The Correlation Coefficient of Hesitancy Fuzzy Graphs in Decision Making

The hesitancy fuzzy graphs(HFGs),an extension of fuzzy graphs,are useful tools for dealing with ambiguity and uncertainty in issues involving decision-making(DM).This research implements a correlation coefficient measure(CCM)to assess the strength of the association between HFGs in this article since CCMs have a high capacity to process and interpret data.The CCM that is proposed between the HFGs has better qualities than the existing ones.It lowers restrictions on the hesitant fuzzy elements’length and may be used to establish whether the HFGs are connected negatively or favorably.Additionally,a CCMbased attribute DM approach is built into a hesitant fuzzy environment.This article suggests the use of weighted correlation coefficient measures(WCCMs)using the CCM concept to quantify the correlation between two HFGs.The decisionmaking problems of hesitancy fuzzy preference relations(HFPRs)are considered.This research proposes a new technique for assessing the relative weights of experts based on the uncertainty of HFPRs and the correlation coefficient degree of each HFPR.This paper determines the ranking order of all alternatives and the best one by using the CCMs between each option and the ideal choice.In the meantime,the appropriate example is given to demonstrate the viability of the new strategies.

Weighted Parameterized Correlation Coefficients of Indeterminacy Fuzzy Multisets and Their Multicriteria Group Decision Making Method with Different Decision Risks

Real-life data introduce noise,uncertainty,and imprecision to statistical projects;it is advantageous to consider strategies to overcome these information expressions and processing problems.Neutrosophic(indeterminate)numbers can flexibly and conveniently represent the hybrid information of the partial determinacy and partial indeterminacy in an indeterminate setting,while a fuzzy multiset is a vital mathematical tool in the expression and processing of multi-valued fuzzy information with different and/or same fuzzy values.If neutrosophic numbers are introduced into fuzzy sequences in a fuzzy multiset,the introduced neutrosophic number sequences can be constructed as the neutrosophic number multiset or indeterminate fuzzy multiset.Motivated based on the idea,this study first proposes an indeterminate fuzzy multiset,where each element in a universe set can be repeated more than once with the different and/or identical indeterminate membership values.Then,we propose the parameterized correlation coefficients of indeterminate fuzzy multisets based on the de-neutrosophication of transforming indeterminate fuzzy multisets into the parameterized fuzzy multisets by a parameter(the parameterized de-neutrosophication method).Since indeterminate decision-making issues need to be handled by an indeterminate decision-making method,a group decision-making method using the weighted parameterized correlation coefficients of indeterminate fuzzy multisets is developed along with decision makers’different decision risks(small,moderate,and large risks)so as to handle multicriteria group decision-making problems in indeterminate fuzzy multiset setting.Finally,the developed group decision-making approach is used in an example on a selection problem of slope design schemes for an open-pit mine to demonstrate its usability and flexibility in the indeterminate group decision-making problem with indeterminate fuzzy multisets.

Multi-attributed decision making for mining methods based on grey system and interval numbers

In the case of unknown weights, theories of multi-attributed decision making based on interval numbers and grey related analysis were used to optimize mining methods. As the representative of independence for the indicator, the smaller the correlation of indicators is, the greater the weight is. Hence, the weights of interval numbers of indicators were determined by using correlation coefficient. Relative closeness based on positive and negative ideal methods was calculated by introducing distance between interval numbers, which made decision making more rational and comprehensive. A new method of ranking interval numbers based on normal distribution was proposed for the optimization of mining methods, whose basic properties were discussed. Finally, the feasibility and effectiveness of this method were verified by theories and practice.

Group decision-making method based on entropy and experts cluster analysis

According to the aggregation method of experts＇ evaluation information in group decision-making,the existing methods of determining experts＇ weights based on cluster analysis take into account the expert＇s preferences and the consistency of expert＇s collating vectors,but they lack of the measure of information similarity.So it may occur that although the collating vector is similar to the group consensus,information uncertainty is great of a certain expert.However,it is clustered to a larger group and given a high weight.For this,a new aggregation method based on entropy and cluster analysis in group decision-making process is provided,in which the collating vectors are classified with information similarity coefficient,and the experts＇ weights are determined according to the result of classification,the entropy of collating vectors and the judgment matrix consistency.Finally,a numerical example shows that the method is feasible and effective.

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.

“效益-成本”多属性区间型决策的联系数新算法

对于属性值是区间数的效益-成本型多属性决策问题,首先把区间数转换成集对分析理论中的二元联系数,再利用二元联系数中不确定性系数取示性值的原理计算出二元联系数的效应值.用此效应值计算每个方案的综合效益与综合成本的商.根据商的大小对方案集中的方案进行优劣排序,由此形成基于区间数向联系数转换的效益-成本型决策模型,此过程思路清晰,算法简明.实例应用及其与其他决策方法的比较,说明了该模型的优越性和推广应用价值.

