基于改进前景理论的直觉模糊随机多准则决策方法

针对方案准则值为直觉模糊数、准则权重信息部分已知的随机多准则决策问题,提出一种基于改进前景理论的决策分析方法.首先,定义一个新的记分函数,据此可将直觉模糊数转化为实数.其次,考虑到决策者并非完全理性及决策者风险态度的差异性,将决策者分为保守型、 中间型及冒险型,引入改进前景理论,根据不同决策者类型调整参数,构建改进前景决策矩阵.再次,建立以准则值总差异最大化且准则权重差异最小化为目标的非线性二次偏差优化定权模型,计算准则权重.进而,结合改进前景决策矩阵及准则权重计算各方案的综合效用值,并以此确定方案的顺序排列.最后,通过算例验证所提出直觉模糊随机多准则决策方法的有效性和合理性.     

Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets

Out of several generalizations of fuzzy set theory for various objectives, the notions introduced by Atanassov, 1983, Atanassov and Gargov, 1989 in defining intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are interesting and very useful in modeling real life problems. Ranking of interval-valued intuitionistic fuzzy sets plays a vital role in decision-making, data analysis, artificial intelligence and socioeconomic system and it was studied in Xu, 2007c, Xu and Chen, 2007a, Ye, 2009. In this paper a new method for ranking interval-valued intuitionistic fuzzy sets has been introduced and studied. The method is illustrated by numerical examples and compared with other methods. And then a new method for handling multi-criteria fuzzy decision-making problems based on interval-valued intuitionistic fuzzy sets is presented in which criterion values for alternatives are interval-valued intuitionistic fuzzy sets. The method proposed here can provide a useful way to efficiently help the decision-maker to make his decision. An illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Intuitionistic fuzzy multi-criteria decision-making method based on evidential reasoning

An approach based on interval belief degrees and fuzzy evidential reasoning analytical algorithm is developed for multi-criteria decision problems with uncertainties. The criteria weights are represented by interval numbers and criteria values by triangular intuitionistic fuzzy numbers. The proposed approach does not need to utilize the theories such as arithmetic operations for Triangular intuitionistic fuzzy numbers, for it can remove the influence of the limitations existed in the arithmetic operations. A numerical example is also provided to illustrate the rationality and utility of the proposed method.     

Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning

Linguistic hesitant fuzzy sets (LHFSs), which can be used to represent decision-makers’ qualitative preferences as well as reflect their hesitancy and inconsistency, have attracted a great deal of attention due to their flexibility and efficiency. This paper focuses on a multi-criteria decision-making approach that combines LHFSs with the evidential reasoning (ER) method. After reviewing existing studies of LHFSs, a new order relationship and Hamming distance between LHFSs are introduced and some linguistic scale functions are applied. Then, the ER algorithm is used to aggregate the distributed assessment of each alternative. Subsequently, the set of aggregated alternatives on criteria are further aggregated to get the overall value of each alternative. Furthermore, a nonlinear programming model is developed and genetic algorithms are used to obtain the optimal weights of the criteria. Finally, two illustrative examples are provided to show the feasibility and usability of the method, and comparison analysis with the existing method is made.     

A new multi-criteria weighting and ranking model for group decision-making analysis based on interval-valued hesitant fuzzy sets to selection problems

The multi-criteria group decision-making methods under fuzzy environments are developed to cope with imprecise and uncertain information for solving the complex group decision-making problems. A team of some professional experts for the assessment is established to judge candidates or alternatives among the chosen evaluation criteria. In this paper, a novel multi-criteria weighting and ranking model is introduced with interval-valued hesitant fuzzy setting, namely IVHF-MCWR, based on the group decision analysis. The interval-valued hesitant fuzzy set theory is a powerful tool to deal with uncertainty by considering some interval-values for an alternative under a set regarding assessment factors. In procedure of the proposed IVHF-MCWR model, weights of criteria as well as experts are considered to decrease the errors. In this regard, optimal criteria’ weights are computed by utilizing an extended maximizing deviation method based on IVHF-Hamming distance measure. In addition, experts’ judgments are taken into account for computing the criteria’ weights. Also, experts’ weights are determined based on proposed new IVHF technique for order performance by similarity to ideal solution method. Then, a new IVHF-index based on Hamming distance measure is introduced to compute the relative closeness coefficient for ranking the candidates or alternatives. Finally, two application examples about the location and supplier selection problems are considered to indicate the capability of the proposed IVHF-MCWR model. In addition, comparative analysis is reported to compare the proposed model and three fuzzy decision methods from the recent literature. Comparing these approaches and computational results shows that the IVHF-MCWR model works properly under uncertain conditions.     

