,emotional shock or hysteria,brain cause,and high fever,who had either retrograde amnesia,anterograde amnesia,transient global amnesia,post-traumatic amnesia,or infantile amnesia.Natural numbers q are used to express the results of the models.To demonstrate the effectiveness and accuracy of the models we are investigating,we compare several existing models with those that have been developed.

基于Vague集和响应面模型的注塑工艺多目标优化

针对注塑工艺多目标优化问题,以塑件的翘曲变形量、顶出时体积收缩率和缩痕深度作为优化目标,选取熔体温度、模具温度、注射时间、保压压力、保压时间等工艺参数为试验因素,采用中心复合试验设计结合模流分析建立试验样本,利用Vague集方法计算各优化目标相似度,通过指标相关性的指标权重确定(CRITIC)法确定各优化目标影响权重,得到综合相似度;建立综合相似度与各工艺参数之间的响应面模型,运用灰狼算法进行工艺参数寻优,得到最优工艺参数组合。结果表明,将Vague集和响应面模型相结合的优化结果显著,为实际生产过程提供了有益参考。

基于Vague集犹豫量化的机舱团队协作式评估方法

针对现有机舱团队协作评估方法不统一且主观随意性太强的缺陷,提出一种基于Vague集犹豫量化的新型评估方法。从机舱团队协作的角度对影响评估的各因素进行提取,采用集合相似系数对重要协作指标量化,并采用C-OWA算子赋权法和变异系数法确定主客观权重,利用最小鉴别信息原理求得组合权重,结合Vague集的犹豫量化特点,通过机舱团队实际操作数据与Vague集评估标准得到各指标的定性评估Vague集,并利用集合相似度分析实现机舱团队协作的综合评估。实例计算结果表明:相对于传统的评估方法,在个体完成度的基础上加入具有犹豫团队协作因素的方法,能对评估结果的犹豫度进行较好地刻画,也能很好地实现定量与定性之间的转化,是一种有效且优越的机舱团队协作式评估方法。

双论域区间值直觉模糊vague粗糙集及其应用

区间值直觉模糊集可诱导出vague集和粗糙集,而后两者的结合具有不确定性深入分析的优势.立足双论域区间值直觉模糊粗糙集,引入vague集进行融合扩张,研究双论域区间值直觉模糊vague粗糙集.首先,定义区间值直觉模糊vague相容类,构建双论域区间值直觉模糊vague粗糙集模型,提出关于双逼近近似和三支决策区域的计算算法,并确立该模型的精确度、粗糙度、依赖度.然后,研究该模型的近似算子与不确定性度量的性质.最后,采用医疗例子进行模型计算、度量测量、性质验证,并得到关于患者临床诊断的患病分析与治疗决策.

舰载雷达干扰效能评估的Vague软专家集方法研究

为了更好地评估舰载雷达干扰效能,本文以雷达导引头为被干扰对象进行研究,提出了基于Vague软专家集的舰载雷达干扰效能评估方法。首先,对雷达导引头进行分析得到评估集、指标集和专家集;然后,由专家打分确定Vague软专家集;最后,计算各评估等级得分,得到评估结果。结合具体计算实例,验证了新方法的有效性和实用性。

一种改进的Vague集相似度量公式及其在生态调度评价中应用

长江防汛期间洪水影响其下游鱼类产卵、生存等鱼类生态平衡,需要合理科学制定长江电站临时日流量生态调度方案以满足特殊时期长江下游鱼类生态需求。采用模糊集相似度作为权衡电站调制效益的准则,以长江下游水电站—向家坝水电站为例,剖析其2013—2023年4-9月份的每日水流量数据,再根据线性插值方法构建流量阈值的Vague集隶属度函数,并创建一种相似度度量公式来评价各月份水文数据。应用所建相似度对4种水文数据方案进行评估,结果得到与每个月份相似度最高的方案。探究结果可以为电站临时生态调度方案的选择和评价提供参考。

