多方参与决策且指标集有差异的方案排序方法

针对多方参与决策且指标集有差异的群体决策问题,提出一种基于模糊软集理论的方案排序方法.依据各方决策者所考虑的指标参数和打分值信息给出多方决策信息的模糊软集表示方法,并利用模糊软集的且运算得到综合各方决策者所考虑指标参数的新模糊软集及其隶属度矩阵;然后在考虑指标权重的前提下构建关于方案的加权比较矩阵,进而通过计算得出的各方案优势度确定方案的排序结果;最后,通过一个算例表明了所提出方法的可行性和有效性.     

A measurement model for experts knowledge-based systems algorithm using fuzzy analytic network process

This study proposes an experts knowledge-based systems measurement model, the model using fuzzy analytic network process (FANP) to resolve the uncertainty and imprecision of evaluations during pre-negotiation stages, where the comparison judgments of a decision maker are represented as fuzzy triangular numbers. A novel fuzzy prioritization method, which derives crisp priorities (criteria weights and scores of alternatives) from consistent and inconsistent fuzzy comparison matrices, is also proposed. The applicability of the proposed model is demonstrated in a government purchase digital video recorder (DVR) system project study. The stability tests indicate the advantages of the proposal model in determining the value of model. Importantly, the proposed model can provide decision makers a reference material, making it highly applicable for academic and commercial purposes.     

Robot selection by using generalized interval-valued fuzzy numbers with TOPSIS

The aim of this paper is to propose a method to aggregate the opinion of several decision makers on different criteria, regarding a set of alternatives, where the judgment of the decision makers are represented by generalized interval-valued trapezoidal fuzzy numbers. A generalized interval valued trapezoidal fuzzy number based technique for order preference by similarity to ideal solution is proposed that can reflect subjective judgment and objective information in real life. The weights of criteria and performance rating values of criteria are linguistic variables expressed as generalized interval-valued trapezoidal fuzzy numbers. Finally, an illustrative example is provided to elaborate the proposed method for the selection of a suitable robot according to our requirements.     

基于前景理论的犹豫模糊TOPSIS多属性决策方法

针对属性权重未知、属性值为犹豫模糊集的决策问题,提出一种前景理论和逼近理想解(TOPSIS)相结合的多属性决策方法.考虑到决策者对指标集的不同偏好,利用犹豫模糊熵的相关理论,提出一种基于犹豫模糊熵的熵权法确定属性权重.将决策者的风险心理因素引入犹豫模糊多属性决策中,定义了犹豫模糊数的前景价值函数,并以此将犹豫模糊决策矩阵转化为价值矩阵,计算出各方案的收益损失比值.最终应用TOPSIS的基本思路,确定备选方案的优劣排序,并通过算例分析验证了所提出方法的有效性.     

多粒度支持直觉模糊粗糙集的多属性决策方法

针对多属性决策中多个相互冲突的属性信息使决策者很难做出决策判断的问题,文中从支持直觉模糊集的角度研究该问题.首先,在支持直觉模糊集的基础上,结合多粒度粗糙集理论,构造乐观、悲观两种多粒度支持直觉模糊粗糙集模型,分析两种模型之间的相互关系,讨论相关性质.然后,利用t-模和t-余模定义拟合函数,提出多粒度支持直觉模糊粗糙集的多属性决策求解方法,同时定义得分函数和精确函数排序决策结果,提取相应的决策规则,设计算法.实例分析表明,文中方法使决策者在处理信息冲突的多属性决策问题时可根据实际需求选择最优决策方案     

A new preference scale mcdm method based on interval-valued intuitionistic fuzzy sets and the analytic hierarchy process

