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.

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.

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.

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.

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.

Interval-Valued Dual Hesitant Fuzzy Hamacher Aggregation Operators for Multiple Attribute Decision Making

As an generalization of hesitant fuzzy set, interval-valued hesitant fuzzy set and dual hesitant fuzzy set, interval-valued dual hesitant fuzzy set has been proposed and applied in multiple attribute decision making. Hamacher t-norm and t-conorm is an generalization of algebraic and Einstein t-norms and t-conorms. In order to combine interval-valued dual hesitant fuzzy aggregation operators with Hamacher t-norm and t-conorm. We first introduced some new Hamacher operation rules for interval-valued dual hesitant fuzzy elements. Then, several interval-valued dual hesitant fuzzy Hamacher aggregation operators are presented, some desirable properties and their special cases are studied. Further, a new multiple attribute decision making method with these operators is given,and an numerical example is provided to demonstrate that the developed approach is both valid and practical.

犹豫Pythagorean模糊语言优先级集结算子及应用

基于犹豫Pythagorean模糊集、直觉模糊语言集和优先级算子研究了属性存在优先级关系的犹豫Pythagorean模糊语言多属性决策问题。定义犹豫Pythagorean模糊语言集,提出犹豫Pythagorean模糊语言数的运算法则、得分函数及其精确函数;根据犹豫Pythagorean模糊语言集和优先级算子提出犹豫Pythagorean模糊语言优先级集结算子;根据犹豫Pythagorean模糊语言优先级集结算子构建能够解决属性存在优先级关系的多属性决策模型,并通过案例验证了该模型的有效性。

毕达哥拉斯犹豫模糊集多属性决策研究

针对属性间相互关联,评价信息为毕达哥拉斯犹豫模糊信息的多属性决策问题,首先通过研究犹豫度对决策结果的影响,提出一种新的毕达哥拉斯犹豫模糊集得分函数,解决了现有得分函数中存在的不足。其次,提出一种最小公倍数规范化原则,解决了现有方法容易引入误差的缺陷。最后,针对属性关联的多属性决策问题,基于λ-模糊测度与Choquet积分,提出了一种拓展交互式多准则决策(interative multi-criteria decision-making,TODIM)方法,既解决了属性关联的问题,又通过前景理论反映了决策者的心理行为特征。实例分析与敏感性分析验证了所提算法的正确性与有效性。

区间Pythagorean犹豫模糊连续熵及灰色关联度的应用

区间Pythagorean犹豫模糊集,可以更加全面完整地描述决策者给出的决策结果,因此它是一个表示不确定现象的强有力的工具。针对模糊信息下的决策问题,提出了一种基于区间Pythagorean犹豫模糊连续熵的多属性决策方法。提出连续区间Pythagorean犹豫模糊有序加权平均(CIPHFOWA)算子,并提出了区间Pythagorean犹豫模糊连续熵,同时给出了属性权重完全未知和部分已知时的权重确定方法;提出了一种基于区间Pythagorean犹豫模糊连续熵—灰色关联度的多属性决策方法,并通过新型农村医疗制度完善情况评价案例说明该方法的可行性和有效性。

基于Pythagorean犹豫模糊集相似测度的多属性决策方法

针对模糊信息下的决策问题,提出了一种基于Pythagorean犹豫模糊相似性测度的多属性决策方法。首先,基于最小公倍数的原理,介绍了一种新的扩充规则用以处理Pythagorean犹豫模糊集(PHFS)之间隶属度(非隶属度)长度不一致的情况,该方法能有效地保持原始信息的信息量。其次,定义了4种Pythagorean犹豫模糊集的相似性测度,并讨论了其相关性质,考虑到决策问题中多个属性的权重,给出了几种加权相似性测度。最后,提出了一种基于Pythagorean犹豫模糊集的TOPSIS方法用以解决多属性决策问题,并通过软件开发项目评估实例验证了该方法的可行性和有效性。

A novel approach to emergency risk assessment using FMEA with extended MULTIMOORA method under interval-valued Pythagorean fuzzy environment

