多值直觉模糊软集

将多值直觉模糊集和软集相结合,提出了多值直觉模糊软集的概念。给出了多值直觉模糊软集的补、交、并“、且”“、或”运算的概念,并基于这些概念研究了若干性质。     

区间直觉模糊连续熵及其多属性决策方法

提出了区间直觉模糊连续熵,并且研究了一种新的处理区间直觉模糊多属性决策问题的方法。基于连续有序加权平均（COWA）算子,给出了区间直觉模糊连续熵的概念,并且证明了区间直觉模糊连续熵满足区间直觉模糊熵的公理化定义的四个条件。在此基础上,针对属性权重信息完全未知的决策问题,通过衡量每一属性所含的信息量来确定属性权重。依据备选方案与理想方案间的加权相关系数,给出了一种新的区间直觉模糊多属性决策方法。实验结果验证了新的决策方法的可行性和有效性。     

直觉模糊多属性决策方法综述

直觉模糊多属性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.按照直觉模糊集的发展形式:直觉模糊集、区间直觉模糊集、直觉三角模糊数和直觉梯形模糊数,分别介绍它们在多属性决策与群决策中的研究现状,并对其未来的发展方向进行了探讨与展望.     

直觉模糊多属性决策的新方法

针对属性值以直觉模糊数形式给出的多属性决策中确定属性权重的问题,提出了一种直觉模糊数熵权的确定方法,依照传统权熵的确定方法的思路,通过一个公式求得直觉模糊熵;然后求得属性的信息熵;根据传统熵权确定公式得到属性权重,进而利用得分函数对方案进行排序;最后通过算例说明该方法的有效性和实用性。     

用区间直觉模糊集方法对属性权重未知的群求解其多属性决策

本文首先提出群区间直觉模糊有序加权几何(groupinterval-valuedintuitionistic fuzzy orderedweighted geometric,GIVIFOWG)算子和群区间直觉模糊有序加权平均(group interval-valued intuitionistic fuzzy ordered weighted averaging,GIVIFOWA)算子.利用GIVIFOWG算子或GIVIFOWA算子聚集群的决策矩阵以获得方案在属性上的综合区间直觉模糊决策矩阵(collectiveinterval-valuedintuitionistic fuzzy decision-matrix,CIVIFDM).然后定义了一个考虑犹豫度的区间直觉模糊熵(interval-valuedintuitionistic fuzzyentropy,IVIFE);通过熵衡量每个属性所含的信息来求解属性权重.最后,提出基于可能度的接近理想解的区间排序法(interval technique for order preference by similarity to an ideal solution,ITOPSIS)和区间得分函数法.在ITOPSIS法中,依据区间距离公式计算候选方案和理想方案的属性加权区间距离,进而采用ITOPSIS准则对各方案进行排序;在区间得分函数法中,算出CIVIFDM中各方案的得分值以及精确值,然后利用区间得分准则对各方案进行排序.实验结果验证了决策方法的有效性和可行性.     

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．     

基于改进熵和新得分函数的区间直觉模糊多属性决策

针对决策信息为区间直觉模糊数且属性权重完全未知的多属性决策问题, 提出基于改进的区间直觉模糊熵和新得分函数的决策方法. 首先, 利用改进的区间直觉模糊熵确定属性权重; 然后, 利用区间直觉模糊加权算术平均算子集成信息, 得到各备选方案的综合属性值, 进而指出现有得分函数存在排序失效或排序不符合实际的不足, 同时给出一个新的得分函数, 并以此对方案进行排序; 最后, 通过实例表明了所提出方法的有效性.

     

基于区间值Vague集的多属性模糊决策方法

区间值Vague集作为Vague集的一种有用推广,已经在系统控制以及智能决策等方面有较为广泛的研究与应用.针对不确定系统处理中常出现的模糊决策问题,通过将决策方案的约束条件属性集转化成区间值Vague集,并综合考虑约束条件属性肯定出现的区间值程度以及肯定不出现的区间值程度和未知是否出现的含糊(犹豫)程度区间,给出一个基于区间值Vague数的记分函数和区间值Vague集的有效的多属性模糊决策方法,使得决策更加合理更具弹性.最后通过一个实例表明我们所提出的方法在不确定系统决策中确是简便可行的.     

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.     