The intuitionistic fuzzy analytic hierarchy process (IF-AHP), in which intuitionistic fuzzy numbers are utilized in defining decision makers’ linguistic judgment, has been used to solve various multi-criteria decision-making problems. Previous theories have suggested that interval-valued intuitionistic fuzzy numbers (IVIFN) with hesitation degree can act as alternative fuzzy numbers that can handle vagueness and uncertainty. This paper proposes a new preference scale in the framework of the interval-valued intuitionistic fuzzy analytic hierarchy process (IVIF-AHP). The comparison matrix judgment is expressed in IVIFN with degree of hesitation. The proposed new preference scale concurrently considers the membership function, the non-membership function and the degree of hesitation of IVIFN. To define the weight entropy of the aggregated matrix of IVIFN, a modified interval-valued intuitionistic fuzzy weighted averaging is proposed, by considering the interval number of the hesitation degree. Three multi-criteria decision-making problems are used to test the proposed method. A comparison of the results is also presented to check the feasibility of the proposed method. It is shown that the ranking order of the proposed method is slightly different from that of the other two methods because of the inclusion of the hesitation degree in defining the preference scale.     

一种改进的模糊软集多参数决策方法

模糊软集多参数决策方法中经常将Zadeh交与代数积使用在数据融合方法中,在一些实际应用中会产生信息缺失,导致决策者无法做出准确的选择。针对这一问题,结合Einstein运算法则提出一种新的数据融合方法,用于解决信息缺失和对象无法排序的问题。所提出的基于模糊软集的多参数决策方法是通过Einstein积运算进行多个参数集合的整合,从而得到一个合成模糊软集,再由合成模糊软集计算得到对照矩阵与得分表,最终得到对象的全排序,为决策者提供判断依据。通过实例结果,可以验证新方法在决策问题中的正确性和有效性。     

A fuzzy group-preferences analysis method for new-product development

This paper reports a new idea-screening method for new product development (NPD) with a group of decision makers having imprecise, inconsistent and uncertain preferences. The traditional NPD analysis method determines the solution using the membership function of fuzzy sets which cannot treat negative evidence. The advantage of vague sets, with the capability of representing negative evidence, is that they support the decision makers with the ability of modeling uncertain opinions. In this paper, we present a new method for new-product screening in the NPD process by relaxing a number of assumptions so that imprecise, inconsistent and uncertain ratings can be considered. In addition, a new similarity measure for vague sets is introduced to produce a ratings aggregation for a group of decision makers. Numerical illustrations show that the proposed model can outperform conventional fuzzy methods. It is able to provide decision makers (DMs) with consistent information and to model situations where vague and ill-defined information exist in the decision process.     

A fuzzy group-preferences analysis method for new-product development

This paper reports a new idea-screening method for new product development (NPD) with a group of decision makers having imprecise, inconsistent and uncertain preferences. The traditional NPD analysis method determines the solution using the membership function of fuzzy sets which cannot treat negative evidence. The advantage of vague sets, with the capability of representing negative evidence, is that they support the decision makers with the ability of modeling uncertain opinions. In this paper, we present a new method for new-product screening in the NPD process by relaxing a number of assumptions so that imprecise, inconsistent and uncertain ratings can be considered. In addition, a new similarity measure for vague sets is introduced to produce a ratings aggregation for a group of decision makers. Numerical illustrations show that the proposed model can outperform conventional fuzzy methods. It is able to provide decision makers (DMs) with consistent information and to model situations where vague and ill-defined information exist in the decision process.     

犹豫直觉模糊集的知识测度及其应用

犹豫直觉模糊集集成了直觉模糊集与犹豫模糊集的优点,能够更好地处理决策者偏好不一致时的不确定性问题。通过考虑决策者提供信息的犹豫性与模糊性,给出了犹豫直觉模糊集上知识测度的公理化定义,并且构建出犹豫直觉模糊集上一类含参知识测度,这类知识测度可以有效地刻画犹豫直觉模糊集所包含的信息量和决策者的态度特征。接下来,基于对该类知识测度中的参数进行讨论,得到一系列代表决策者不同态度特征的知识测度,进一步验证了知识测度与决策者态度系数的变化成正比。最后,基于犹豫直觉模糊集的知识测度提出多属性群决策方法,并将此方法应用于某互联网公司的空调安装公司选择的案例中,证明了所提出的知识测度具有有效性与实用性。     

