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.

Solution of Matrix Game with Triangular Intuitionistic Fuzzy Pay-Off Using Score Function

Using score function in a matrix game is very rare. In the proposed paper we have considered a matrix game with pay-off as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. A new concept of score function has been developed to defuzzify the pay-off matrix and solution of the matrix game has been obtained. A numerical example has been given in support of the proposed method.

Method based on fuzzy linguistic scale and FIOWGA operator for decision-making problems

In this paper, we present a fuzzy linguistic scale, which is characterized by triangular fuzzy numbers on [1/9, 9], for the comparison between two alternatives, and introduce a possibility degree formula for comparing triangular fuzzy numbers. We utilize the fuzzy linguistic scale to construct a linguistic preference matrix, and propose a fuzzy induced ordered weighted geometric averaging (FIOWGA) operator to aggregate linguistic preference information. A method based on the fuzzy linguistic scale and FIOWGA operator for decision-making problems is presented. Finally, an illustrative example is given to verify the developed method and to demonstrate its feasibility and effectiveness.

煤炭企业安全投入的MDC-TIFLNs-AHP方法及其应用

为深入探究煤炭企业安全投入缺乏以及投入结构欠合理等问题,建立一个将多维度调控(MDC)权重、直觉三角模糊语言数(TIFLNs)及层次分析法(AHP)相结合,用以确定安全投入结构的MDC-TIFLNs-AHP方法。首先采用直觉三角模糊语言关联混合平均(R-TIFLNHA)算子算出评价权重向量;其次融合AHP及MDC权重计算各层次总体权重向量;最终对某煤炭企业各类安全投入进行排序。经计算得出,工业卫生投入最重要,之后依次为教育宣传投入、安全技术投入以及个体防护投入,与前人研究结果一致,验证了方法的正确性。结果表明,用MDC-TIFLNs-AHP能够完善安全投入结构、实现安全生产管理目标;合理的安全投入结构有助于企业安全生产,工业卫生及教育宣传的投入至关重要。

Multi-Criteria Decision Making Based on Correlation Coefficient of Triangular Intuitionistic Fuzzy Numbers

We study a multi-criteria fuzzy decision-making method based on weighted triangular intuitionistic fuzzy number correlation coefficients. Under the scenario that criteria weights for alternatives are completely unknown, triangular intuitionistic fuzzy method can not only supplement the insufficiency of the method based on the distance but also endow more information to the estimation and reduce the loss of evaluation information.Among the triangular numbers, two boundary numbers are the maximum and minimum values of the interval respectively, and the medium number is the most possible value under subjective estimation. Using this method,we propose a new way to obtain the criteria weights with more information quantity. By ranking the relative closeness of the weighted correlation coefficients between each alternative, and the critical and ideal alternatives,we show the method to figure out the most suitable alternative based on the expected criteria. An illustrative example is also taken into account to prove the effectiveness of the model.

3D printing process selection model based on triangular intuitionistic fuzzy numbers in cloud manufacturing

The distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platforms,there raises the concern over the validation of virtual product designs and their manufacturing procedures for novices as well as users with 3D printing experience before physical products are produced through the cloud platform.This paper presents a 3D model to help users validate their designs and requirements not only in the traditional digital 3D model properties like shape and size,but also in physical material properties and manufacturing properties when producing physical products like surface roughness,print accuracy and part cost.These properties are closely related to the process of 3D printing and materials.In order to establish the 3D model,the paper analyzes the model of the 3D printing process selection in the cloud platform.Triangular intuitionistic fuzzy numbers are applied to generate a set of 3D printers with the same process and material.Based on the 3D printing process selection model,users can establish the 3D model and validate their designs and requirements on physical material properties and manufacturing properties before printing physical products.