广义区间梯形模糊软集在群偏好集结中的应用

针对群推荐中个体偏好信息如何集成群体偏好信息,不同用户对商品关注的属性不完全相同,以及用户对商品属性权重分配不同的复杂问题,提出区间梯形模糊软集的群偏好集结模型。首先,结合广义区间梯形模糊集和软集的概念建立广义区间梯形模糊软集的概念,定义其基本运算性质;其次,将模糊语言映射成广义区间梯形模糊数,利用广义区间梯形模糊软集的并、交运算,以及广义区间梯形模糊数的重心算法进行排序,将个体用户的偏好信息集结成群偏好信息;最后,以汽车的推荐为例介绍群偏好集结算法。算例结果显示,用该模型解决群体偏好集结是合理和有效的。     

A new multiple criteria decision making method based on intuitionistic fuzzy information

The risk attitude of a decision maker is considered in the decision process. Inspired by mean-variance type utility functions in the financial risk management, a new class of decision functions are defined based on the weighted score function and the weighted accuracy function in the intuitionistic fuzzy setting. By choosing a suitable parameter value, the decision maker’s risk attitude can be flexibly reflected by our decision function. The new method can be applied for both the exactly known and partly known criteria weight situations. For the latter case, it is only necessary to solve one linear programming problem. The developed models and algorithms are then extended to multiple criteria decision making problems with the interval-valued intuitionistic fuzzy information. Numerical examples are provided to illustrate the practicality, flexibility and efficiency of our new algorithms.     

A possibility degree method for interval-valued intuitionistic fuzzy multi-attribute group decision making

The ranking of interval-valued intuitionistic fuzzy sets (IVIFSs) is very important for the interval-valued intuitionistic fuzzy decision making. From the probability viewpoint, the possibility degree of comparison between two interval-valued intuitionistic fuzzy numbers (IVIFNs) is defined by using the notion of 2-dimensional random vector, and a new method is then developed to rank IVIFNs. Hereby the ordered weighted average operator and hybrid weighted average operator for IVIFNs are defined based on the Karnik–Mendel algorithms and employed to solve multi-attribute group decision making problems with IVIFNs. The individual overall attribute values of alternatives are obtained by using the weighted average operator for IVIFNs. By using the hybrid weighted average operator for IVIFNs, we can obtain the collective overall attribute values of alternatives, which are used to rank the alternatives. A numerical example is examined to illustrate the effectiveness and flexibility of the proposed method in this paper.     

A method based on distance measure for interval-valued intuitionistic fuzzy group decision making

In this paper we introduce some relations and operations of interval-valued intuitionistic fuzzy numbers and define some types of matrices, including interval-valued intuitionistic fuzzy matrix, interval-valued intuitionistic fuzzy similarity matrix and interval-valued intuitionistic fuzzy equivalence matrix. We study their properties, develop a method based on distance measure for group decision making with interval-valued intuitionistic fuzzy matrices and, finally, provide an illustrative example.     

A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets

In this paper we present a new approach to solve multi-attribute decision making problems in intuitionistic fuzzy environment. This approach is based on a new ranking method of intuitionistic fuzzy sets, in which the evaluated values (in the form of intervals) of the same alternative with different attributes are considered as one unified entity. According to people’s intuition, the ranking method proposed in this paper is mainly grounded on a revised score function and a revised accuracy function of intuitionistic fuzzy sets. Different from the traditional methods, in this new approach, the degree of membership, the degree of nonmembership and the degree of hesitation are considered with various importance in reflecting the true image of the respective alternative. Furthermore, an optimization model is established to estimate the relative degree of importance of each quantity. Finally, two practical examples are provided to illustrate our approach.     

广义直觉模糊几何Bonferroni平均及其多属性决策

针对直觉模糊环境中的信息集成问题,基于阿基米德T-范数和S-范数,提出新的广义直觉模糊几何Bonferroni平均算子。该算子不仅能够考虑到每种属性的重要性,而且可以有效地捕获属性间的内在联系。首先,基于阿基米德T-范数和S-范数的直觉模糊运算法则,提出一种新的广义直觉模糊几何Bonferroni平均算子,并研究该算子的几种优良性质,包括幂等性、单调性、有界性和置换不变性;其次,探讨了广义直觉模糊几何Bonferroni平均算子的几类特殊形式;最后,基于提出的算子构建一种新的直觉模糊多属性决策方法,并结合区域经济发展研究实例。实验结果表明,提出的决策方法是可行的和有效的,并且使得决策者能够依据其态度进行决策。     

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.     

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.     

基于区间直觉模糊集的模糊多目标群决策

为提高数据决策的准确性,结合区间直觉模糊集理论,对模糊多目标群决策算法进行优化。并针对部分权重信息并不一定完整的情况,利用迭代计算的方式向最优决策逐步逼近。实例显示,该算法具有时间复杂度低、便于计算机实现等特点,并说明了算法的有效性和准确性。