基于直觉梯形模糊数的信息不完全确定的多准则决策方法

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,提出一种基于直觉梯形模糊的信息不完全确定的多准则决策方法.该方法利用权系数的不完全确定信息,建立关于各方案综合直觉梯形模糊数与理想解和负理想解的Hamming距离的优化模型.通过求解优化模型可得到各准则的最优权系数,进而得到各方案与相对理想解的贴近度,再根据贴近度得到方案集的一个排序.实例分析表明了该方法的有效性和可行性.     

基于TOPSIS 的区间直觉模糊数排序法

基于传统的逼近理想解排序法(TOPSIS) 思想, 运用区间直觉模糊数的欧氏距离, 给出区间直觉模糊数相对于最大区间直觉模糊数的贴近度公式, 并给出区间直觉模糊数贴近度所具有的优良性质, 这些性质表明贴近度作为排序指标是合理的. 通过与文献中有关区间直觉模糊数排序法的对比分析, 表明基于贴近度的排序方法具有更高的区分能力. 运用新的排序指标提出一种区间直觉模糊多属性决策方法, 并通过实例表明了所提出方法的有效性．

     

区间直觉模糊连续交叉熵及其多属性决策方法

在区间直觉模糊（IVIF）环境下,利用连续有序加权平均（COWA）算子定义了一种新的区间直觉模糊数间的交叉熵,即区间直觉模糊连续交叉熵。依据提出的区间直觉模糊连续交叉熵定义了直觉模糊数间的连续交叉熵距离。基于TOPSIS的思想得到备选方案与理想方案的加权距离,并且计算备选方案与理想方案的相对贴近度,依据相对贴近度选择最优方案。其中,针对属性权重信息不完全确定条件下的决策问题,提出了以区间直觉模糊连续交叉熵最大为准则的规划模型;针对属性权重信息完全未知的情况,根据交叉熵理论确定属性权重向量。实验结果验证了新的决策方法的可行性和有效性。     

一种考虑区间直觉模糊集的多属性匹配决策方法

针对属性及属性权重均为区间直觉模糊数（IVIFN）的多属性匹配决策问题,提出一种匹配决策方法．首先根据区间直觉模糊数加权绝对值距离的定义,以逼近理想解法的思想,构建一方主体与另一方潜在对象最优匹配度的分式规划模型,并通过Charnes-Cooper变换,将原模型化为线性规划模型并求解模型得到双方的匹配度矩阵;然后,以匹配度最大为目标,建立一种双目标区间优化模型,通过线性加权转为单目标优化模型并求解得到匹配结果．最后,算例说明了所提方法的可行性和有效性．     

基于直觉梯形模糊数的信息不完全确定的多准则决策方法

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,提出一种基于直觉梯形模糊的信息不完全确定的多准则决策方法.该方法利用权系数的不完全确定信息,建立关于各方案综合直觉梯形模糊数与理想解和负理想解的Hamming距离的优化模型,通过求解优化模型可得到各准则的最优权系数,进而得到各方案与相对理想解的贴近度,再根据贴近度得到方案集的一个排序.实例分析表明了该方法的有效性和可行性.

     

考虑时间序列的动态大群体应急决策方法

针对专家权重和属性权重未知、阶段权重未知且与时间序列有关的动态大群体应急决策问题,提出一种考虑时间序列的动态大群体应急决策方法.首先,提出一个考虑区间直觉模糊数犹豫度的距离公式,定义区间直觉模糊数贴近度,综合考虑贴近度和相似度,用模糊聚类法对大群体专家偏好信息进行聚类;其次,基于现有区间直觉模糊熵公式的不足,提出一个新的区间直觉模糊熵公式,基于此公式考虑专家之间知识水平的差异和各个阶段偏好信息不具遗传性等特点,计算得出专家在不同属性下的权重和属性在各阶段下的权重;再次,考虑时间序列对各阶段权重的影响,构建相对熵模型,对阶段权重进行合理确定,进而利用加权平均算子得到整个决策过程中各方案的综合决策偏好;然后,利用区间直觉模糊数的得分函数和精确函数对方案进行排序,选出最优方案;最后,通过与以往文献的方法对比分析验证所提出方法的有效性和优越性.     

