基于不完备信息系统的三角模糊数决策粗糙集

在不完备信息系统中,针对用区间值表示一个未知参量时,整个区间内取值机会被认为是均等的,得到的结果可能会产生过大误差的问题,将三角模糊数引入到决策粗糙集中,提出了一种基于不完备信息系统的三角模糊数决策粗糙集。首先,定义了一种描述不完备信息的相似关系;然后,针对不完备信息系统中的缺失值,利用三角模糊数来获取损失函数,构建了三角模糊数决策粗糙集模型;实例表明,本文提出的方法不仅能够弥补用区间数表示的不足,而且可以突出可能性最大的主值,从而减少分类误差。     

区间直觉模糊信息的集成方法及其在决策中的应用

对区间直觉模糊信息的集成方法进行了研究.定义了区间直觉模糊数的一些运算法则,并基于这些运算法则,给出区间直觉模糊数的加权算术和加权几何集成算子.定义了区间直觉模糊数的得分函数和精确函数,进而给出了区间直觉模糊数的一种简单的排序方法.最后提供了一种基于区间直觉模糊信息的决策途径,并进行了实例分析.     

模糊数决策粗糙集

考虑到实际决策问题中损失函数的不确定性特征,从贝叶斯理论出发,将模糊数损失函数引入决策粗糙集,提出模糊数决策粗糙集模型。首先,讨论在贝叶斯期望风险最小决策的语义下模糊数决策粗集理论基本模型的构建过程。其次,分析模糊数决策粗集理论的相关数学性质和准则。最后,通过一个企业信用评佑问题来阐明模糊数决策粗糙集模型的应用过程。     

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.     

基于区间二型模糊熵的多属性决策方法

针对属性权重信息完全未知的区间二型模糊多属性决策问题,提出了一种基于区间二型模糊熵的多属性决策方法。为了量化区间二型模糊集的不确定信息,通过引入模糊因子、犹豫因子和区间因子建立了区间二型模糊熵的公理化准则,并分别基于欧氏距离、海明距离和广义距离给出了三种熵计算公式。同时,根据决策问题中总体不确定性最小化的原则,结合熵公式构建数学规划模型来确定属性权重,利用得分函数给出了具体的决策步骤,并通过实例分析验证了该决策方法的有效性和灵活性。     

基于直觉模糊集改进算子的多目标决策方法

定义了三角和区间直觉模糊集的一些运算法则,给出了直觉模糊集两个改进算子,即三角模糊数加权算术平均算子（FIFWAA） 和区间直觉模糊数加权几何平均算子（FIFWGA）。在此基础上, 提出用精确函数解决记分函数无法决策的问题,以保证记分函数的严密性与合理性。给出了一种属性权重不完全确定且属性值以三角和区间直觉模糊数给出的多目标决策方法,通过实例分析结果证明了运用直觉模糊集改进算子进行多目标决策方法的有效性和正确性。     

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。     

基于模糊数风险最小化的拓展决策粗糙集模型

决策粗糙集模型中损失函数一般是基于单值的。考虑到实际决策问题中损失函数的不确定特征,为了处理一般的情形,引入模糊数来表示损失函数。从模糊数学的角度出发,通过一系列模糊运算得出决策阈值α、β的模糊分布,并据此给出决策规则。同时,对比区间决策粗糙集模型,给出获得更紧凑的阈值α、β上、下确界的方法。最后,通过一个石油投资的例子来阐明该模型的应用过程。     

基于灰色关联分析和D-S证据理论的区间直觉模糊决策方法

针对方案的指标值为区间直觉模糊数的决策问题,提出了一种基于灰色关联分析和D-S证据理论的决策方法. 定义了区间记分函数和区间数点算子, 并通过其将区间直觉模糊数转化为记分函数;利用记分函数以及灰色关联方法确定各指标的不确信度, 进而构建出不同指标下各方案的Mass函数, 通过D-S合成法则进行信息融合,确定最优方案.最后,通过算例表明, 本文提出的方法可得到满意结果并显著降低决策的不确定性.     

