Multi-Criteria Group Decision-Making Method Based on an Improved Single-Valued Neutrosophic Hamacher Weighted Average Operator and Grey Relational Analysis

This paper proposes a multi-criteria decision-making (MCGDM) method based on the improved single-valued neutrosophic Hamacher weighted averaging (ISNHWA) operator and grey relational analysis (GRA) to overcome the limitations of present methods based on aggregation operators. First, the limitations of several existing single-valued neutrosophic weighted averaging aggregation operators (i.e. , the single-valued neutrosophic weighted averaging, single-valued neutrosophic weighted algebraic averaging, single-valued neutrosophic weighted Einstein averaging, single-valued neutrosophic Frank weighted averaging, and single-valued neutrosophic Hamacher weighted averaging operators), which can produce some indeterminate terms in the aggregation process, are discussed. Second, an ISNHWA operator was developed to overcome the limitations of existing operators. Third, the properties of the proposed operator, including idempotency, boundedness, monotonicity, and commutativity, were analyzed. Application examples confirmed that the ISNHWA operator and the proposed MCGDM method are rational and effective. The proposed improved ISNHWA operator and MCGDM method can overcome the indeterminate results in some special cases in existing single-valued neutrosophic weighted averaging aggregation operators and MCGDM methods.

A New Method to Evaluate Linear Programming Problem in Bipolar Single-Valued Neutrosophic Environment

A bipolar single-valued neutrosophic set can deal with the hesitation relevant to the information of any decision making problem in real life scenarios,where bipolar fuzzy sets may fail to handle those hesitation problems.In this study,we first develop a new method for solving linear programming problems based on bipolar singlevalued neutrosophic sets.Further,we apply the score function to transform bipolar single-valued neutrosophic problems into crisp linear programming problems.Moreover,we apply the proposed technique to solve fully bipolar single-valued neutrosophic linear programming problems with non-negative triangular bipolar single-valued neutrosophic numbers(TBSvNNs)and non-negative trapezoidal bipolar single-valued neutrosophic numbers(TrBSvNNs).

Novel applications of bipolar single-valued neutrosophic competition graphs

Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We define bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms.

Linguistic Single-Valued Neutrosophic Power Aggregation Operators and Their Applications to Group Decision-Making Problems

Linguistic single-valued neutrosophic set(LSVNS)is a more reliable tool,which is designed to handle the uncertainties of the situations involving the qualitative data.In the present manuscript,we introduce some power aggregation operators(AOs)for the LSVNSs,whose purpose is to diminish the influence of inevitable arguments about the decision-making process.For it,first we develop some averaging power operators,namely,linguistic single-valued neutrosophic(LSVN)power averaging,weighted average,ordered weighted average,and hybrid averaging AOs along with their desirable properties.Further,we extend it to the geometric power AOs for LSVNSs.Based on the proposed work;an approach to solve the group decision-making problems is given along with the numerical example.Finally,a comparative study and the validity tests are present to discuss the reliability of the proposed operators.

Aczel-Alsina Weighted Aggregation Operators of Simplified Neutrosophic Numbers and Its Application in Multiple Attribute Decision Making

The simplified neutrosophic number(SNN)can represent uncertain,imprecise,incomplete,and inconsistent information that exists in scientific,technological,and engineering fields.Hence,it is a useful tool for describing truth,falsity,and indeterminacy information in multiple attribute decision-making(MADM)problems.To suit decision makers’preference selection,the operational flexibility of aggregation operators shows its importance in dealing with the flexible decision-making problems in the SNN environment.To solve this problem,this paper develops the Aczel-Alsina aggregation operators of SNNs for MADM problems in view of the Aczel-Alsina operational flexibility.First,we define the Aczel-Alsina operations of SNNs.Then,the Aczel-Alsina aggregation operators of SNNs are presented based on the defined Aczel-Alsina operations of SNNs.Next,a MADM method is established using the proposed aggregation operators under the SNN environment.Lastly,an illustrative example about slope treatment scheme choices is provided to indicate the practicality and efficiency of the established method.By comparison with the existing relative MADM methods,the results show that the established MADM method can overcome the insufficiency of decision flexibility in the existing MADM methods and demonstrate the metric of flexible decision-making.