Fuzzy决策中有限方案的群体一致性评价方法与算法

运用三角模糊数的概念提出两种有限方案的群体评价方法：１）根据个体加权向量提出衡量个体间一致性的相似度量函数，由此构造个体、群体的一致性指标，并给出群体一致性的定义，用个体指标提出由个体加权向量寻求群体加权向量的两种方法；２）利用三角模糊数构造语言评价集，并给出一种基于语言的方案评价方法与算法。

AGGREGATION AND DECISION MAKING USING INTUITIONISTIC MULTIPLICATIVE TRIANGULAR FUZZY INFORMATION

The intuitionistic triangular fuzzy set is a generalization of the intuitionistic fuzzy set. In practical applications, we find that the results derived by using the traditional intuitionistic triangular fuzzy aggregation operators based on intuitionistic triangular fuzzy sets are sometimes inconsistent with intuition. To overcome this issue, based on the [1/9, 9] scale, we define the concepts of intuitionistic multiplicative triangular fuzzy set and intuitionistic multiplicative triangular fuzzy number, and then we discuss their operational laws and some desirable properties. Based on the operational laws, we develop a series of aggregation operators for intuitionistic multiplicative triangular fuzzy information, and then apply them to propose an approach to multi-attribute decision making under intuitionistic fuzzy environments. Finally, we use a practical example involving the evaluation of investment alternatives of an investment company to demonstrate our aggregation operators and decision making approach.

基于三角直觉模糊数的多阶段任务系统可靠性评估

针对多阶段任务系统(Phased Mission System,PMS)可靠性评估中对系统或部件退化规律认识不清、主观知识不完备、环境变化等原因造成部件的信息不足或不精确问题,基于三角直觉模糊数(Triangular Intuitionistic Fuzzy Number,TIFN)和二元决策图(Binary Decision Diagram,BDD)模型,提出了一种PMS可靠性评估方法。首先,定义了TIFN的指数运算法则,证明了其满足的性质;其次,通过多位专家对部件平均故障时间(Mean Time to Failure,MTTF)进行评估,利用TIFN量化专家意见,建立了直觉模糊失效率评估模型,构建了一种计算TIFN的隶属度和非隶属度的方法,根据TIFN的运算法则和指数分布函数定义了部件的模糊失效函数;最后,运用示例说明了该方法的有效性,并与传统PMS-BDD方法、模糊故障树方法和直觉模糊故障树方法进行了对比分析。

基于改进TOPSIS的三角直觉模糊多属性群决策方法

针对属性值为三角直觉模糊数,决策者权重已知的多属性群决策问题,提出基于灰色关联度的TOPSIS多属性群决策方法。首先根据决策者对各个属性的打分评级结果,将模糊的语言变量转化为三角直觉模糊数,集结决策者评价信息矩阵,基于属性值离差最大化求出各属性的权重向量,计算备选方案加权决策矩阵;其次,引入灰色关联度,基于模糊正理想点和模糊负理想点计算每个备选方案的灰色关联度,计算每个备选方案的相对贴近度,从而确定每个备选方案的顺序;最后,通过实例分析,验证该方法的有效性。

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。

基于三角模糊数犹豫直觉模糊集的多属性智能决策

通过剖析现实生活中数据对象复杂性以及决策人思考的犹豫模糊性,提出了基于三角模糊数的犹豫直觉模糊集决策方法。首先,给出了三角模糊数犹豫直觉模糊集的定义,构建并证明了三角犹豫直觉模糊元及模糊数的基本运算法则和集成算子。其次,通过对三角犹豫直觉模糊元的得分函数和精确函数的定义,实现了三角犹豫直觉模糊数下的对象间的取值比较,针对三角犹豫直觉模糊数下多属性决策分析中的不确定性权重求解难题,提出了一种基于得分函数和最大熵理论的最优权重求解模型,并构建遗传算法模型实施最优化求解。最后,给出了三角犹豫直觉模糊数下的多属性智能决策算法,并以算例证明了所提方法的可行性和有效性。

三角模糊数直觉模糊Bonferroni平均算子及其应用

针对决策信息为三角模糊数直觉模糊数(TFNIFN)且属性间存在相互关联的多属性群决策(MAGDM)问题,提出了一种基于三角模糊数直觉模糊加权Bonferroni平均(TFNIFWBM)算子的决策方法。首先,基于TFNIFN的运算法则和Bonferroni平均(BM)算子,定义了三角模糊数直觉模糊BM算子和TFNIFWBM算子;然后,研究了这些算子的一些性质,建立基于TFNIFWBM算子的MAGDM模型,结合排序方法进行决策。最后通过MAGDM算例验证了该算子的有效性与可行性。

一种基于三角模糊数的多属性群决策方法

针对方案的属性评估信息和属性权重是模糊语言形式的多属性群决策问题,先将语言信息转化为三角模糊数;然后利用三角模糊数的性质,构造了集结决策者权威性和意见一致性的组合一致性指标,并在此基础上提出了一种模糊多属性群决策算法。最后,通过企业信用状态评估实例及其组合一致性指标的灵敏度分析证明了整个算法的可行性和有效性。