基于二元联系数的区间直觉模糊数多准则决策方法

针对准则值为区间直觉模糊数且准则权重为区间数的多准则决策问题,提出一种基于二元联系数的区间直觉模糊型多准则决策方法.首先,介绍区间直觉模糊数和二元联系数;其次,研究区间数转化为联系数、二元联系数转化为实数的3种转化方法,对传统区间数和二元联系数的运算结果进行比较;再次,将区间型贴近度转化为基于二元联系数的实数进行方案优选;最后,运用算例表明所提出方法的优越性和可行性.     

A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets

Ranking methods, similarity measures and uncertainty measures are very important concepts for interval type-2 fuzzy sets (IT2 FSs). So far, there is only one ranking method for such sets, whereas there are many similarity and uncertainty measures. A new ranking method and a new similarity measure for IT2 FSs are proposed in this paper. All these ranking methods, similarity measures and uncertainty measures are compared based on real survey data and then the most suitable ranking method, similarity measure and uncertainty measure that can be used in the computing with words paradigm are suggested. The results are useful in understanding the uncertainties associated with linguistic terms and hence how to use them effectively in survey design and linguistic information processing.     

Interval type-2 fuzzy membership function generation methods for pattern recognition

Type-2 fuzzy sets (T2 FSs) have been shown to manage uncertainty more effectively than T1 fuzzy sets (T1 FSs) in several areas of engineering [4], [6], [7], [8], [9], [10], [11], [12], [15], [16], [17], [18], [21], [22], [23], [24], [25], [26], [27] and [30]. However, computing with T2 FSs can require undesirably large amount of computations since it involves numerous embedded T2 FSs. To reduce the complexity, interval type-2 fuzzy sets (IT2 FSs) can be used, since the secondary memberships are all equal to one [21]. In this paper, three novel interval type-2 fuzzy membership function (IT2 FMF) generation methods are proposed. The methods are based on heuristics, histograms, and interval type-2 fuzzy C-means. The performance of the methods is evaluated by applying them to back-propagation neural networks (BPNNs). Experimental results for several data sets are given to show the effectiveness of the proposed membership assignments.     

Uncertainty measures for interval type-2 fuzzy sets

Fuzziness (entropy) is a commonly used measure of uncertainty for type-1 fuzzy sets. For interval type-2 fuzzy sets (IT2 FSs), centroid, cardinality, fuzziness, variance and skewness are all measures of uncertainties. The centroid of an IT2 FS has been defined by Karnik and Mendel. In this paper, the other four concepts are defined. All definitions use a Representation Theorem for IT2 FSs. Formulas for computing the cardinality, fuzziness, variance and skewness of an IT2 FS are derived. These definitions should be useful in IT2 fuzzy logic systems design using the principles of uncertainty, and in measuring the similarity between two IT2 FSs.     

Parameter Optimization of Interval Type-2 Fuzzy Neural Networks Based on PSO and BBBC Methods

Interval type-2 fuzzy neural networks (IT2FNNs) can be seen as the hybridization of interval type-2 fuzzy systems (IT2FSs) and neural networks (NNs). Thus, they naturally inherit the merits of both IT2FSs and NNs. Although IT2FNNs have more advantages in processing uncertain, incomplete, or imprecise information compared to their type-1 counterparts, a large number of parameters need to be tuned in the IT2FNNs, which increases the difficulties of their design. In this paper, big bang-big crunch (BBBC) optimization and particle swarm optimization (PSO) are applied in the parameter optimization for Takagi-Sugeno-Kang (TSK) type IT2FNNs. The employment of the BBBC and PSO strategies can eliminate the need of backpropagation computation. The computing problem is converted to a simple feed-forward IT2FNNs learning. The adoption of the BBBC or the PSO will not only simplify the design of the IT2FNNs, but will also increase identification accuracy when compared with present methods. The proposed optimization based strategies are tested with three types of interval type-2 fuzzy membership functions (IT2FMFs) and deployed on three typical identification models. Simulation results certify the effectiveness of the proposed parameter optimization methods for the IT2FNNs.      