基于区间直觉模糊集的多准则决策方法

研究基于区间直觉模糊集的多准则决策方法.首先定义了区间直觉模糊点算子,并讨论了其性质;然后对区间直觉模糊集定义了一系列得分函数,并给出两种基于区间直觉模糊集的多准则决策方法.将该方法应用于区间直觉模糊集多准则决策问题,所得结果推广了有关直觉模糊集的相关结果.     

Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making

Multi-attribute group decision making (MAGDM) is an important research topic in decision theory. In recent decades, many useful methods have been proposed to solve various MAGDM problems, but very few methods simultaneously take them into account from the perspectives of both the ranking and the magnitude of decision data, especially for the interval-valued intuitionistic fuzzy decision data. The purpose of this paper is to develop a soft computing technique based on maximizing consensus and fuzzy TOPSIS in order to solve interval-valued intuitionistic fuzzy MAGDM problems from such two aspects of decision data. To this end, we first define a consensus index from the perspective of the ranking of decision data, for measuring the degree of consensus between the individual and the group. Then, we establish an optimal model based on maximizing consensus to determine the weights of experts. Following the idea of TOPSIS, we calculate the closeness indices of the alternatives from the perspective of the magnitude of decision data. To identify the optimal alternatives and determine their optimum quantities, we further construct a multi-choice goal programming model based on the derived closeness indices. Finally, an example is given to verify the developed method and to make a comparative analysis.     

一种新的区间直觉模糊集决策方法: 区间证据组合的角度

基于证据理论,提出一种新的区间直觉模糊集决策模型.首先采用区间直觉模糊集表示属性值,将区间直觉模糊数转换为区间BPA;然后利用基于区间数的组合规则进行融合;最后将融合后的区间BPA转换为经典BPA用于决策,可直接方便地实现多属性数据的融合.该模型的优点在于:简单直观,能更有效地反映原始信息的不确定度;通用性好,可以推广到其他区间直觉模糊集的应用领域.算例结果表明了所提出模型的有效性.     

A soft computing method of performance evaluation with MCDM based on interval-valued fuzzy numbers

This study presented a new performance evaluation method for tackling fuzzy multicriteria decision-making (MCDM) problems based on combining VIKOR and interval-valued fuzzy sets. The performance evaluation problem often exists in complex administrative processes in which multiple evaluation criteria, subjective/objective assessments and fuzzy conditions have to be taken into consideration simultaneously in management. Here, the subjective, imprecise, inexact and uncertain evaluation processes are modeled as fuzzy numbers by means of linguistic terms, as fuzzy theory can provide an appropriate tool to deal with such uncertainties. However, the presentation of linguistic expressions in the form of ordinary fuzzy sets is not clear enough [15] and [21]. Interval-valued fuzzy sets can provide more flexibility [4] and [14] to represent the imprecise/vague information that results, and it can also provide a more accurate modeling. This paper presents the interval-valued fuzzy VIKOR, which aims to solve MCDM problems in which the weights and performances of criteria are unequal by using the concepts of interval-valued fuzzy sets. A case study for evaluating the performances of three major intercity bus companies from an intercity public transport system is conducted to illustrate the effectiveness of the method.     

模糊多准则决策方法研究综述

模糊多准则决策是当前决策领域的一个研究热点,在实际决策中有着广泛的应用.为此,介绍了基于模糊数、直觉模糊集和Vague集的多准则决策方法和语言多准则决策方法的研究现状,定义了直觉梯形模糊数和区间直觉梯形模糊数,扩展了模糊数和直觉模糊集.最后探讨了目前模糊多准则决策要解决的问题和发展方向.     