MCDM technique using single-valued neutrosophic trigonometric weighted aggregation operators

Motivated based on the trigonometric t-norm and t-conorm,the aims of this article are to present the trigonometric t-norm and t-conorm operational laws of SvNNs and then to propose the SvNN trigonometric weighted average and geometric aggregation operators for the modelling of a multiple criteria decision making(MCDM)technique in an inconsistent and indeterminate circumstance.To realize the aims,this paper first proposes the trigonometric t-norm and t-conorm operational laws of SvNNs,which contain the hybrid operations of the tangent and arctangent functions and the cotangent and inverse cotangent functions,and presents the SvNN trigonometric weighted average and geometric operators and their properties.Next,an MCDM technique is proposed in view of the presented two aggregation operators in the circumstance of SvNNs.In the end,an actual case of the choice issue of slope treatment schemes is provided to indicate the practicability and effectivity of the proposed MCDM technique.

Investigation on the Indeterminate Information of Rock Joint Roughness through a Neutrosophic Number Approach

To better estimate the rock joint shear strength,accurately determining the rock joint roughness coefficient(JRC)is the first step faced by researchers and engineers.However,there are incomplete,imprecise,and indeterminate problems during the process of calculating the JRC.This paper proposed to investigate the indeterminate information of rock joint roughness through a neutrosophic number approach and,based on this information,reported a method to capture the incomplete,uncertain,and imprecise information of the JRC in uncertain environments.The uncertainties in the JRC determination were investigated by the regression correlations based on commonly used statistical parameters,which demonstrated the drawbacks of traditional JRC regression correlations in handling the indeterminate information of the JRC.Moreover,the commonly used statistical parameters cannot reflect the roughness contribution differences of the asperities with various scales,which induces additional indeterminate information.A method based on the neutrosophic number(NN)and spectral analysis was proposed to capture the indeterminate information of the JRC.The proposed method was then applied to determine the JRC values for sandstone joint samples collected from a rock landslide.The comparison between the JRC results obtained by the proposed method and experimental results validated the effectiveness of the NN.Additionally,comparisons made between the spectral analysis and common statistical parameters based on the NN also demonstrated the advantage of spectral analysis.Thus,the NN and spectral analysis combined can effectively handle the indeterminate information in the rock joint roughness.

P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees

In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting.

单值三角Neutrosophic交叉熵的TOPSIS方法

多准则决策(Multi-Criteria Decision Making,MCDM)问题涉及到大量不精确、不完整和不一致的信息,而单值三角Neutrosophic数(Single Valued Triangular Neutrosophic Numbers,SVTrN-numbers)作为Neutrosophic数(Neutrosophic Numbers,NN)的一个分支可以有效地处理这类问题。同时交叉熵很适合度量决策信息的差异程度,但是现有的交叉熵测度存在不足。考虑到SVTrN-numbers具有的优势,结合TOPSIS理论,提出一种新的交叉熵测度,并对其性质进行证明,据此提出了一个SVTrN-numbers环境下解决MCDM问题的新方法。通过一个案例表明交叉熵公式的合理性。

Cotangent Similarity Measure of Consistent Neutrosophic Sets and Application to Multiple Attribute Decision-Making Problems in Neutrosophic Multi-Valued Setting