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.     

基于集成算子的改进IITFN多属性群决策方法

对区间直觉梯形模糊数决策方法进行研究。定义了区间直觉梯形模糊数期望值、得分函数和精确函数,进而给出了区间直觉梯形模糊数的一种新的排序方法。另一方面,给出了有序加权平均算子和混合集成算子。建立了基于区间直觉梯形模糊数的多属性群决策方法,给出了相应的群决策方法。实例分析验证了所提出方法的有效性。     

基于区间直觉梯形模糊数的多属性决策方法

对区间直觉梯形模糊数进行研究．探讨了区间直觉梯形模糊数的运算法则及其性质;给出了区间直觉梯形模糊数的加权算术平均和加权几何平均算子,定义了区间直觉梯形模糊数的得分函数和精确函数,进而给出其排序方法;建立了基于区间直觉梯形模糊数的多属性决策模型,并提出了相应的决策方法．实例分析验证了所提出方法的有效性．     

基于直觉梯形模糊TOPSIS的多属性群决策方法

提出一种改进的逼近理想解排序(TOPSIS)方法,即直觉梯形模糊TOPSIS多属性群决策方法。首先,应用直觉梯形模糊数形式表示方案属性偏好和属性权重信息且专家权重完全未知;然后,利用直觉梯形模糊数间距离测度和期望值及直觉梯形模糊加权平均算子来确定决策者权重信息和属性权重信息;进而给出直觉梯形模糊环境下方案优选的算法;最后,通过算例进一步说明了该直觉梯形模糊TOPSIS方法的有效性。     

A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information

This article proposes an approach to handle multi-attribute decision making (MADM) problems under the interval-valued intuitionistic fuzzy environment, in which both assessments of alternatives on attributes (hereafter, referred to as attribute values) and attribute weights are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). The notion of relative closeness is extended to interval values to accommodate IVIFN decision data, and fractional programming models are developed based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to determine a relative closeness interval where attribute weights are independently determined for each alternative. By employing a series of optimization models, a quadratic program is established for obtaining a unified attribute weight vector, whereby the individual IVIFN attribute values are aggregated into relative closeness intervals to the ideal solution for final ranking. An illustrative supplier selection problem is employed to demonstrate how to apply the proposed procedure.     

Interval-valued intuitionistic fuzzy mathematical programming method for hybrid multi-criteria group decision making with interval-valued intuitionistic fuzzy truth degrees

As an important component of group decision making, the hybrid multi-criteria group decision making (MCGDM) is very complex and interesting in real applications. The purpose of this paper is to develop a novel interval-valued intuitionistic fuzzy (IVIF) mathematical programming method for hybrid MCGDM considering alternative comparisons with hesitancy degrees. The subjective preference relations between alternatives given by each decision maker (DM) are formulated as an IVIF set (IVIFS). The IVIFSs, intuitionistic fuzzy sets (IFSs), trapezoidal fuzzy numbers (TrFNs), linguistic variables, intervals and real numbers are used to represent the multiple types of criteria values. The information of criteria weights is incomplete. The IVIFS-type consistency and inconsistency indices are defined through considering the fuzzy positive and negative ideal solutions simultaneously. To determine the criteria weights, we construct a novel bi-objective IVIF mathematical programming of minimizing the inconsistency index and meanwhile maximizing the consistency index, which is solved by the technically developed linear goal programming approach. The individual ranking order of alternatives furnished by each DM is subsequently obtained according to the comprehensive relative closeness degrees of alternatives to the fuzzy positive ideal solution. The collective ranking order of alternatives is derived through establishing a new multi-objective assignment model. A real example of critical infrastructure evaluation is provided to demonstrate the applicability and effectiveness of this method.     

