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。

基于区间Pythagorean模糊WA算子的TOPSIS多属性群决策研究

针对区间Pythagorean模糊的混合型多属性群决策问题,构建基于区间Pythagorean模糊集的WA算子模型,并提出了一种基于区间Pythagorean模糊TOPSIS决策方法。首先,基于决策者权重与属性权重完全未知的基础下,将区间Pythagore-an模糊应用到TOPSIS群决策中;其次,利用区间Pythagorean模糊数WA算子将多个决策者评价矩阵集合成综合评价矩阵,并基于TOPSIS决策方法计算各个方案的相对贴近度;最后,通过产业与高校耦合创新算例分析解释验证了本文方法的合理性与有效性。

Pythagorean模糊环境下的三支多属性决策方法

将后悔理论与逼近理想解排序(TOPSIS)法相结合,提出了一种新的三支多属性决策方法,旨在减少决策者的后悔情绪,提高决策满意度.首先,通过评价信息表确定各属性下备选方案的状态集,计算各方案的条件概率.其次,结合TOPSIS和后悔理论,计算相对损失函数,进而确定期望损失,并建立三支决策规则,对方案进行排序并划分为接受域、延迟决策域或拒绝域.最后,以城市轨道交通站点选择为例,进行案例对比分析,验证了该方法的可行性和有效性;接着进行参数分析,以验证该方法的稳定性.

Fuzzy Multi-Criteria Decision Support System for the Best Anti-Aging Treatment Selection Process through Normal Wiggly Hesitant Fuzzy Sets

This socialized environment among educated and developed people causes themto focusmore on their appearance and health,which turns them towards medical-related treatments,leading us to discuss anti-aging treatment methods for each age group,particularly for urban people who are interested in this.Some anti-aging therapies are used to address the alterations brought on by aging in human life without the need for surgery or negative effects.Five anti-aging therapies such as microdermabrasion or dermabrasion,laser resurfacing anti-aging skin treatments,chemical peels,dermal fillers for aged skin,and botox injections are considered in this study.Based on the criteria of safety risk,investment cost,customer happiness,and side effects,the optimal alternative is picked.As a result,a NormalWiggly Hesitant Pythagorean Fuzzy Set(NWHPFS)is constructed and used in Multi-Criteria Decision-Making(MCDM)using traditional wavy mathematical approaches.The entropy approach is utilized to determine weight values,and the Normal Wiggly Hesitant Pythagorean-VlseKriterijumska Optimizacija I Kompromisno Resenje(NWHPF-VIKOR)method is utilized to rank alternatives using MCDM methodologies.Sensitivity analysis and comparative analysis were performed to ensure the robustness and reliability of the proposed method.The smart final choice will undoubtedly assist Decision Makers(DM)in making the right judgments,and the MCDM approach will undoubtedly assist individuals in understanding the medicine.

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.

Fuzzy Risk Assessment Method for Airborne Network Security Based on AHP-TOPSIS

With the exponential increase in information security risks,ensuring the safety of aircraft heavily relies on the accurate performance of risk assessment.However,experts possess a limited understanding of fundamental security elements,such as assets,threats,and vulnerabilities,due to the confidentiality of airborne networks,resulting in cognitive uncertainty.Therefore,the Pythagorean fuzzy Analytic Hierarchy Process(AHP)Technique for Order Preference by Similarity to an Ideal Solution(TOPSIS)is proposed to address the expert cognitive uncertainty during information security risk assessment for airborne networks.First,Pythagorean fuzzy AHP is employed to construct an index system and quantify the pairwise comparison matrix for determining the index weights,which is used to solve the expert cognitive uncertainty in the process of evaluating the index system weight of airborne networks.Second,Pythagorean fuzzy the TOPSIS to an Ideal Solution is utilized to assess the risk prioritization of airborne networks using the Pythagorean fuzzy weighted distance measure,which is used to address the cognitive uncertainty in the evaluation process of various indicators in airborne network threat scenarios.Finally,a comparative analysis was conducted.The proposed method demonstrated the highest Kendall coordination coefficient of 0.952.This finding indicates superior consistency and confirms the efficacy of the method in addressing expert cognition during information security risk assessment for airborne networks.

Three- and Four-Dimensional Generalized Pythagorean Numbers

The Pythagorean triples (a, b | c) of planar geometry which satisfy the equation a2+b2=c2 with integers (a, b, c) are generalized to 3D-Pythagorean quadruples (a, b, c | d) of spatial geometry which satisfy the equation a2+b2+c2=d2 with integers (a, b, c, d). Rules for a parametrization of the numbers (a, b, c, d) are derived and a list of all possible nonequivalent cases without common divisors up to d2 is established. The 3D-Pythagorean quadruples are then generalized to 4D-Pythagorean quintuples (a, b, c, d | e) which satisfy the equation a2+b2+c2+d2=e2 and a parametrization is derived. Relations to the 4-square identity are discussed which leads also to the N-dimensional case. The initial 3D- and 4D-Pythagorean numbers are explicitly calculated up to d2, respectively, e2.

