New approach to determine the priorities from interval fuzzy preference relations

An approach is proposed to solve the problem how to obtain the priorities from interval fuzzy preference relations. Firstly, another expression of interval numbers is given. Then, some basic definitions on consistency and weak transitivity of real and interval fuzzy preference relations are described. Based on these definitions, a two-phase process for determining the priorities from interval fuzzy preference relations is presented. Finally, two exam- ples are used to illustrate the use of the proposed approach.

Group Decision Making With Consistency of Intuitionistic Fuzzy Preference Relations Under Uncertainty

Intuitionistic fuzzy preference relation(IFPR) is a suitable technique to express fuzzy preference information by decision makers(DMs). This paper aims to provide a group decision making method where DMs use the IFPRs to indicate their preferences with uncertain weights. To begin with, a model to derive weight vectors of alternatives from IFPRs based on multiplicative consistency is presented. Specifically, for any IFPR,by minimizing its absolute deviation from the corresponding consistent IFPR, the weight vectors are generated. Secondly,a method to determine relative weights of DMs depending on preference information is developed. After that we prioritize alternatives based on the obtained weights considering the risk preference of DMs. Finally, this approach is applied to the problem of technical risks assessment of armored equipment to illustrate the applicability and superiority of the proposed method.

Group Decision-Making Method with Incomplete Intuitionistic Fuzzy Preference Relations Based on a Generalized Multiplicative Consistent Concept

Based on the analyses of existing preference group decision-making(PGDM)methods with intuitionistic fuzzy preference relations(IFPRs),we present a new PGDM framework with incomplete IFPRs.A generalized multiplicative consistent for IFPRs is defined,and a mathematical programming model is constructed to supplement the missing values in incomplete IFPRs.Moreover,in this study,another mathematical programming model is constructed to improve the consistency level of unacceptably multiplicative consistent IFPRs.For group decisionmaking(GDM)with incomplete IFPRs,three reliable sources influencing the weights of experts are identified.Subsequently,a method for determining the weights of experts is developed by simultaneously considering three reliable sources.Furthermore,a targeted consensus process(CPR)is developed in this study with reference to the actual situation of the consensus level of each IFPR.Meanwhile,in response to the proposed multiplicative consistency definition,a novel method for determining the optimal priority weights of alternatives is redefined.Lastly,based on the above theory,a novel GDM method with incomplete IFPRs is developed,and the comparative and sensitivity analysis results demonstrate the utility and superiority of this work.

Selection method of risk response schemes for mining project based on fuzzy preference relations

To overcome the subjectivity of experts in the process of risk response scheme selection, according to the theory of group decision making, a selection method and flow of the risk response schemes for a mining project was proposed based on fuzzy preference relation and consistency induced ordered weighted averaging (C-IOWA) operator,which can overcome the loss of information in the process of group decision making to a great degree, and improve its efficiency and quality.A numeric example was introduced to illustrate the application of the method, also validating the method as scientific and practicable.

Priority approach based on quadratic programming model to fuzzy preference relation

We investigate the decision-making problem with a finite set of alternatives,in which the decision information takes the form of a fuzzy preference relation. We develop asimple and practical approach to obtaining the priority vector of a fuzzy preference relation. Theprominent characteristic of the developed approach is that the priority vector can generally beobtained by a simple formula, which is derived from a quadratic programming model. We utilize theconsistency ratio to check the consistency of fuzzy preference relation. If the fuzzy preferencerelation is of unacceptable consistency, then we can return it to the decision maker to reconsiderstructuring a new fuzzy preference relation until the fuzzy preference relation with acceptableconsistency is obtained. We finally illustrate the priority approach by two numerical examples. Thenumerical results show that the developed approach is straightforward, effective, and can easily beperformed on a computer.

AN APPROACH TO GROUP DECISION MAKING BASED ON INTERVAL FUZZY PREFERENCE RELATIONS

In this paper, we investigate group decision making problems where the decision information given by decision makers takes the form of interval fuzzy preference relations. We first give an index to measure the similarity degree of two interval fuzzy preference relations, and utilize the similarity index to check the consistency degree of group opinion. Furthermore, we use the error-propagation principle to determine the priority vector of the aggregated matrix, and then develop an approach to group decision making based on interval fuzzy preference relations. Finally, we give an example to illustrate the developed approach.