Application of TOPSIS Method in Support of Decisions Made in Staff Management Issues

Evaluation model was proposed which refers to fuzzy formalism of the personnel management issues taking account their specific characteristics. Application of TOPSIS （technique for order Performance by similarity to ideal solution） method for evaluation and regulation of alternatives based on hierarchically structured criteria of qualitative character by multiple experts to intellectually support decisions made in staff management issues is reviewed in the article. Candidate selection experiment based on criteria system formed using TOPSIS method for evaluation of candidates during solution of hiring problems reviewed and obtained results were compared with results obtained using Matlab program package.

E-Sh风险下的证券组合投资多目标决策模型

从 E- Sh风险的角度建立并研究了允许卖空与不允许卖空情形下证券组合投资多目标决策模型 。

基于G1-变异系数法的矿产资源项目海外投资决策模型研究

通过分析矿业海外投资面临的风险因素,建立了矿业资源海外投资风险评价指标体系,针对当前主流的矿业投资风险评价方法所存在的缺陷,综合运用G1法及变异系数法,构建了基于动态组合赋权的矿业资源海外投资风险评价模型,并进行了实例分析。研究结果表明:所建立的投资决策模型弥补了评价指标单一赋权方法的缺陷,兼顾主、客观2种赋权方法的优点,使赋权既具有专家的经验智慧,又能反映客观条件的新变化,为比较、分析投资风险提供了更为直接的新方法。

改进TOPSIS的多属性决策方法

针对逼近理想点排序法(technique for order preference by similarity to ideal solution,TOPSIS)存在的缺陷,提出基于Tanimoto系数和基于对称差的2种改进TOPSIS。改善或解决TOPSIS存在指标相关性问题、特殊样本集合无法比较优劣问题和样本数据动态变化时产生的逆序现象等缺陷;在稳定性、特异性、敏感性和有效性4方面对经典TOPSIS模型、改进Tanimoto模型和改进对称差模型进行对比验证,给出2种改进模型的适用场景。结果表明,2种方法各具有一定的优势。

Integrated Expert Analytical System for Assessment of Oil-and-Gas Saturation of Strata

The present research deals with the problem of development of an integrated expert-analytical system for optimum selection of calculated oil-field-geophysical parameters of oil and gas deposits with the purpose of increasing the accuracy of assessment of the reserves of oil and gas deposits. The purpose of the system is to make current adequate decisions on determining of oil-and-gas saturation of strata and future identification of the most significant methods for that, with these methods forming the foundation of knowledge bases for oil-and-gas deposits of the Apsheron peninsula of Azerbaijan. The system architecture allows for expanding the system with its subsequent transformation into a cluster of expert-analytical systems. A logical model of the proposed system is presented. The paper contains a detailed description of the mechanism of operation of the system as a whole and of its individual blocks. Mathematical and formal-logical bases of the intelligent system are explained. The system is equipped with a tool for dynamic statistical analysis of decisions made by it, with representation of the results in real-time mode. The results of the system testing on specific oil-and-gas deposit of the Apsheron peninsula of Azerbaijan in 2013 are given.

基于改进直觉模糊熵与Dice测度的VIKOR应急决策

针对不确定信息环境下决策属性权重未知的应急决策问题,提出一种改进直觉模糊熵权与Dice距离测度的VIKOR决策模型.首先,分析现有直觉模糊熵存在的不足,提出一种考虑隶属度、非隶属度以及犹豫度综合影响的改进直觉模糊熵;其次,引入Dice系数,结合犹豫度的特点构建直觉模糊Dice距离测度;然后,将直觉模糊熵权与直觉模糊Dice距离测度运用到基于直觉模糊的VIKOR方法中,并定义了群体贴近度公式,进而构建契合现实环境的应急决策模型;最后通过地震灾害后的应急决策算例,验证了该模型的合理性和有效性.

概率犹豫模糊集的再定义及其在群决策中的应用

为了更好地解决概率犹豫模糊集多属性群决策问题,构建了一种在不同维度下比较各方案综合属性值大小的决策模型.首先,以二维坐标形式给出概率犹豫模糊集(PHFS)中的隶属度和概率,并在此基础上建立概率犹豫模糊元(PHFE)的二维几何距离模型和二维离差程度系数模型;其次,对PHFS中的隶属度赋予相应的评审专家权重,并用三维坐标刻画隶属度、概率和评审专家权重,以此建立PHFE的三维几何距离模型和三维离差程度系数模型;再次,在二维与三维条件下分别计算2种维度下PHFE的综合值,并利用Maclaurin对称平均算子对以上2种维度下各个PHFE的综合值进行集结并排序;最后,利用实例对在2种维度下建立的算法进行了验证分析.结果显示所建立的算法均可对各方案进行有效地排序,但由于在三维视角下建立的决策模型能够反映评审专家的偏好问题,因此该模型的决策效果相对更好.