TIFNs-AHP在煤炭企业安全投入中的应用

为解决煤炭企业存在的安全投入欠缺、投入结构不合理的问题,建立一种直觉三角模糊数(TIFNs)与层次分析法(AHP)相结合的安全投入结构确定新方法,即TIFNs-AHP方法。首先给出一种直觉三角模糊有序加权平均(TIFNOWA)算子,并用其计算初始评价权重;然后用AHP法计算通过集成多专家、多时点及数据稳定权重等信息的总体权重;最后将某煤炭企业各类预防性安全投入按重要性排序,依次为:工业卫生投入—教育宣传投入—安全技术投入—个体防护投入。结果表明,合理安排安全投入结构至关重要;工业卫生投入及教育宣传投入是预防安全事故的重要保障。

基于模糊TOPSIS方法的汽车形态设计方案评价

为准确获取汽车形态设计评价指标,依据汽车形态特征群及用户与专家问卷初选汽车形态评价指标;采用文献研究与公信度评测筛除低效用度指标,从而实现汽车形态评价指标体系的科学构建。为解决汽车形态方案选择的复杂性与主观性问题,提出一种结合三角模糊数、语言变量与逼近理想解排序法的模糊逼近理想解排序法评价方法,产生各方案的整体形态得分,最终获得分数最高的优选方案。依据敏感性分析确立评价指标权重对评价过程的影响。通过四款宝马汽车形态方案评价论证了所提方法的可行性并确立最优形态方案。敏感性分析证明了汽车形态评价指标权重对最优方案评价过程具有比较敏感的影响,是评价过程的最重要影响因素。

三角直觉模糊决策的变权方法

研究了属性值为三角直觉模糊数的多属性决策问题,提出了一种基于变权综合的决策方法。首先,针对三角直觉模糊数,提出一种新的三角直觉模糊排序方法;其次,定义了三角直觉模糊变权加权算术平均算子和三角直觉模糊变权加权几何平均算子;然后,提出一种基于三角直觉模糊变权集成算子的多属性决策方法;最后,数值算例说明了该方法的有效性。

基于模糊多指标评价方法的配送中心选址优化决策

研究如何在评价的基础上确定配送中心选址的优化决策,从供应链管理的实际需要出发,分析了影响配送中心选址的主要因素,建立了由公共设施、经营环境、交通运输、宏观环境以及社会效益等五方面指标所组成的评价指标体系,由此给出了一种使定性和定量的方法有机结合的模糊多指标评价方法.最后,通过一个算例说明所给出方法的应用步骤与可行性.

IIFLNs-AHP及其在煤矿安全状况评价中的应用

为了评价煤矿的安全现状,同时实现对各类安全隐患的排查,构建了基于层次分析法(AHP)耦合区间直觉模糊语言数(IIFLNs)进行计算的IIFLNs-AHP评价模型。首先提出了区间直觉模糊语言关联混合几何(R-IIFLNHG)算子,并由其算出评价权重向量;其次结合层次分析法(AHP)运用提出的权重聚合计算公式来确定各层次指标重要程度,并对指标进行排序。以某煤矿为例,运用IIFLNs-AHP进行计算,同时根据计算结果找到了隐含的各类安全隐患,其计算分析结果与现场情况及前人研究结论基本一致,从而验证了IIFLNs-AHP的正确性。结果表明,IIFLNs-AHP能够较好地对煤矿各类安全评价指标进行排序,有助于确定指标体系中的薄弱环节,并可据此实现对安全管理有针对性的改进与完善。

大规模定制模式下基于三角直觉模糊信息的生产指派问题研究

针对大规模定制模式下生产指派面临的模糊不确定性等问题,探讨如何运用三角直觉模糊数构建生产指派模型进而确定最满意的生产指派方案。首先,运用三角直觉模糊数刻画、设计基于顾客个性化需求与企业产出的相对偏差、产品价格与交货期等影响因素的顾客满意度函数和企业利润函数。其次,建立了兼顾企业利润和顾客满意度的调和函数,据此构建了生产指派模型,并证明该模型有可行解和最优解,然后说明模型的求解方法。最后,通过具体实例说明生产指派模型的求解过程及其有效性、合理性。