A neutrosophic multi-valued set(NMVS)is a crucial representation for true,false,and indeterminate multivalued information.Then,a consistent single-valued neutrosophic set(CSVNS)can effectively reflect the mean and consistency degree of true,false,and indeterminate multi-valued sequences and solve the operational issues between different multi-valued sequence lengths in NMVS.However,there has been no research on consistent single-valued neutrosophic similarity measures in the existing literature.This paper proposes cotangent similarity measures and weighted cotangent similarity measures between CSVNSs based on cotangent function in the neutrosophic multi-valued setting.The cosine similarity measures showthe cosine of the angle between two vectors projected into amultidimensional space,rather than their distance.The cotangent similaritymeasures in this study can alleviate several shortcomings of cosine similarity measures in vector space to a certain extent.Then,a decisionmaking approach is presented in viewof the established cotangent similarity measures in the case of NMVSs.Finally,the developed decision-making approach is applied to selection problems of potential cars.The proposed approach has obtained two different results,which have the same sort sequence as the compared literature.The decision results prove its validity and effectiveness.Meantime,it also provides a new manner for neutrosophic multi-valued decision-making issues.

On Single Valued Neutrosophic Regularity Spaces

This article aims to present new terms of single-valued neutrosophic notions in theˇSostak sense,known as singlevalued neutrosophic regularity spaces.Concepts such as r-single-valued neutrosophic semi￡-open,r-single-valued neutrosophic pre-￡-open,r-single valued neutrosophic regular-￡-open and r-single valued neutrosophicα￡-open are defined and their properties are studied as well as the relationship between them.Moreover,we introduce the concept of r-single valued neutrosophicθ￡-cluster point and r-single-valued neutrosophicγ￡-cluster point,r-θ￡-closed,andθ￡-closure operators and study some of their properties.Also,we present and investigate the notions of r-single-valued neutrosophicθ￡-connectedness and r-single valued neutrosophicδ￡-connectedness and investigate relationship with single-valued neutrosophic almost￡-regular.We compare all these forms of connectedness and investigate their properties in single-valued neutrosophic semiregular and single-valued neutrosophic almost regular in neutrosophic ideal topological spaces inˇSostak sense.The usefulness of these concepts are incorporated to multiple attribute groups of comparison within the connectedness and separateness ofθ￡andδ￡.

基于中智数的突发事件网络舆情辅助决策方法研究

为解决当前应急决策研究大多侧重于数学模型构建且决策数据偏主观假定,导致客观性、实用性及智能性不足的问题,提出基于深度学习和情感倾向分析的单值中智数智能获取方法,并将其应用于突发事件应急决策。首先,利用Python编程技术对突发事件网络舆情数据进行抓取、预处理、统计分析和可视化,得到量化的单值中智数;其次,利用中智数本身具有的不确定性特点,基于精确函数和信息熵客观确定属性权重;最后,利用案例推理(CBR)方法对备选方案进行排序和择优。研究结果表明:所提方法能够对突发事件网络舆情进行实时监测,可以客观智能获取决策数据从而实现对台风灾害的量化评估。研究结果可为相关部门有效应对突发事件网络舆情提供智能辅助决策支持。

带有模糊流量限制的最大流问题

定义构造区间中智数的基本运算,提出中智逻辑并给出数学定义,通过概率论期望的概念提出中智数学期望的定义.结合图论,提出用区间中智数表示网络流中每条弧上的模糊信息,通过改进区间中智数运算并运用增广链算法调整流网络流量,给出中智最大流问题的中智线性规划模型.最后通过算例给出算法具体实现步骤,得到中智环境下的最大流以及流量的波动率,结果说明运算可行,算法合理有效.

考虑失效相关性的系统可靠性分配方法

为弥补部件相关失效对系统可靠性分配结果的影响,提出一种新的可靠性分配方法。将影响系统可靠性分配的因素分为复杂度、技术水平、环境条件、可维修性、运行时间和成本敏感性,用于确定组成部件可靠性分配权重的大小。其中,前3个因素为客观因素,对其进行定量描述并确定其大小;后3个因素为主观因素,通过使用LNNWMM算子刻画这三者的综合得分。通过Copula函数建立系统可靠性分配模型,并以THP6513重型数控卧式铣镗床主轴系统为例,分别对部件相关失效和独立失效的子系统可靠性分配结果进行对比。结果表明,考虑失效相关性的6个子系统可靠性分别为0.972 0、0.983 5、0.982 9、0.977 8、0.981 9和0.979 8,均略低于部件独立失效的各子系统的可靠性,能降低产品的制造和维修成本。

面向不完备单值中智信息的三支决策模型

首先,给出了单值中智信息系统和不完备单值中智信息系统的概念,在此基础上,利用平均值法将一个不完备单值中智信息系统补全为完备的单值中智信息系统;然后,基于补全的单值中智信息系统给出了对象间的相似度的定义,进一步建立了面向不完备单值中智信息的三支决策模型;最后,通过例子阐述了模型的具体应用,并讨论了模型中的参数对决策结果的影响.