On Optimal Priority Modelling of Group Intuitionistic Fuzzy Preference Relations with Normal Uncertainty Distribution

The uncertainty distribution can more effectively express the uncertainty of decision makers' judgments during a pairwise comparison of any alternatives. This paper investigates the priority models of group intuitionistic fuzzy preference relations with normal uncertainty distribution. The mathematical equivalence between the membership, non-membership degree interval fuzzy preference relation and the intuitionistic fuzzy preference relation is constructed, showing that there exists an inverse relationship between the priority of alternatives using these two types of interval preference relations. The new optimal models regarded the event that the deviation between the ideal judgement meeting the multiplicative consistency and the actual judgement obeying normal uncertainty distribution shall not exceed a threshold value under the given belief degree as a constraint, and regarded the minimum sum of all the threshold values as the objective function. The chance constraint was introduced to measure the degree to which multiplicative consistency can be realized under different belief degrees. The priority model provides a new method for simulating uncertainty and fuzziness in the real-world decision making environment.

Approaches to Improving Consistency of Interval Fuzzy Preference Relations

This article introduces a consistency index for measuring the consistency level of an interval fuzzy preference relation（IFPR）.An approach is then proposed to construct an additive consistent IFPR from a given inconsistent IFPR.By using a weighted averaging method combining the original IFPR and the constructed consistent IFPR,a formula is put forward to repair an inconsistent IFPR to generate an IFPR with acceptable consistency.An iterative algorithm is subsequently developed to rectify an inconsistent IFPR and derive one with acceptable consistency and weak transitivity.The proposed approaches can not only improve consistency of IFPRs but also preserve the initial interval uncertainty information as much as possible.Numerical examples are presented to illustrate how to apply the proposed approaches.

基于Fuzzy偏好关系的一种方案排序方法

如何根据Ｆｕｚｚｙ 偏好关系选择最优方案或进行方案的排序是一个重要的研究内容·针对Ｆｕｚｚｙ 偏好关系提出了一种新的方案排序方法·首先描述了Ｆｕｚｚｙ 偏好关系及其含义， 然后建立了一个最优化模型并通过求解该模型来得到方案的参考排序值， 使最终方案的排序结果最大程度地反映决策者的偏好， 最后给出了一个算例·

带有Fuzzy偏好关系的多属性决策方法

针对多属性决策分析中决策者给出关于方案的Fuzzy偏好关系 ,提出了一种新的多属性决策方法·该方法是通过建立一个线性目标规划模型来确定属性的权重向量并相应地进行方案的排序 ,得到的方案排序结果体现了决策者给出的方案偏好信息与决策矩阵的集成 ,并最大程度地反映了决策者的偏好·最后给出了一个算例·

基于广义Fuzzy偏好关系的决策方法探讨

提出了广义模糊偏好关系的概念.设计了互补化排序和加性一致化排序两种排序方法,讨论了两种排序方法的相关性质.基于这两种排序方法,定义了冗余一致性指标和加性一致性指标,并讨论了采用加权算术平均算子(WAA 算子)或有序加权平均算子(OWA 算子)对广义模糊偏好关系进行集结,其群体偏好一致性(包括冗余一致性和加性一致性)的相关性质.对进一步完善基于模糊偏好关系的群决策模型具有理论和现实意义.

基于优化模型的“专精特新”企业竞争力评价

近年来,国家大力培育“专精特新”企业,但分析“专精特新”企业竞争力的评价研究仍不够深入。研究借鉴国内外相关评价指标,从“专精特新”概念出发,构建包括四个维度,12个具体指标的竞争力评价体系。运用基于区间模糊偏好关系的决策方法确定指标权重,并邀请专家对四家河南省“专精特新”企业的竞争力进行具体评价。根据评价结果,结合企业特点和发展现状,提出具体建议。为促进“专精特新”企业的发展提供借鉴。

加性一致性驱动的勾股模糊偏好决策方法

为进一步完善和发展传统偏好决策理论,在直觉模糊偏好关系加性一致性概念的启发下,构建了两个可与勾股模糊偏好关系(Pythagorean fuzzy preference relations, PFPRs)相互转化的传统模糊偏好关系,并在此基础上定义了PFPRs的加性一致性测度,设计了加性一致性驱动的勾股模糊偏好决策方法,通过具体实例对所提勾股模糊偏好决策方法的有效性和合理性进行了数值验证。理论分析和数值验证结果表明,所提加性一致性驱动的勾股模糊偏好决策方法具有结构清晰、计算量可控、逻辑性和可操作性强、决策结果合理有效等优点。