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

Experts use Pythagorean fuzzy hypersoft sets(PFHSS)in their investigations to resolve the indeterminate and imprecise information in the decision-making process.Aggregation operators(AOs)perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception.In this paper,we extend the concept of PFHSS to interval-valued PFHSS(IVPFHSS),which is the generalized form of intervalvalued intuitionistic fuzzy soft set.The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set.It is the most potent method for amplifying fuzzy data in the decision-making(DM)practice.Some operational laws for IVPFHSS have been proposed.Based on offered operational laws,two inventive AOs have been established:interval-valued Pythagorean fuzzy hypersoft weighted average(IVPFHSWA)and interval-valued Pythagorean fuzzy hypersoft weighted geometric(IVPFHSWG)operators with their essential properties.Multi-criteria group decision-making(MCGDM)shows an active part in contracts with the difficulties in industrial enterprise for material selection.But,the prevalent MCGDM approaches consistently carry irreconcilable consequences.Based on the anticipated AOs,a robust MCGDMtechnique is deliberate formaterial selection in industrial enterprises to accommodate this shortcoming.A real-world application of the projectedMCGDMmethod for material selection(MS)of cryogenic storing vessels is presented.The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.

一种基于包含关系的Vague集新相似度量方法

针对已有相似度量方法考虑因素不全面的情况,本文从二次投票出发同时考虑了二次投票中支持度、反对度和未知度的包含关系,合理设置系数,提出一种新的基于包含关系的Vague集相似度量方法,理论证明新相似度量方法满足相似度量的基本准则。分别选取小样本和大样本与已有相似度量方法进行比较,提出了一种新的相似度区分能力的定义。实验结果表明:对于小样本数据,本文提出的相似度量方法区分能力最大为0.14;对于大样本数据,本文提出的相似度量方法区分能力最大为119.8。将新相似度量方法分别应用于故障诊断、模式识别和多准则决策中,结果表明新的相似度量方法能够有效和合理地区分数据。

On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions

The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.

融合云概念的粗糙Vague集的三支决策模型

Vague集是模糊集的扩展模型,从正反两方面来描述事物的不确定性,粗糙Vague集比粗糙模糊集更具有普遍性。目前,三支决策的阈值主要是由单个专家给出,不能反映认知过程中复杂的不确定性形式。针对这一问题,提出了一种融合云概念的粗糙Vague集的三支决策模型。使用基于密度中心的云概念群决策方法求解损失函数,不仅保证综合评价的精度,还为损失函数提供了新的语义解释。构建了粗糙Vague集的三支决策模型并揭示了其误分类代价随着粒度细化而单调递减的规律。通过实验验证了该方法的可行性,克服了现有模糊集在三支决策中对事物不确定性表达不够清楚的缺点。

基于Vague集-可拓模型的断层富水区桥梁运营安全评估

为了探究断层富水区复杂地质环境对桥梁运营安全状况的影响并科学合理做出评估,从富水性特征、地质构造、桥梁结构参数、运营监测和安全管理5方面出发构建断层富水区桥梁多层次评估指标体系,将含有语言变量的Vague集设计主观权重与简洁高效的EW法设计客观权重相结合,并通过距离函数优化分配系数优化组合赋权,基于物元可拓理论建立断层富水区桥梁运营安全状态综合评估模型并应用于甘肃省某座桥梁实例中,引入安全性级别变量特征值确定评估桥梁的安全等级。研究结果表明:待评桥梁安全等级为Ⅱ级,运营状态比较安全,评估结果与现场情况基本相符,验证其评估模型的客观性与适用性。研究结果可为此类区域桥梁的加固养护提供决策依据。

Fuzzy description logic based on vague sets

To enable the representation and reasoning for fuzzy ontologies with expressive fuzzy knowledge on the semantic web, a new fuzzy extension of description logics called vague ALC which is based on vague sets is presented. The definition of vague set is introduced and then the syntax and semantics of vague ALC are formally defined. The forms of axioms and assertions in the vague ALC knowledge bases are specified. Finally, the tableau algorithm is developed for the reasoning in the vague ALC. The vague ALC based on vague set uses two degrees of membership instead of a single membership degree in the fuzzy sets and is more accurate in representing the imprecision in the degrees of membership. The vague ALC has more expressive power than ALC and can represent fuzzy knowledge and perform reasoning tasks based on them. Therefore, the vague ALC can enable the representation and reasoning for fuzzy ontologies with expressive fuzzy knowledge on the semantic web.