基于直觉模糊数的信息不完全的多准则规划方法

定义了直觉模糊数和直觉梯形模糊数及其期望值.针对权系数信息不完全确定和准则值为直觉梯形模糊数的多准则决策问题,提出了信息不完全确定的直觉梯形模糊多准则决策的规划方法.该方法利用权系数的不完全信息构造方案集综合期望值的最优线性规划模型,求解该模型得到各准则的最优权系数,进而得到各方案综合期望值的区间数.利用区间数可能度法对其进行比较,得到整个方案集的排序.实例分析说明了该方法的有效性和可行性.     

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WC-OWA算子的随机多准则决策方法

针对准则权重信息不完全确定且准则值为正态分布随机变量的多准则决策问题,提出一种基于WC—OWA算子的多准则决策方法．该方法根据正态分布3σ原则,将正态分布准则值转化为区间数．并利用连续区间有序加权平均算子集结区间数,通过方案贴近度和加权的连续区间有序加权平均算子建立非线性规划模型,利用遗传算法对模型进行求解,得到准则的最优权系数,进而确定方案的排序．实例分析表明了所提出方法的有效性和可行性．     

基于情绪感知的语言多属性决策方法

情绪对于决策有着重要影响,由于缺乏有效的决策者情绪状态获取方法,当前考虑情绪状态的语言多属性决策方法研究偏少.随着物联网技术的发展,通过可穿戴传感器能够便捷地获取决策者脑电信号,进而可感知其情绪状态.为此,研究基于情绪感知的语言多属性决策方法.首先,提出基于SVM概率输出模型的情绪感知方法,根据决策者脑电信号,实时、准确感知决策者情绪状态的概率分布;其次,提出基于云模型的语言评价定量化方法,一方面考虑语言评价的模糊性与随机性,另一方面考虑决策者情绪状态因素,定量化语言评价;然后,提出基于前景理论的方案排序方法,在情绪泛化假设下,根据综合前景值将各方案排序;最后,通过实例验证该决策方法的可行性和有效性.     

Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets

Decision making is one of the most complex administrative processes in management. In circumstances where the members of the decision making team are uncertain in determining and defining the decision making criteria, fuzzy theory provides a proper tool to encounter with such uncertainties. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper the interval-valued fuzzy TOPSIS method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy sets concepts.     

基于直觉模糊熵的直觉语言多准则决策方法

针对现有直觉模糊熵方法中存在的一些问题,提出一种新的直觉模糊熵,并将其与现有的几种直觉模糊熵计算结果进行比较.针对准则权重信息不完全且准则值为直觉语言数的多准则决策问题,通过建立基于模糊熵的决策模型来求解准则的最优权系数,并利用直觉语言加权算数平均算子(IL-WAA)求出方案的综合准则值,进而由直觉语言数的记分函数确定方案的排序.最后,通过算例分析验证了该方法的有效性和合理性.     

Group multi-criteria decision making based upon interval-valued fuzzy numbers: An extension of the MULTIMOORA method

Multi criteria decision making (MCDM) often involves uncertainty which can be tackled by employing the fuzzy set theory. Type-2 fuzzy sets offer certain additional means for the latter purpose. This paper therefore extends the MULTIMOORA method with type-2 fuzzy sets viz. generalized interval-valued trapezoidal fuzzy numbers. The proposed method thus provides the means for multi-criteria decision making related to uncertain assessments. Utilization of aggregation operators also enables to facilitate group multi-criteria decision making. A numerical example of personnel selection demonstrates the possibilities of application of the proposed method in the field of human resource management and performance management in general.     

基于前景理论的风险型混合模糊多准则群决策

针对准则值为模糊数的风险型多准则群决策问题,提出一种基于前景理论的多准则群决策方法.首先运用方差分析原理构建群决策参考点;然后分析区间数、三角模糊数、梯形模糊数等无量纲化方法,给出各类模糊数的价值函数计算方法,并提出群体信息集成决策步骤;最后通过算例表明所提出方法的有效性和可行性.     

基于期望值-混合熵的区间概率模糊随机多准则决策方法

定义了区间概率模糊随机变量及其期望值和混合熵.针对准则权重确知并且准则值为区间概率模糊随机变量的多准则决策问题,提出一种基于期望值-混合熵的决策方法.该方法首先给出了区间概率模糊随机变量的期望值-混合熵度量;然后基于此度量建立优化模型,通过计算得到各方案的期望值-混合熵区间;再采用可能度的方法得到方案集的排序.最后通过实例说明了该方法的有效性和可行性.