基于模糊一致性调整算法的推荐系统评估研究

考虑到一致性调整和排序权重向量确定方法是犹豫模糊语言群决策中的2个重要课题,构造基于一致性调整算法的犹豫模糊语言群决策模型。具体来说,该模型首先运用对数最小二乘法计算犹豫模糊语言偏好关系(hesitant fuzzy linguistic preference relation,HFLPR)的排序权重向量;其次,将一致性指数最小的语言偏好关系对应的排序权重向量作为HFLPR的序权重向量;随后,基于一致性调整算法建立了一种收敛的犹豫模糊语言群决策模型。该模型既没有改变原始犹豫模糊语言术语集,又可以尽可能地避免信息的损失;最后,将建立的模型应用于推荐系统的优选过程。实验表明,构建的群决策算法更合理有效。

改进的直觉模糊得分函数及其决策应用

直觉模糊数之间的比较问题一直都是直觉模糊决策理论的核心课题。针对已有得分函数区分能力不足、构造过于复杂等问题,从全新视角出发,提出新的直觉模糊得分函数,并对其适用性进行必要拓展,定义了用于定量比较两个直觉模糊数区分程度的新可能度公式;基于所提公式,构建了适用于直觉模糊环境的新型多属性决策方法,并将其应用于具体的决策实践。理论分析和实验结果表明,新得分函数是对Ata-nassov偏序关系的精炼,能够在直觉模糊数集中建立起更为合理、可信的弱序关系;所提公式具有一定优势,能够有效拓展所提得分函数的适用性;基于可能度矩阵构建的直觉模糊多属性决策方法在决策过程中具有较强的自检能力,能够通过保证决策过程的正确性来确保最终结果的可靠性,且便于大规模决策运用。

基于多种方法的信阳市水资源系统韧性评价

随着经济社会的发展,水资源系统面临的风险日益严重,探究水资源系统韧性对合理利用水资源、促进水资源可持续发展具有重要意义。根据信阳市水资源实际情况,从抵抗性、恢复性、适应性层面选取18个指标确立信阳市水资源系统韧性评价指标体系,基于熵权法确定各评价指标权重,采用模糊综合评价法、灰关联分析法、TOPSIS法,分别从评价对象的优劣等级、评价对象与最优方案之间关联度和评价对象与最优方案的接近程度等3个方面对信阳市2012—2021年的水资源系统韧性展开评价。结果表明:模糊综合评价法能更好地界定水资源系统韧性的评价标准;基于模糊综合评价法,2012—2021年信阳市水资源系统韧性水平主要为等级Ⅱ和Ⅲ,变化趋势总体是上升的,但仍存在提升的空间。

Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game

The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan＇s binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium.

An Evaluation of Abidjan Container Terminal Competitive Position in West Africa Using a Fuzzy Quantified SWOT Framework

This article proposes a quantified SWOT framework which integrates fuzzy linguistic preference relation to evaluate the competitive position of Abidjan container terminal in West Africa. The integration of fuzzy linguistic preference relation in the quantified SWOT framework circumvents the difficulties in terms of data collection and consistency of judgment matrices prevailing in the conventional AHP and Fuzzy AHP. Moreover, the study provides relevant evidences about the key internal and external attributes shipping lines considered as important and hence the attributes that ports/ terminals most need to enhance in order to improve their attractiveness and be well positioned in the market. On the other hand, the change in terminals competitive position between 2010 and 2013 highlights that the difficulties of West African ports in attracting customers in the sub-region are not only related to internal problems such as inadequate infrastructures, facilities or inefficiency, but significant political and economic constraint outside the ports constraints their competitiveness.

Fuzzy Set Based Models and Methods of Decision Making and Power Engineering Problems

The results of research into the use of fuzzy set based models and methods of multicriteria decision making for solving power engineering problems are presented. Two general classes of models related to multiobjective (X,M> models) and multiattribute (X,R> models) problems are considered. The analysisX,M> of models is based on the use of the Bellman-Zadeh approach to decision making in a fuzzy environment. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. Several techniques based on fuzzy preference modeling are considered for the analysis of?X,R> models. A review of the authors’ results associated with the application of these models and methods for solving diverse types of problems of power system and subsystems planning and operation is presented. The recent results on the use ofX,M> andX,R> models and methods of their analysis for the allocation of reactive power sources in distribution systems and for the prioritization in maintenance planning in distribution systems, respectively, are considered.

基于区间犹豫模糊偏好关系的多属性决策方法

在现有的区间偏好关系和犹豫偏好关系基础上,首先定义了具有专家犹豫优先度的乘性一致性区间犹豫模糊偏好关系,并提出了其一致性和评价对象优先权重之间的关系;其次,基于模糊决策思想,建立线性规划模型,求出对应评价对象的区间权重向量;最后将模型应用于实例中,说明其可行性。