A novel similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers with applications to pattern recognition and medical diagnosis

Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.

Entropy measures of type-2 intuitionistic fuzzy sets and type-2 triangular intuitionistic trapezodial fuzzy sets

In order to measure the uncertain information of a type- 2 intuitionistic fuzzy set （T21FS）, an entropy measure of T21FS is presented by using the constructive principles. The proposed entropy measure is also proved to satisfy all of the constructive principles. Further, a novel concept of the type-2 triangular in- tuitionistic trapezoidal fuzzy set （T2TITrFS） is developed, and a geometric interpretation of the T2TITrFS is given to comprehend it completely or correctly in a more intuitive way. To deal with a more general uncertain complex system, the constructive principles of an entropy measure of T2TITrFS are therefore proposed on the basis of the axiomatic definition of the type-2 intuitionisic fuzzy entropy measure. This paper elicits a formula of type-2 triangular intuitionistic trapezoidal fuzzy entropy and verifies that it does sa- tisfy the constructive principles. Two examples are given to show the efficiency of the proposed entropy of T2TITrFS in describing the uncertainty of the type-2 intuitionistic fuzzy information and illustrate its application in type-2 triangular intuitionistic trapezodial fuzzy decision making problems.

An explicit finite volume element method for solving characteristic level set equation on triangular grids

Level set methods are widely used for predicting evolutions of complex free surface topologies,such as the crystal and crack growth,bubbles and droplets deformation,spilling and breaking waves,and two-phase flow phenomena.This paper presents a characteristic level set equation which is derived from the two-dimensional level set equation by using the characteristic-based scheme.An explicit finite volume element method is developed to discretize the equation on triangular grids.Several examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time.The proposed level set method is also coupled with the Navier-Stokes equations for two-phase immiscible incompressible flow analysis with surface tension.The Rayleigh-Taylor instability problem is used to test and evaluate the effectiveness of the proposed scheme.

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.

随机模拟半偏减法集对势的区域水资源承载力评价方法

为准确评价区域水资源承载力状态,探讨以联系数和集对势为理论基础构建评价模型,分析普通半偏减法集对势的整体结构及物理意义,为进一步挖掘联系数半偏减法集对势的不确定信息,建立了联系数差异度系数与半偏减法集对势差异度系数的关系,提出了半偏减法集对势差异度系数的三角模糊数随机模拟方法,建立了随机模拟半偏减法集对势差异度系数的区域水资源承载力评价方法。将评价方法应用于安徽省蚌埠市水资源承载力评价中,发现态势变化呈现由偏反势过渡到均势再到偏反势;评价等级值整体处于2~3级之间,说明蚌埠市整体水资源承载状态较差,但有好转趋势。评价模型应用结果与实际情况吻合,为保障区域水资源高质量发展提供了新的评价方法。

三角模糊不完备三支群决策及其在糖尿病诊断中的应用

为同时应对不确定信息表示与风险信息融合对群决策带来的挑战,构建一种三角模糊不完备三支群决策方法,并将其应用于糖尿病诊断决策。首先,针对信息不确定性蕴含的模糊性和不完备性,分别引入三角模糊集和不完备信息系统的概念。通过与多粒度三支决策结合,构建了可调多粒度三角模糊概率粗糙集模型。然后,根据离差最大化法计算属性权重与专家权重,结合ELECTRE(elimination et choice translating reality)方法建立了三角模糊多属性群决策方法。最后,通过对糖尿病患者数据的案例分析和评估,验证了所提方法的可行性和有效性。该方法不仅从不确定信息表示、风险信息融合和最优粒度选择的视角丰富了多粒度三支群决策理论,而且推动了糖尿病智能诊断方面的应用。

连续型直觉模糊集的逻辑相似度

直觉模糊集的相似度被广泛用于模式识别等人工智能领域.为了解决无限论域上直觉模糊集的相似性度量问题,并将直觉模糊集的相似度分析纳入到逻辑推理的框架之中,借助逻辑算子构造了连续论域上的2种直觉模糊集相似度,一种是先积分后聚合,另一种是先聚合后积分,证明了其满足相似度的4个条件.进一步,考虑到实际应用中各属性权重的差异,提出了连续论域上的满足归一化条件的加权直觉逻辑相似度,证明了其满足相似度的4个条件.最后,将所提出的2类相似度应用于模式识别和市场预测等领域,均得到了与直观吻合的结果.

