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.

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.

Novel Scheme for Robust Confusion Component Selection Based on Pythagorean Fuzzy Set

The substitution box,often known as an S-box,is a nonlinear component that is a part of several block ciphers.Its purpose is to protect cryptographic algorithms from a variety of cryptanalytic assaults.A Multi-Criteria Decision Making(MCDM)problem has a complex selection procedure because of having many options and criteria to choose from.Because of this,statistical methods are necessary to assess the performance score of each S-box and decide which option is the best one available based on this score.Using the Pythagorean Fuzzy-based Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS)method,the major objective of this investigation is to select the optimal S-box to be implemented from a pool of twelve key choices.With the help of the Pythagorean fuzzy set(PFS),the purpose of this article is to evaluate whether this nonlinear component is suitable for use in a variety of encryption applications.In this article,we have considered various characteristics of S-boxes,including nonlinearity,algebraic degree,strict avalanche criterion(SAC),absolute indicator,bit independent criterion(BIC),sum of square indicator,algebraic immunity,transparency order,robustness to differential cryptanalysis,composite algebraic immunity,signal to noise ratio-differential power attack(SNR-DPA),and confusion coefficient variance on some standard S-boxes that are Advanced Encryption Following this,the findings of the investigation are changed into Pythagorean fuzzy numbers in the shape of a matrix.This matrix is then subjected to an analysis using the TOPSIS method,which is dependent on the Pythagorean fuzzy set,to rank the most suitable S-box for use in encryption applications.

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.

Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Hypersoft set theory is a most advanced form of soft set theory and an innovative mathematical tool for dealing with unclear complications.Pythagorean fuzzy hypersoft set(PFHSS)is the most influential and capable leeway of the hypersoft set(HSS)and Pythagorean fuzzy soft set(PFSS).It is also a general form of the intuitionistic fuzzy hypersoft set(IFHSS),which provides a better and more perfect assessment of the decision-making(DM)process.The fundamental objective of this work is to enrich the precision of decision-making.A novel mixed aggregation operator called Pythagorean fuzzy hypersoft Einstein weighted geometric(PFHSEWG)based on Einstein’s operational laws has been developed.Some necessary properties,such as idempotency,boundedness,and homogeneity,have been presented for the anticipated PFHSEWG operator.Multi-criteria decision-making(MCDM)plays an active role in dealing with the complications of manufacturing design for material selection.However,conventional methods of MCDM usually produce inconsistent results.Based on the proposed PFHSEWG operator,a robust MCDM procedure for material selection in manufacturing design is planned to address these inconveniences.The expected MCDM method for material selection(MS)of cryogenic storing vessels has been established in the real world.Significantly,the planned model for handling inaccurate data based on PFHSS is more operative and consistent.

基于Pythagorean模糊环境下MABAC方法的网络货运平台车货匹配研究

针对网络货运平台车货匹配过程中存在的平台间的价格战、卡车司机间的抢单、平台推荐匹配方案不合理问题,在Pythagorean模糊环境下采用MABAC(多属性边界近似区域比较)决策方法,在考虑货主特殊要求的同时对平台接收到的货物订单进行匹配。在考虑车主、货主、平台三方利益的前提下建立车货匹配评价指标体系;采用Pythagorean模糊数表示专家评价语言,采用反正切Pythagorean模糊熵计算指标权重和专家权重;依据MABAC方法对备选方案进行择优排序。

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.

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.

基于IPFS-DEMATEL-ISM的容器安全威胁关键战术要素研究

为解决电力能源企业“上云”引发的云原生容器安全威胁问题,提出融合区间毕达哥拉斯模糊集(IPFS)、决策试验与评价实验室(DEMATEL)和解释结构模型法(ISM)识别容器安全关键战术要素。首先,基于IPFS提取安全专家对容器入侵威胁战术要素的经验判断,其次,应用DEMATEL和ISM识别容器安全威胁的关键战术要素及要素间的层级拓扑关系。结果表明:持久化和权限提升2个战术阶段的中心度和原因度较高,在整个云原生安全威胁体系中居于核心地位,这2个阶段的安全攻击行为需持高优先级关注;执行和持久化战术阶段的威胁攻击是云原生容器安全的本质要素,初始访问、窃取凭证以及横向移动战术阶段的威胁最直接影响云原生容器安全。研究提出的IPFS-DEMATEL-ISM法相较DEMATEL-ISM和集成三角模糊数的DEMATEL-ISM法在识别容器安全威胁关键战术要素时具有更好区分度和简约解释性。