An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers

This article proposes an approach to resolve multiple attribute group decision making (MAGDM) problems with interval-valued intuitionistic trapezoidal fuzzy numbers (IVITFNs). We first introduce the cut set of IVITFNs and investigate the attitudinal score and accuracy expected functions for IVITFNs. Their novelty is that they allow the comparison of IVITFNs by taking into accounting of the experts’ risk attitude. Based on these expected functions, a ranking method for IVITFNs is proposed and a ranking sensitivity analysis method with respect to the risk attitude is developed. To aggregate the information with IVITFNs, we study the desirable properties of the interval-valued intuitionistic trapezoidal fuzzy weighted geometric (IVITFWG) operator, the interval-valued intuitionistic trapezoidal fuzzy ordered weighted geometric (IVITFOWG) operator, and the interval-valued intuitionistic trapezoidal fuzzy hybrid geometric (IVITFHG) operator. It is worth noting that the aggregated value by using these operators is also an interval-valued intuitionistic trapezoidal fuzzy value. Then, based on these expected functions and aggregating operators, an approach is proposed to solve MAGDM problems in which the attribute values take the form of interval-valued intuitionistic fuzzy numbers and the expert weights take the form of real numbers. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

Fuzzy heterogeneous multiattribute decision making method for outsourcing provider selection

One of the critical activities for outsourcing success is outsourcing provider selection, which may be regarded as a type of fuzzy heterogeneous multiattribute decision making (MADM) problems with fuzzy truth degrees and incomplete weight information. The aim of this paper is to develop a new fuzzy linear programming method for solving such MADM problems. In this method, the decision maker’s preferences are given through pair-wise alternatives’ comparisons with fuzzy truth degrees, which are expressed with trapezoidal fuzzy numbers (TrFNs). Real numbers, intervals, and TrFNs are used to express heterogeneous decision information. Giving the fuzzy positive and negative ideal solutions, we define TrFN-type fuzzy consistency and inconsistency indices based on the concept of the relative closeness degrees. The attribute weights are estimated through constructing a new fuzzy linear programming model, which is solved by using the developed fuzzy linear programming method with TrFNs. The relative closeness degrees of alternatives can be calculated to generate their ranking order. An example of the IT outsourcing provider selection problem is analyzed to demonstrate the implementation process and applicability of the method proposed in this paper.     

Aggregating decision information into Atanassov's intuitionistic fuzzy numbers for heterogeneous multi-attribute group decision making

The aim of this paper is to propose a new aggregation method to solve heterogeneous MAGDM problem which involves real numbers, interval numbers, triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), linguistic values and Atanassov's intuitionistic fuzzy numbers (AIFNs). Firstly, motivated by the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS), we propose a new general method for aggregating crisp values, TFNs, TrFNs and linguistic values into AIFNs. Thus all the group decision matrices for each alternative which involves heterogeneous information are transformed into an Atanassov's intuitionistic fuzzy decision matrix which only contains AIFNs. To determine the attribute weights, a multiple objective Atanassov's intuitionistic fuzzy programming model is constructed and solved by converting it into a linear program. Subsequently, comparison analyses demonstrate that the proposed aggregated technology can overcome the drawbacks of existing methods. An example about cloud computing service evaluation is given to verify the practicality and effectiveness of the proposed method.     

Multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets

In this paper, we present a new method for multicriteria fuzzy decision making based on interval-valued intuitionistic fuzzy sets, where interval-valued intuitionistic fuzzy values are used to represent evaluating values of the decision-maker with respect to alternatives. First, we propose a new method for ranking interval-valued intuitionistic fuzzy values. Based on the proposed fuzzy ranking method of interval-valued intuitionistic fuzzy values, we propose a new method for multicriteria fuzzy decision making. The proposed multicriteria fuzzy decision making method outperforms Ye’s method (2009) due to the fact that the proposed method can overcome the drawback of Ye’s method (2009), where the drawback of Ye’s method is that it can not distinguish the ranking order between alternatives in some situations. The proposed method provides us with a useful way for dealing with multicriteria fuzzy decision making problems based on interval-valued intuitionistic fuzzy sets.