混合中智数的新度量及在三支决策中的应用

在多属性三支决策中,有一类方法需要计算各方案期望损失和理想损失之间的距离,通常利用欧式距离和余弦相似度来计算.而在数据源为混合中智数的三支决策中,这两个度量对于某些值存在不可分辨的情况.为此,对传统的欧式距离和余弦相似度进行了改进,在计算隶属度、犹豫度和非隶属度的基础上,增添了犹豫度补集这一因素.并将改进后的度量应用在混合中智数的三支决策中.最后,通过实例对比和分析验证新度量的有效性和合理性.

Human Immunodeficiency Virus (HIV) infection model based on triangular neutrosophic cubic hesitant fuzzy number

In this paper,we define the basic concept of triangular neutrosophic cubic hesitant fuzzy number and their properties.We develop a triangular neutrosophic cubic hesitant fuzzy ordered weighted arithmetic averaging (TNCIIFOWAA) operator and a triangular neu-trosophic cubic hesitant fuzzy ordered weighted geometric averaging (TNCIIFOWGA) operator to aggregate triangular neutrosophic cubic hesitant fuzzy number (TNCHFN) information and investigate their properties.Furthermore,a multiple attribute decision-making method based on the TNCHFOWAA operator and triangular neutrosophic cubic hesitant fuzzy ordered weighted geometric (TNCHFOWG) operator and the score function of TNCHFN is established under a TNCHFN environment.Finally,an illustrative example of investment alternatives is given to demonstrate the application and effec-tiveness of the developed approach.

基于云模型的区间中智数多属性群决策TOPSIS方法

区间中智数是中智数的扩展,能够更好地描述不确定评价信息。云模型具有期望、熵和超熵三个参数特征,用于反映定性概念整体的定量特征。针对属性权重未知、属性值为区间中智数的多属性群决策问题,提出了基于云模型的扩展TOPSIS方法。首先介绍中智数、区间中智数的概念与基本运算规则以及云模型概念、综合云、浮动云及云之间的Hamming距离计算公式;然后,针对属性权重未知,提出了基于变异系数的权重确定方法;进一步基于云模型提出了扩展的TOPSIS排序方法;最后通过一个实例说明了本方法的排序过程。

基于区间中智集的ELECTRE方法及其在多属性决策中的应用

针对多属性决策中信息的不确定性,不完全性和不一致性,考虑到不同数据类型的可能度问题,文章提出了基于区间中智数的ELECTRE方法。首先介绍了区间中智集和可能度,然后针对传统的以实数表示评价信息的ELECTRE方法的不足,将ELECTRE方法与区间中智数相结合提出一个扩展的ELECTRE方法,在方案属性值用区间中智数表示的基础上,计算每个方案相对于其他方案的相对优先度和相对劣势度,并根据净优势度对方案进行排序。最后用一个实例验证该方法的可行性和有效性。

精细语言中智数及其多属性决策方法

提出一种精细语言中智数(RLNN)及其在多属性决策中的应用.首先定义了精细语言中智数以及它的运算规则,然后提出了两种基于精细语言中智数集成算子并研究了它们的性质.运用这两种算子研究了属性值为精细语言中智数的多属性决策方法,最后使用一个决策实例来验证所提出方法的可行性.实验结果表明,在处理多属性决策问题时,当属性包含子属性时,通过精细语言中智数可以获得更精细的评估值,并使决策结果更加合理.