Purpose-The application of the traditional failure mode and effects analysis(FMEA)technique has been widely questioned in evaluation information,risk factor weights and robustness of results.This paper develops a novel FMEA framework with extended MULTIMOORA method under interval-valued Pythagorean fuzzy environment to solve these problems.Design/methodology/approach-This paper introduces innovatively interval-value Pythagorean fuzzy weighted averaging(IVPFWA)operator,Tchebycheff metric distance and interval-value Pythagorean fuzzy weighted geometric(IVPFWG)operator into the MULTIMOORA submethods to obtain the risk ranking order for emergencies.Finally,an illustrative case is provided to demonstrate the practicality and feasibility of the novel fuzzy FMEA framework.Findings-The feasibility and validity of the proposed method are verified by comparing with the existing methods.The calculation results indicate that the proposed method is more consistent with the actual situation of project and has more reference value.Practical implications-The research results can provide supporting information for risk management decisions and offer decision-making basis for formulation of the follow-up emergency control and disposal scheme,which has certain guiding significance for the practical popularization and application of risk management strategies in the infrastructure projects.Originality/value–A novel approach using FMEA with extended MULTIMOORA method is developed under IVPF environment,which considers weights of risk factors and experts.The method proposed has significantly improved the integrity of information in expert evaluation and the robustness of results.

基于Pythagorean犹豫模糊集成算子的多属性决策方法及其应用

基于Pythagorean犹豫模糊集理论,提出了基于Pythagorean犹豫模糊环境下的集成算子来研究多属性决策问题。首先提出了Pythagorean犹豫模糊有序加权算术平均算子和Pythagorean犹豫模糊有序加权几何平均算子;基于对Pythagorean犹豫模糊决策信息本身及其信息顺序位置重要性的兼顾,又提出了Pythagorean犹豫模糊混合算术平均算子和Pythagorean犹豫模糊混合几何平均算子;最后,提出了基于Pythagorean犹豫模糊信息集成的多属性决策方法,并通过智慧医疗评估体系的例子说明提出的决策方法的可行性.

基于Hamacher区间模糊算法的技术状态评估权重确定

针对复杂装备技术状态评估权重确定过程中存在的专家犹豫和权重确定动态性不足的问题,结合区间值犹豫模糊熵、毕达哥拉斯模糊集和Hamacher算子,提出Hamacher区间模糊算法。综合各专家对各元素重要性的打分,构建区间值犹豫模糊集,改进区间值犹豫模糊熵,并对模糊集中各犹豫模糊元运算得到区间值犹豫模糊熵矩阵;令区间值犹豫模糊熵为隶属度,打分区间差值为犹豫度,得到毕达哥拉斯模糊集,运用Hamacher区间模糊算法计算得到各元素重要度得分函数,将得分函数归一化得到最终元素权重。算例结果表明,该验证方法对技术状态评估具有适用性。

一种结合勾股模糊相似度的多属性决策方法

为了解决现有勾股模糊相似度度量中由于忽略犹豫度而造成度量不精确的问题,提出一种新的相似度的度量方法.首先,在属性值为勾股模糊数的条件下,将勾股模糊相似度定义结合灰色关联分析的思想应用于多属性决策,提出一种新的结合勾股模糊相似度的灰色关联分析多属性决策方法,并设计了该方法的算法.通过一个翔实的算例分析证实了提出方法的正确性和有效性,证明其为多属性决策的一种新的可行方法.通过两组实验结果的对比,提出的方法比其他方法的决策更贴近实际结果,验证了该方法的可靠性.该算法还避免了人工计算,具有高效性.