Pythagorean犹豫模糊环境下城市更新社会排斥风险评估研究

针对城市更新中社会排斥风险问题,通过文献研究和案例推理从原住区居民视角构建城市更新社会排斥风险评估指标体系,运用Pythagorean犹豫模糊集量化城市更新社会排斥风险值,运用Pythagorean犹豫模糊熵和交叉熵计算专家权重和准则权重,结合矢量投影法和TOPSIS法的思想计算综合贴近度,据此对风险因素进行重要性排序。结果表明:由城市更新带来的空间变化对原住区居民产生的社会排斥风险主要集中于政治排斥风险和劳动力市场排斥风险;其中决策排除、被迫失业、交往次数减少、主观参与意识薄弱、自愿性失业等问题将是城市更新社会排斥风险产生的主要因素。基于评估结果,提出了防范城市更新社会排斥风险的建议。

融合改进FCM与PFS的知识供需匹配

为提升知识资源的有效配置,缓解用户“知识迷向”问题,设计一套知识供需匹配方法。依据DBSCAN算法确定FCM算法的聚类数目,增强聚类效果;基于改进FCM进行区域划分实现匹配空间压缩,提升算法效率。在此基础上,构建模糊关联匹配度模型,通过融合Zadeh与PFS模糊算子改进相似度计算,兼顾用户需求与既有知识间的相关度,确定匹配结果。实验分析表明,其在知识匹配有效性方面具有一定的比较优势。

On some new fuzzy entropy measure of Pythagorean fuzzy sets for decision-making based on an extended TOPSIS approach

Fuzzy entropy measures are valuable tools in decision-making when dealing with uncertain or imprecise information.There exist many entropy measures for Pythagorean Fuzzy Sets(PFS)in the literature that fail to deal with the problem of providing reasonable or consistent results to the decision-makers.To deal with the shortcomings of the existing measures,this paper proposes a robust fuzzy entropy measure for PFS to facilitate decision-making under uncertainty.The usefulness of the measure is illustrated through an illustration of decision-making in a supplier selection problem and compared with existing fuzzy entropy measures.The Technique for Order Performance by Similarity to Ideal Solution(TOPSIS)approach is also explored to solve the decision-making problem.The results demonstrate that the proposed measure can effectively capture the degree of uncertainty in the decision-making process,leading to more accurate decision outcomes by providing a reliable and robust ranking of alternatives.

A hybrid heterogeneous Pythagorean fuzzy group decision modelling for crowdfunding development process pathways of fintech‑based clean energy investment projects

This study aims to evaluate the crowdfunding alternatives regarding new service development process pathways of clean energy investment projects.In this framework,a new model has been generated by considering the consensus-based group decisionmaking with incomplete preferences,Pythagorean fuzzy decision-making trial and evaluation laboratory(DEMATEL)and technique for order preference by similarity to ideal solution(TOPSIS).Moreover,a comparative evaluation has been performed with Vise Kriterijumska Optimizacija I.Kompromisno Resenje methodology and sensitivity analysis has been made by considering 4 different cases.The main contribution is to identify appropriate crowdfunding-based funding alternatives for the improvement of the clean energy investments with a novel MCDM model.By considering the iteration technique and consensus-based analysis,the missing parts in the evaluations can be completed and opposite opinion problems can be reduced.Furthermore,with the help of hybrid MCDM model by combining DEMATEL and TOPSIS,more objective results can be reached.It is concluded that the analysis results are coherent and reliable.The findings indicate that the full launch is the most significant criterion for equity and debt-based crowdfunding alternatives.On the other side,the analysis has the highest weight for reward and donation-based alternatives whereas design is the most essential item regarding the royalty-based alternative.Additionally,it is also defined that equity-based crowdfunding alternative is the most significant for the service development process of clean energy investment projects.In this way,it will be possible to provide a continuous resource for clean energy investment projects.On the other hand,by providing financing with equity,there will be no fixed financing cost for clean energy investors.If these investors make a profit,they distribute dividends with the decision of their authorized bodies.

基于ELECTRE的Pythagorean模糊群决策方法

针对具有复杂性和模糊性且决策准则较多的群决策问题,提出一种基于ELECTRE的Pythagorean模糊群决策方法.首先给出Pythagorean模糊集的定义,随后提出Pythagorean模糊下的和谐集、不和谐集的概念,进而探讨了Pythagorean模糊下的全局和谐性指数、全局不和谐性指数,最后构建了Pythagorean模糊下偏好关系的群决策方法,并进行了案例分析.结果表明ELECTRE法和Pythagorean模糊集相结合不仅能有效降低模型复杂度,而且应用领域将得到进一步扩展.