考虑外部环境变化的分阶段动态群决策方法

研究决策者权重部分未知的概率犹豫模糊分阶段动态群决策问题.针对外部环境的变化,结合符号距离测度,提出考虑外部环境变化的分阶段群决策方法.首先,基于元素的方差及个数差异定义概率犹豫模糊元的犹豫度公式,并在此基础上定义概率犹豫模糊元的符号距离公式.然后,根据外部环境的变化会导致每个时序阶段获得的信息存在差异的特点,构建动态决策模型以确定各个时序阶段的决策者权重,进而分阶段集结信息,形成决策过程方案链.最后,通过算例分析验证了所提出方法的有效性与合理性.     

Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q‐rung orthopair fuzzy environment

A Q‐rung orthopair fuzzy set (q‐ROFS) originally proposed by Yager (2017) is a new generalization of orthopair fuzzy sets, which has a larger representation space of acceptable membership grades and gives decision makers more flexibility to express their real preferences. In this paper, for multiple attribute decision‐making problems with q‐rung orthopair fuzzy information, we propose a new method for dealing with heterogeneous relationship among attributes and unknown attribute weight information. First, we present two novel q‐rung orthopair fuzzy extended Bonferroni mean (q‐ROFEBM) operator and its weighted form (q‐ROFEWEBM). A comparative example is provided to illustrate the advantages of the new operators, that is, they can effectively model the heterogeneous relationship among attributes. We prove that some existing known intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are special cases of the proposed q‐ROFEBM and q‐ROFEWEBM operators. Meanwhile, several desirable properties are also investigated. Then, a new knowledge‐based entropy measure for q‐ROFSs is also proposed to obtain the attribute weights. Based on the proposed q‐ROFWEBM and the new entropy measure, a new method is developed to solve multiple attribute decision making problems with q‐ROFSs. Finally, an illustrative example is given to demonstrate the application process of the proposed method, and a comparison analysis with other existing representative methods is also conducted to show its validity and superiority.     

Interactive fuzzy programming for fuzzy random two-level linear programming problems through probability maximization with possibility

This paper considers two-level linear programming problems involving fuzzy random variables under cooperative behavior of the decision makers. Through the introduction of fuzzy goals together with possibility measures, the formulated fuzzy random two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. By adopting probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.     

Interactive fuzzy stochastic multi-level 0–1 programming using tabu search and probability maximization

In this paper, we consider interactive fuzzy programming for multi-level 0–1 programming problems involving random variable coefficients both in objective functions and constraints. Following the probability maximization model together with the concept of chance constraints, the formulated stochastic multi-level 0–1 programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present interactive fuzzy programming. In the proposed interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating satisfactory levels of the decision makers with considerations of overall satisfactory balance among all levels. For solving the transformed deterministic problems efficiently, we also introduce novel tabu search for general 0–1 programming problems. A numerical example for a three-level 0–1 programming problem is provided to illustrate the proposed method.     

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。     

Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP

The lack of consistency in decision making can lead to inconsistent conclusions. In fuzzy analytic hierarchy process (fuzzy AHP) method, it is difficult to ensure a consistent pairwise comparison. Furthermore, establishing a pairwise comparison matrix requires judgments for a level with n criteria (alternatives). The number of comparisons increases as the number of criteria increases. Therefore, the decision makers judgments will most likely be inconsistent. To alleviate inconsistencies, this study applies fuzzy linguistic preference relations (Fuzzy LinPreRa) to construct a pairwise comparison matrix with additive reciprocal property and consistency. In this study, the fuzzy AHP method is reviewed, and then the Fuzzy LinPreRa method is proposed. Finally, the presented method is applied to the example addressed by Kahraman et al. [C. Kahraman, D. Ruan, I. Do?an, Fuzzy group decision making for facility location selection, Information Sciences 157 (2003) 135-153]. This study reveals that the proposed method yields consistent decision rankings from only n − 1 pairwise comparisons, which is the same result as in Kahraman et al. research. The presented fuzzy linguistic preference relations method is an easy and practical way to provide a mechanism for improving consistency in fuzzy AHP method.     