广义毕达哥拉斯犹豫模糊集混合加权距离测度及决策应用

在毕达哥拉斯犹豫模糊数的距离基础上,定义毕达哥拉斯犹豫模糊集(Pythagorean hesitant fussy set,PHFS)的加权距离测度和有序加权距离测度,在兼顾属性权重和位置权重的基础上,提出广义PHFS混合加权距离测度(D_(GPHFHWA)),并研究其性质和特殊形式。针对属性值为毕达哥拉斯犹豫模糊数且属性权重未知的多属性决策问题,利用毕达哥拉斯犹豫模糊指数熵确定属性权重,并结合逼近理想解排序法(technique for order preference by similarity to an ideal solution,TOPSIS)思想,提出基于D_(GPHFHWA)测度的决策方法。最后,通过实例验证所提方法是有效、合理的。

毕达哥拉斯犹豫模糊集成算子及其决策应用

针对毕达哥拉斯犹豫模糊多属性决策中,集成算子的重要作用以及集成算子不完善的情况,较为系统地研究了毕达哥拉斯犹豫模糊集成算子。为此,在毕达哥拉斯犹豫模糊数的运算和运算法则基础上,定义了毕达哥拉斯犹豫模糊有序加权平均算子(PHFOWA)、广义有序加权平均算子(GPHFOWA)和混合平均算子(PHFHA),以及毕达哥拉斯犹豫模糊有序加权几何平均算子(PHFOWG)、广义有序加权几何平均算子(GPHFOWG)和混合几何平均算子(PHFHG),并结合数学归纳法分别给出了它们的计算公式,讨论了它们的有界性、单调性和置换不变性等性质。建立了基于毕达哥拉斯犹豫模糊集成算子的多属性决策方法,并应用算例和相关方法比较说明了决策方法的可行性与有效性。

基于累积前景理论和VIKOR的毕达哥拉斯犹豫模糊风险型多属性决策方法

针对属性权重未知,且属性值为毕达哥拉斯犹豫模糊数(PHFN)的风险型多属性决策问题,考虑到决策者的有限理性行为,提出基于累积前景理论(CPT)和多准则妥协优化解(VIKOR)的决策方法。首先,定义PHFN的分散率,并构建优化模型确定属性权重。其次,将CPT融入PHFN环境,定义PHFN的价值函数,并结合决策权重函数计算方案在各属性下的综合前景值。进一步,构建综合前景值矩阵,在此基础上运用VIKOR法确定方案排序。最后,通过风险投资项目选择的应用案例说明所提方法是可行、有效的。

基于DEMATEL和VIKOR的犹豫毕达哥拉斯模糊多属性决策方法

为了解决复杂模糊不确定环境下多属性决策问题,提出一种基于DEMATEL和VIKOR的犹豫毕达哥拉斯模糊多属性决策方法。首先根据决策者给定的属性评价值,利用DEMATEL方法确定属性权重,通过VIKOR方法对方案进行排序;其次对于排序结果不一致的情况,利用Kendall-W系数进行事前一致性检验,利用本文所提组合模糊Borda方法进行排序;再利用Spearman系数进行事后一致性检验。最后通过实例说明该方法的可行性与有效性。

毕达哥拉斯模糊熵的公理化定义和计算公式

介绍了毕达哥拉斯模糊集的定义;提出了毕达哥拉斯模糊熵的公理化定义和计算公式,在完整地考虑隶属度、非隶属度、犹豫度这3个变量的关系之后,对毕达哥拉斯模糊熵的公理化定义进行了修改,提出了改进的毕达哥拉斯模糊熵定义和计算公式;说明了改进的毕达哥拉斯模糊熵的优势,并用实例验证了毕达哥拉斯模糊熵计算公式的有效性和科学性。

毕达哥拉斯三角犹豫模糊Muirhead平均算子的目标威胁评估应用

为了更加完整地描述不确定信息,将三角模糊数与毕达哥拉斯犹豫模糊集结合,提出了毕达哥拉斯三角犹豫模糊集。针对信息集成过程中数据属性之间存在关联关系的问题,将Heronian平均算子、Muirhead平均算子拓展到毕达哥拉斯三角犹豫模糊集中,提出了毕达哥拉斯三角犹豫模糊Heronian平均算子和毕达哥拉斯三角犹豫模糊Muirhead平均算子。考虑不同属性的输入变量的重要程度不同,提出了它们的加权形式。最后,针对毕达哥拉斯三角犹豫模糊环境下的多属性决策问题,提出了基于PHTFWMM算子的多属性决策方法,并通过算例说明了该方法的有效性。