基于区间层次分析法和Vague集的雷达装备可靠性评估

针对雷达装备在鉴定定型阶段可靠性评估的实际需求,构建了定性指标与定量指标相结合的雷达装备可靠性指标体系。通过引入区间层次分析法(IAHP)确定指标权重,有效解决了专家评估过程中犹豫度无法反映的问题,使权重更为准确可靠。同时,结合Vague集理论较传统模糊集更为灵活的特点,建立了雷达装备可靠性综合评价模型。针对某型雷达装备在鉴定定型阶段提出的三种方案进行可靠性评估。通过实例验证了该方法的可行性,为研制方对雷达装备可靠性的的后续改进提供了理论依据。

一种新的集合理论Vague Rough sets

将不确定理论Vague集合和Rough集合相结合,提出一种新的集合理论VagueRoughsets.并讨论了其不确定性性质,如模糊度粗糙度等。

基于Vague集的雷达电子防护优先级决策方法

针对区域多雷达目标电子防护优先级决策问题,提出了一种基于Vague集的雷达电子防护优先级决策方法。首先以雷达的本质能力即探测目标能力为驱动,建立了表征雷达电子防护优先级的指标体系,并根据指标属性进行了规范化处理;在此基础上,基于指标体系中同时包含定量指标和模糊区间指标特点,提出了采用灰色加权关联的Vague集多属性决策方法求解区域内多个雷达的电子防护优先级排序。算例结果分析表明,无论是定量指标还是模糊区间指标,所提方法求解的电子防护优先级排序结果均与指标参数分布特性高度吻合,排序结果相对客观,可信度高。

基于Vague Sets-topsis理论的爆破方案优选

为了解决复杂框架结构楼房爆破拆除过程中如何选择爆破方案的技术难题,建立改进的Vague Sets-topsis综合评价指标模型,对爆破方案进行优选。首先对爆破方案中的关键参数建立评审指标集;然后利用逼近理想解的排序法,计算出各个方案的综合优越度,从而确定各个爆破方案的优劣;最后以铁四院前大楼爆破为例,采用改进的Vague Sets-topsis理论模型对"内向折叠爆破"(S1)、"双向折叠爆破"(S2)和"单向折叠双切口爆破"(S3)等不同方案的关键参数进行综合对比分析,得到方案的最优排序为:S3>S2>S1。实际爆破拆除实例表明:S3拆除效果良好,证明采用改进的Vague Sets-topsis理论模型可以用于复杂框架结构楼房控制爆破拆除优选。

Fully implicational methods for approximate reasoning based on interval-valued fuzzy sets

The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Set with Their Application to Solve Multi-Attribute Group Decision Making Problem

Interval-valued Pythagorean fuzzy soft set(IVPFSS)is a generalization of the interval-valued intuitionistic fuzzy soft set(IVIFSS)and interval-valued Pythagorean fuzzy set(IVPFS).The IVPFSS handled more uncertainty comparative to IVIFSS;it is the most significant technique for explaining fuzzy information in the decision-making process.In this work,some novel operational laws for IVPFSS have been proposed.Based on presented operational laws,two innovative aggregation operators(AOs)have been developed such as interval-valued Pythagorean fuzzy soft weighted average(IVPFSWA)and interval-valued Pythagorean fuzzy soft weighted geometric(IVPFSWG)operators with their fundamental properties.A multi-attribute group decision-making(MAGDM)approach has been established utilizing our developed operators.A numerical example has been presented to ensure the validity of the proposed MAGDM technique.Finally,comparative studies have been given between the proposed approach and some existing studies.The obtained results through comparative studies show that the proposed technique is more credible and reliable than existing approaches.

A vague-set-based fuzzy multi-objective decision making model for bidding purchase

A vague-set-based fuzzy multi-objective decision making model is developed for evaluating bidding plans in a bid- ding purchase process. A group of decision-makers (DMs) first independently assess bidding plans according to their experience and preferences, and these assessments may be expressed as linguistic terms, which are then converted to fuzzy numbers. The resulting decision matrices are then transformed to objective membership grade matrices. The lower bound of satisfaction and upper bound of dissatisfaction are used to determine each bidding plan’s supporting, opposing, and neutral objective sets, which together determine the vague value of a bidding plan. Finally, a score function is employed to rank all bidding plans. A new score function based on vague sets is introduced in the model and a novel method is presented for calculating the lower bound of sat- isfaction and upper bound of dissatisfaction. In a vague-set-based fuzzy multi-objective decision making model, different valua- tions for upper and lower bounds of satisfaction usually lead to distinct ranking results. Therefore, it is crucial to effectively contain DMs’ arbitrariness and subjectivity when these values are determined.