基于演化四元减法集对势模糊数随机模拟的旱灾风险评估

为有效评估旱灾风险,将五元联系数中的不确定性差异度项分解到偏同差异度项和偏反差异度项上,得到演化四元减法集对势,并对其中的差异度系数进行三角模糊数随机模拟,建立基于演化四元减法集对势模糊数随机模拟的旱灾风险评估模型,并应用于淮南市旱灾风险评估。结果表明:淮南市2008—2017年旱灾风险等级整体处于2~3级,属于弱中险状态,但在2014年后等级呈小幅上升趋势;在旱灾风险评估子系统中,危险性子系统、暴露性子系统和灾损敏感性子系统风险等级均逐渐降低,有向好的发展趋势,而抗旱能力子系统等级逐渐增高;单位面积水资源量、灌溉指数、复种指数、水田面积比和森林覆盖率被识别为主要障碍因子。基于演化四元减法集对势模糊数随机模拟的旱灾风险评估方法包含了五元减法集对势的计算结果,且其计算结果是一个等级置信区间,可综合反映旱灾风险变化的多因素影响、不确定性等特点。

Square-Free Pure Triangular Decomposition of Zero-Dimensional Polynomial Systems

Triangular decomposition with different properties has been used for various types of problem solving.In this paper,the concepts of pure chains and square-free pure triangular decomposition(SFPTD)of zero-dimensional polynomial systems are defined.Because of its good properties,SFPTD may be a key way to many problems related to zero-dimensional polynomial systems.Inspired by the work of Wang(2016)and of Dong and Mou(2019),the authors propose an algorithm for computing SFPTD based on Gr¨obner bases computation.The novelty of the algorithm is that the authors make use of saturated ideals and separant to ensure that the zero sets of any two pure chains are disjoint and every pure chain is square-free,respectively.On one hand,the authors prove the arithmetic complexity of the new algorithm can be single exponential in the square of the number of variables,which seems to be among the rare complexity analysis results for triangular-decomposition methods.On the other hand,the authors show experimentally that,on a large number of examples in the literature,the new algorithm is far more efficient than a popular triangular-decomposition method based on pseudodivision,and the methods based on SFPTD for real solution isolation and for computing radicals of zero-dimensional ideals are very efficient.

三角模糊集算法在电子信息分布式多模块检索仿真中的应用研究

三角模糊集算法,作为一种基于模糊逻辑的数学工具,能够有效处理不确定性和模糊性问题,因此在信息检索中显示出巨大的潜力。三角模糊集是模糊数学中的基本概念,通过定义隶属函数为三角形的模糊集合,能够简化模糊信息的处理过程,提高算法的效率和检索的准确性。本文深入探讨了三角模糊集算法在电子信息分布式多模块检索中的具体应用,包括模糊化处理和相似度计算等关键技术。最后,通过仿真研究,验证了该算法在提高检索系统性能方面的有效性。

基于五元半偏减法集对势模糊数随机模拟方法的旱灾风险评估

为准确客观地评估旱灾风险等级,应用集对分析半偏减法集对势和三角模糊数随机模拟方法确定差异度系数,得到评估样本联系数在显著性水平下的置信区间,由联系数值与评价等级间的关系建立映射函数确定评价样本等级区间,构建了基于五元半偏减法集对势模糊数随机模拟的旱灾风险评估方法,并应用于江淮分水岭地区旱灾风险评估实际问题中。结果表明:在时间变化方面,2008—2017年六安市旱灾风险等级呈先上升后降低的趋势,合肥、淮南和滁州三市都处于波动状态,10年间旱灾风险等级总体呈下降趋势;在空间变化方面,江淮分水岭地区旱灾风险北部高于南部、东部高于西部,淮南市旱灾风险等级最高,六安市最低。基于五元半偏减法集对势模糊数随机模拟的旱灾风险评估方法的计算结果范围包含五元半偏减法集对势方法的计算结果,进一步验证了五元半偏减法集对势法评价结果的可靠性。