Comparative Analysis of Pythagorean MCDM Methods for the Risk Assessment of Childhood Cancer

According to the World Health Organization(WHO),cancer is the leading cause of death for children in low and middle-income countries.Around 400,000 kids get diagnosed with this illness each year,and their survival rate depends on the country in which they live.In this article,we present a Pythagorean fuzzy model that may help doctors identify the most likely type of cancer in children at an early stage by taking into account the symptoms of different types of cancer.The Pythagorean fuzzy decision-making techniques that we utilize are Pythagorean Fuzzy TOPSIS,Pythagorean Fuzzy Entropy(PF-Entropy),and Pythagorean Fuzzy PowerWeighted Geometric(PFPWG).Ourmodel is fed with nineteen symptoms and it diagnoses the risk of eight types of cancers in children.We develop an algorithm for each method and calculate its complexity.Additionally,we consider an example to make a clear understanding of our model.We also compare the final results of various tests that prove the authenticity of this study.

基于区间毕达哥拉斯犹豫模糊熵和交叉熵的ELECTRE II决策方法

针对属性权重完全未知或部分已知,属性值为区间毕达哥拉斯犹豫模糊数的多属性决策问题,提出了基于区间毕达哥拉斯犹豫模糊熵和交叉熵的ELECTRE II法。首先给出区间毕达哥拉斯犹豫模糊数的区间形式的得分函数和精度函数,定义新的距离测度。然后基于区间毕达哥拉斯犹豫模糊数的模糊因子、直觉因子和幅度因子,给出熵和交叉熵公式,并证明其性质,提出了基于熵和交叉熵确定属性权重的方法。最后提出了区间毕达哥拉斯犹豫模糊环境下的改进的ELECTRE II法,利用综合优势值对方案进行排序,并通过算例和比较分析验证了该方法的可行性和有效性。

基于Pythagorean模糊语言集多属性群决策方法

为了解决直觉语言集不能够处理隶属于与非隶属于语言值的程度之和大于1的情况,提出了Pythagorean模糊语言集。针对Pythagorean模糊语言信息的集成问题,定义了Pythagorean模糊语言数的运算法则及其得分函数、精确函数,提出了Pythagorean模糊语言加权平均(PFLWA)算子、Pythagorean模糊语言有序加权平均(PFLOWA)算子、Pythagorean模糊语言混合平均(PFLHA)算子,并讨论了相应的性质。然后基于组合权重的PFLWA算子与拓展的TOPSIS,提出了两种多属性群决策方法。最后通过实例验证了该方法的有效性。

基于改进STPA-DEMATEL的智能航电系统致因要素分析

针对智能航电系统在非线性耦合运行场景下产生的预期功能安全(safety of the intended functionality,SOTIF)问题,提出一种将系统理论过程分析(systematic theory process analysis,STPA)与决策试验与评价实验法(decision-making trial and evaluation laboratory,DEMATEL)相结合的致因分析框架。首先,在定义系统级危险的基础上构建安全控制结构,识别其不安全控制行为并提取与智能化缺陷相关的STPA致因要素。接下来,引入毕达哥拉斯模糊加权平均算子和闵可夫斯基距离对传统DEMATEL方法进行优化,专家根据控制反馈回路对致因要素进行评价并计算其中心度与原因度。最后,分析STPA致因要素与SOTIF致因属性之间的映射关系,给出关键致因要素的风险减缓措施。以单一飞行员驾驶(single-pilot operation,SPO)模式下的虚拟驾驶员助理系统为例说明了所提方法的可行性与有效性。研究结果表明,改进的STPA-DEMATEL方法可以有效识别关键致因要素,且能够克服专家评价的模糊性与不确定性,为智能航电系统的安全性设计提供了参考依据。

Pythagorean模糊环境下基于交叉熵和TOPSIS的多准则决策方法

考虑到Pythagorean模糊集(Pythagorean Fuzzy Set,PFS)具有的优势,提出了一个Pythagorean模糊环境下解决多准则决策(Multicriteria Decision Making,MCDM)问题的新方法。根据TOPSIS理论计算Pythagorean模糊环境下的正、负理想解,同时提出两个Pythagorean模糊集之间的交叉熵定义,并对其性质给予证明。计算每个方案各自和正、负理想解之间的交叉熵,再根据相对贴近度对所有方案进行排序。通过一个在绿色环境下的供应商选择的算例验证了有效性和实用性。