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。

城市轨道交通线路建设时序研究

为合理决策轨道交通建设时序,将城市轨道交通线路建设时序的确定视为多因素决策问题,提出基于Pythagorean模糊熵的优劣解距离法。将传统的一次性静态建设时序确定过程转化为多次动态决策,综合考虑决策者在不同时段对决定线路建设时序的各影响因素重视程度不同,为影响因素指标赋权,计算各时段未确定建设时序的线路与理想解的综合贴近度,进而确定线路建设时序。应用所提出的决策方法确定重庆市城市轨道交通第四期规划线路建设时序,与实际规划时序基本一致。

基于云模型的Pythagorean模糊语言多属性决策方法

针对专家给出的属性值为Pythagorean模糊语言且专家权重与属性权重均未知的多属性决策问题进行了研究,提出一种基于云模型的多属性决策方法。首先,根据Pythagorean模糊语言决策信息的距离熵计算得到属性权重;其次,计算决策矩阵间的距离从而得到各决策专家权重;再次,构建Pythagorean模糊云模型决策矩阵并利用专家权重和属性权重进行信息集结;最后,基于TOPSIS方法求取正、负理想解,依据理想解计算各方案贴近度并据此对各备选方案进行排序选择。案例分析表明,该方法优化了复杂环境下的决策,避免了决策信息的丢失,能够较好地解决决策信息的不确定性和决策过程的随机性,具有一定的可行性和有效性。

基于IVPTFWA算子的TOPSIS决策及其评价研究

将区间Pythagorean模糊数与三角模糊数相结合,提出了区间Pythagorean三角模糊数,并定义了一种新的集结算子—基于区间Pythagorean三角模糊数的加权平均算子(IVPTFWA).首先,定义了一种新的基于IVPTFWA算子的Hamming距离;其次,给出了一种基于IVPTFWA算子的TOPSIS多属性群决策方法;最后,通过算例分析说明文中方法的有效性与科学性.研究发现:IVPTFWA算子避免了Pythagorean模糊数存在的隶属度偏差,缓解了决策过程中的信息流失;同时增大了各方案的贴近度,使得决策结果更加科学与准确.

Pythagorean Neutrosophic Planar Graphs with an Application in Decision-Making

Graph theory has a significant impact and is crucial in the structure of many real-life situations.To simulate uncertainty and ambiguity,many extensions of graph theoretical notions were created.Planar graphs play a vital role in modelling which has the property of non-crossing edges.Although crossing edges benefit,they have some drawbacks,which paved the way for the introduction of planar graphs.The overall purpose of the study is to contribute to the conceptual development of the Pythagorean Neutrosophic graph.The basic methodology of our research is the incorporation of the analogous concepts of planar graphs in the Pythagorean Neutrosophic graphs.The significant finding of our research is the introduction of Pythagorean Neutrosophic Planar graphs,a conceptual blending of Pythagorean Neutro-sophic and Planar graphs.The idea of Pythagorean Neutrosophic multigraphs and dual graphs are also introduced to deal with the ambiguous situations.This paper investigates the Pythagorean Neutrosophic planar values,which form the edges of the Pythagorean neutrosophic graphs.The concept of Pythagorean Neutrosophic dual graphs,isomorphism,co-weak and weak isomorphism have also been explored for Pythagorean Neutrosophic planar graphs.A decision-making algorithm was proposed with a numerical illustra-tion by using the Pythagorean Neutrosophic fuzzy graph.

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.

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.

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.

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.

Complete population transfer between next-adjacent energy levels of a transmon qudit

The utilization of qudits in quantum systems has led to significant advantages in quantum computation and information processing.Therefore,qudits have gained increased attention in recent research for their precise and efficient operations.In this work,we demonstrate the complete population transfer between the next-adjacent energy levels of a transmon qudit using the Pythagorean coupling method and energy level mapping.We achieve a|0>to|2>transfer with a process fidelity of 97.76%in the subspace spanned by|0>to|2>.Moreover,the transfer operation is achieved within a remarkably fast timescale,as short as 20 ns.This study may present a promising avenue for enhancing the operation flexibility and efficiency of qudits in future implementations.

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.

Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers:Application in Complex Decision Aid Systems

The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making.The PFS is known to address the levels of participation and non-participation.To begin,we introduce the novel concept of a PFZN,which is a hybrid structure of Pythagorean fuzzy sets and the ZN.The PFZN is graded in terms of membership and non-membership,as well as reliability,which provides a strong advice in real-world decision support concerns.The PFZN is a useful tool for dealing with uncertainty in decision-aid problems.The PFZN is a practical way for dealing with such uncertainties in decision-aid problems.The list of aggregation operators:PFZN Einstein weighted averaging and PFZN Einstein weighted geometric,is established under the novel Pythagorean fuzzy ZNs.It is a more precise mathematical instrument for dealing with precision and uncertainty.The core of this research is to develop a numerical algorithmto tackle the uncertainty in real-life problems using PFZNs.To show the applicability and effectiveness of the proposed algorithm,we illustrate the numerical case study related to determining the optimal agricultural field.The main purpose of this work is to describe the extended EDAS approach,then compare the proposed methodology with many other methodologies now in use,and then demonstrate how the suggested methodology may be applied to real-world problems.In addition,the final ranking results that were obtained by the devised techniques weremore efficient and dependable in comparison to the results provided by other methods presented in the literature.