心脏外科重症监护室设备安全风险的预见性分析与应对策略研究

目的:开展心脏外科重症监护室(ICU)设备安全风险的预见性分析,探讨安全风险应对管理策略的应用价值。方法:针对心脏外科ICU设备安全风险控制管理中的问题进行系统失效模式及后果分析(SFMEA),采用三角模糊软集评价信息融合算法进行安全风险等级评价,按优先级顺序不同开展分层管理。选取医院心脏外科ICU临床在用的89台医疗设备,根据管理模式不同分为对照组(79台)和观察组(82台,含对照组72台和新增加的10台),对照组设备采用经验性管理,观察组设备采用预见性管理。对比两组设备的系统稳定性、设备安全性和临床服务满意度。结果:观察组设备操作部件及功能、机械部件及功能、电气源路及功能、信号采集及处理和数据输出与存储发生失效平均占比分别为(1.49±1.02)%、(1.91±1.37)%、(2.21±1.16)%、(0.97±0.67)%和(0.61±0.43)%,均低于对照组,其差异有统计学意义(t=3.119,t=3.705,t=4.713,t=3.871,t=4.306;P<0.05);观察组常规检测设备、急救治疗设备、专用治疗设备及基础医疗设备的风险占比分别为7.69%(1/13)、10.53%(2/19)、0.00%(0/8)和11.90%(5/42),均低于对照组,其差异有统计学意义(χ^(2)=4.887,χ^(2)=4.039,χ^(2)=5.333,χ^(2)=4.082;P<0.05);医院相关工作人员对观察组设备临床服务质量的满意度为94.59%,高于对照组,其差异有统计学意义(χ^(2)=5.731,P<0.05)。结论:基于三角模糊软集评价信息融合算法的心脏外科ICU设备安全风险预见性分析与应对管理策略能够提高心脏外科ICU设备安全风险的预见性,提升医疗设备系统稳定性,改善医疗设备临床诊疗安全性,提高医疗设备管理满意度。

基于半偏减法集对势三角模糊数随机模拟方法的水资源承载力评价

为深入挖掘三元联系数所蕴含的不确定性信息,基于三元半偏减法集对势并充分考虑各联系数分量间的相互转化,二次构造三元联系数,再依据三角模糊数和偏联系数理论确定联系数分量的取值区间,采用随机模拟法计算一定置信水平下的联系数值区间,由此构建基于半偏减法集对势三角模糊数随机模拟方法的水资源承载力评价模型(WRCC-SPSS),并应用于江淮丘陵区水资源承载力评价中,同时与现有常用方法进行对比分析。结果表明:2011—2018年江淮丘陵区域水资源承载力状态稳步提升,其中合肥市承载力水平最差;在二次构造联系数时,对不确定项作进一步划分,从而降低了联系数分量的不确定性,同时采用三角模糊数和随机模拟法确定联系数分量,可获得联系数的置信取值区间,所得结果更为可靠;实例应用结果与现有研究方法评价结果总体一致,WRCC-SPSS方法聚焦不确定性,物理内涵丰富,可实现承载力水平的动态评价。

Multi Criteria Decision Making for Evaluation and Ranking of Cancer Information

Cancer is a disease that is rapidly expanding in prevalence all over the world.Cancer cells canmetastasize,or spread,across the body and impact several different cell types.Additionally,the incidence rates of several subtypes of cancer have been on the rise in India.The countermeasures for the cancer disease can be taken by determining the specific expansion rate of each type.To rank the various forms of cancer’s rate of progression,we used some of the available data.Numerous studies are available in the literature which show the growth rate of cancer by different techniques.The accuracy of the scheme in determining the highest growth rate may vary due to the variation in the dependent factors.Within the context of this research,the Fuzzy triangular technique for order preference by similarity to ideal solution(TOPSIS),is utilized to rank the various categorizations of cancer with the help of four groups of medical professionals acting in the capacity of decision-makers.The number of decision-makers may variate according to the required accuracy of results.The findings of the three-dimensional Fuzzy TOPSIS analysis categorize each variety of cancer according to the rate at which it spreads over time.Numerical results along with visual representation are presented to examine the efficiency of our proposed work.