Development of an interval-valued fuzzy linear-programming method based on infinite α-cuts for water resources management

An interval-valued fuzzy linear-programming (IVFL) method based on infinite α-cuts is developed for water resources management in this study. The introduction of interval parameters and interval-valued fuzzy parameters into the objective function and constraints makes it possible for dealing with individual uncertainty and dual uncertainties existing in many real-world cases. A two-step infinite α-cuts (TSI) solution method is communicated to the solution process to discretize infinite α-cuts to interval-valued fuzzy membership functions. Application to an agricultural irrigation problem indicates that interval-valued fuzzy sets can represent dual uncertainties in modeling parameters, and the solution method is able to generate decisions with enhanced reliability. It is also indicated that the objective (i.e. system net benefit) can be increased with the growth of violation risk, in association with a set of different allocation schemes. As the key segment of interval-valued fuzzy membership functions that could significantly affect system performance can be identified through the analysis of decision alternatives under different risk levels of constraint violation, the IVFL method provides decision makers flexibility in selecting an appropriate decision scheme according to their preference and practical conditions.     

Hesitant fuzzy best-worst multi-criteria decision-making method and its applications

Best-worst method (BWM) is extended to uncertain situations, hesitant fuzzy best-worst method (HFBWM) is proposed by using hesitant fuzzy multiplicative preference relation for multiple-criteria group decision-making problems. The reference comparison of the best criterion and the worst criterion are described by the linguistic terms, which are expressed in hesitant fuzzy elements, of the decision makers. Weights of criteria are calculated by using score function. Using the concept of BWM, nonlinearly constrained optimization problems are formed to obtain hesitant fuzzy weights (HFWs) of different criteria and alternatives. To check the reliability of the HFBWM, consistency ratio is proposed. The advantage and suitability of the proposed HFBWM are determined by three case studies. The results indicate that the HFBWM, due to higher comparison consistency as compared to BWM, obtain plausible preference ranking for alternatives.     

基于毕达哥拉斯模糊幂加权平均算子的多属性群决策方法

研究了毕达哥拉斯模糊环境下的多属性群决策问题。首先,将毕达哥拉斯模糊信息引入幂平均加权算子,提出毕达哥拉斯模糊幂加权平均（PFPWA） 算子,并研究所提算子的基本性质。然后,在毕达哥拉斯模糊数（PFN） 为信息输入的框架内,提出基于毕达哥拉斯模糊幂加权平均算子的群决策方法。所提出的方法使用毕达哥斯拉信息使得决策者的信息表达更加灵活,并且在信息集结过程中采用幂加权平均算子能够同时考虑专家权威与评估信息的可信度。最后,通过案例分析验证了所提方法的可行性和有效性。     

An integrated method for supplier selection from the perspective of risk aversion

A lot of investigations have been published in the supplier selection area. However, few papers consider the problem from the perspective of risk aversion. In this paper, generalized intuitionistic fuzzy soft set (GIFSS) combined with extending gray relational analysis (GRA) method is proposed to select an appropriate supplier from the perspective of risk aversion in group decision-making environment. The proposed approach consists of two phases. In the first phase, the weights of decision makers are determined by using an extended GRA method with intuitionistic fuzzy soft set (IFSS). In traditional GRA method, the ideal reference is expressed in a vector, while, in this paper, the ideal reference for all individual decisions is expressed in a matrix, which is suitable for risk aversion. The weight of decision makers is utilized to aggregate individual opinions of decision makers. In the next phase, to eliminate the bias of decision makers in the choice of supplier and rule out the possibility of errors occurring in the evaluation of alternatives, the general manager will further validate it by utilized the GIFSS. Finally, a numerical example for supplier selection is given to illustrate application of the method, and the comparisons with other methods are also made.