基于指派问题的公安情报决策方法

指派问题是线性规划、整数规划、图论和组合最优化的典型问题。公安情报决策工作应用定量分析作为决策辅助工具。指派问题引入公安情报决策,旨在完善定量方法群,为决策者提供科学依据。利用指派问题标准解法——匈牙利解法,运算公安情报决策中指派问题的数学模型时,并未考虑人员完成任务的水平优劣,引入效果系数λ可改善这一情况。

零件疲劳平均失效率计算方法研究

失效率、平均失效率、平均剩余寿命决定了结构的寿命分布和可靠度,在机械产品的可靠性研究中具有非常重要的作用。基于可靠性度量的基本指标,推导寿命分布为两参数威布尔分布时疲劳可靠性系数与可靠度的关系,提出基于疲劳可靠性系数计算结构失效率和平均失效率的方法,并给出相应的计算过程,形成不同寿命度量指标下较为简便的计算方法。利用已有的整体搭接壁板结构疲劳寿命试验数据,采用本文所提方法与传统积分方法对整体搭接壁板结构进行疲劳平均失效率计算和误差分析。结果表明:所推导的计算公式形式简单,便于计算,且具有高度准确性,本文所提计算方法对机械结构的故障模式影响及危害性分析(FMECA)和维修决策的制定具有指导意义。

基于熵和关联系数的区间直觉模糊决策方法

针对决策信息为区间直觉模糊数且属性权重完全未知的多属性决策问题,提出了一种基于熵和关联系数的决策方法。首先,构建了一种新的区间直觉模糊熵,并提出基于该区间直觉模糊熵的属性权重确定方法。然后,提出了考虑属性权重的区间直觉模糊关联系数,进一步基于以上原理给出了解决属性权重完全未知且属性值为区间直觉模糊数的多属性决策问题的决策步骤。最后,依据以上决策步骤,通过算例的计算表明了该方法的简单性与有效性。

对偶犹豫模糊集的相关系数及其应用

对偶犹豫模糊集因其可以给决策者提供更多的决策信息成为模糊决策的热点研究问题,相关性指标可以用来度量两个模糊信息之间的相关关系,熵可以用来度量模糊信息的不确定程度。提出了一种基于对偶犹豫模糊集相关系数和熵的模糊多属性群决策方法。定义了对偶犹豫模糊集相关系数的概念,讨论了其基本性质;提出了两种对偶犹豫模糊集的熵,在此基础上,给出了模糊多属性群决策的权重确定方法;基于对偶犹豫模糊集相关系数和熵,提出了一种属性权重完全未知条件下的模糊多属性群决策方法;通过案例分析说明了该方法的有效性和可行性。

考虑权重折衷系数的模糊识别方法及在水资源评价中的应用

针对过去单一考虑主观权重或客观权重的多目标识别模式的缺陷,通过引入主观权重与客观权重折衷系数的概念,提出了一种新的兼顾主观与客观统一的模糊识别的非线性模型,并给出了计算方法。模型同时考虑了决策者意图和方案本身属性,因而可使方案排序结果更为合理适用,最后将其应用于区域水资源可持续利用程度的评价中,实例表明,该模型科学实用。

基于集对分析的工程评标未知权重多属性决策

基于工程项目管理需要统筹考虑各投标单位的情况,通过对工程项目评标管理进行分析,建立基于集对分析的工程评标未知权重多属性决策模型。该模型利用集对分析理论,结合指标值之间的差异性,全面又突出重点地构建工程评标模型。将集对分析与灰色关联分析相结合,利用关联度对差异度系数赋值,建立评标分级模型。为避免权重赋值的主观性,采用变异系数法确定指标权重,以提高权重的客观性与适应性。构造正、反同一度矩阵,使决策更加全面。研究结果表明:采用该模型所得结果与其他所得结果的平均关联度达到83.3%,从而验证了该模型的合理性与可行性。

模糊多属性决策的折衷方法

在假设属性指标和权重都是模糊数的条件下,利用两个模糊矢量的分量期望值构成的向量的夹角作为这两个模糊矢量的夹角,提出了模糊矢量投影的概念,以权重矢量作为标准衡量各个方案尺度,将模糊多属性理想矢量与模糊多属性指标构成的模糊矢量之差和模糊负理想矢量与模糊多属性指标构成的模糊矢量之差在模糊权重上的投影系数组合大小作为衡量各个方案优劣的准则,投影系数越大,方案越优,并给出该准则的算法及说明该准则的一个例子。