区间值模糊推理的逻辑度量空间

为了探寻适合区间值模糊推理的条件,本文研究区间值逻辑度量空间。本文提出一种新的基于区间值双剩余蕴涵算子的区间值模糊集的距离度量。由4个著名的区间值双剩余诱导相应的距离度量,做成4个度量空间,分别研究4个度量空间的性质。进一步,证明基于区间值Łukasiewicz剩余蕴涵的度量空间和区间值Goguen剩余蕴涵的度量空间适合做区间值模糊推理。最后,在基于区间值Łukasiewicz剩余蕴涵度量空间中,证明基于区间值Łukasiewicz剩余蕴涵的模糊推理全蕴涵算法是鲁棒的,为区间值模糊推理算法的应用提供了坚实的理论基础。

Lipschitz equivalence of self-similar sets with triangular pattern

In this paper, we discuss the Lipschitz equivalence of self-similar sets with triangular pattern. This is a generalization of {1, 3, 5}-{1, 4, 5} problem proposed by David and Semmes. It is proved that if two such self-similar sets are totally disconnected, then they are Lipschitz equivalent if and only if they have the same Hausdorff dimension.

基于耦合评价模型的采场污染等级研究

针对目前采场作业环境复杂,现有评价方法比较单一模糊的情况,提出引入集对分析中联系数来描述采场作业环境中各影响因素与评价标准间的模糊性,并用改进的三角模糊数对集对分析中同异反模型差异度系数的连续过程进行刻画和描述,最终构建出基于联系数的动态三角模糊数决策模型。通过在实例分析中采用矿井的监测数据进行评价,发现构建模型评价结果与其它方法基本一致,表明多元联系数值的大小能更形象反应不同区段采场环境的污染程度,可以为采场作业环境评价提供一种新的方法,所得结果更加客观和精确,对现场生产有重要的现实意义。

三角模糊数的模糊故障树分析及其应用

新型装备缺乏贮存实验数据与现场数据，无法沿用常规方法对其进行贮存可靠性分析．讨论了新型装备贮存可靠性研究的方法，给出了用三角模糊数进行模糊故障树分析的方法与步骤，以及模糊重要度分析的新方法——中值法，为新型装备贮存可靠性研究提供了技术途径．

基于集对分析与三角模糊数的滨海湿地生态系统健康评价

滨海湿地是海洋和陆地相互作用形成的生态交错带,对自然环境变化和人类活动作用响应最为敏感,使其成为相对脆弱的生态系统。科学评价滨海湿地生态系统健康状况及其胁迫因子,对湿地生态系统恢复重建与可持续发展具有重要的现实意义。针对湿地生态系统评价问题的不确定性和模糊性特征,运用压力-状态-响应(PSR)模型构建滨海湿地生态系统健康评价指标体系,运用层次分析法确定了各指标的权重,根据集对分析原理定量描述评价样本与评价标准等级之间隶属关系的模糊性,利用分段三角模糊数表示集对差异度系数的连续变化过程和不确定性,进而建立了基于集对分析与三角模糊数耦合的滨海湿地生态系统健康评价模型,并将该模型应用于海兴湿地生态系统健康现状评价。结果表明:海兴湿地生态健康综合联系数为-0.380,相应的级别特征值为3.760,系统整体处于一般病态水平。其中压力系统、状态系统和响应系统的级别特征值分别为3.580、3.976和2.948,说明海兴湿地生态系统的自然状态受到了人类活动过度干扰,外界胁迫引起系统的结构失调和服务功能衰退。影响系统健康的主要因子为农药施用强度、水资源开发利用率、湿地面积退化率、水体富营养化、环保投资占GDP比重、湿地保护意识等。该模型计算过程简单直观,评价结果客观合理,在湿地生态系统健康评价中具有参考价值。

带有三角直觉模糊数的多属性决策的TOPSIS

本文的研究目的是属性值为三角直觉模糊数的多属性决策。首先定义了三角直觉模糊数的距离、三角直觉模糊数正、负理想方案及其与每个方案的距离,然后建立了每个方案与三角直觉模糊数正理想方案的相对贴近度计算方法,给出所有方案的排序。数值实例说明了该方法的有效性和实用性,可为解决直觉模糊多属性决策提供新途径。