区间二型模糊相似度与包含度

相似度与包含度是模糊集合理论中的两个重要概念,但对于二型模糊集合的研究还较为少见．鉴于此,提出了新的区间二型模糊相似度与包含度．首先选择了二者的公理化定义;然后基于公理化定义提出了新的计算公式,并讨论了二者的相互转换关系;最后通过实例来验证二者的性能,并将区间二型模糊相似度与Yang-Shih聚类方法相结合,用于高斯区间二型模糊集合的聚类分析,得到了合理的层次聚类树．仿真实例表明新测度具有一定的实用价值．     

Aggregation Using the Linguistic Weighted Average and Interval Type-2 Fuzzy Sets

The focus of this paper is the linguistic weighted average (LWA), where the weights are always words modeled as interval type-2 fuzzy sets (IT2 FSs), and the attributes may also (but do not have to) be words modeled as IT2 FSs; consequently, the output of the LWA is an IT2 FS. The LWA can be viewed as a generalization of the fuzzy weighted average (FWA) where the type-1 fuzzy inputs are replaced by IT2 FSs. This paper presents the theory, algorithms, and an application of the LWA. It is shown that finding the LWA can be decomposed into finding two FWAs. Since the LWA can model more uncertainties, it should have wide applications in distributed and hierarchical decision-making.     

Data-driven modeling and optimization of thermal comfort and energy consumption using type-2 fuzzy method

In the research domain of intelligent buildings and smart home, modeling and optimization of the thermal comfort and energy consumption are important issues. This paper presents a type-2 fuzzy method based data-driven strategy for the modeling and optimization of thermal comfort words and energy consumption. First, we propose a methodology to convert the interval survey data on thermal comfort words to the interval type-2 fuzzy sets (IT2 FSs) which can reflect the inter-personal and intra-personal uncertainties contained in the intervals. This data-driven strategy includes three steps: survey data collection and pre-processing, ambiguity-preserved conversion of the survey intervals to their representative type-1 fuzzy sets (T1 FSs), IT2 FS modeling. Then, using the IT2 FS models of thermal comfort words as antecedent parts, an evolving type-2 fuzzy model is constructed to reflect the online observed energy consumption data. Finally, a multiobjective optimization model is presented to recommend a reasonable temperature range that can give comfortable feeling while reducing energy consumption. The proposed method can be used to realize comfortable but energy-saving environment in smart home or intelligent buildings.     

Local consistency adjustment strategy and DEA – driven interval type-2 trapezoidal fuzzy decision-making model and its application for fog-haze factor assessment problem

This paper aims to develop a novel decision-making method with interval type-2 trapezoidal fuzzy preference (IT2TrFPR), which can deal with the complex decision information presented in the form of interval type-2 trapezoidal fuzzy numbers. In this paper, we mainly propose a novel interval type-2 trapezoidal fuzzy decision-making method with local consistency adjustment strategy and data envelopment analysis (DEA). Considering the harm of fog-haze pollution to the environment and human life, we apply the decision-making method to the problem about influence factors of for-haze weather. Firstly, we introduce the definition of IT2TrFPR that sufficiently expresses the uncertainty of original decision-making information. After that, we show the definition of the order consistency and additive consistency for IT2TrFPR. Considering that the original IT2TrFPR given by decision-makers usually does not satisfy the characteristic of consistency, to transform the unacceptable additive consistent IT2TrFPRs into acceptable ones, we design a consistency-improving algorithm that uses the local adjustment approach to preserve the original decision-making information as much as possible and avoids the original information loss. Then, an output-oriented interval type-2 trapezoidal fuzzy DEA model and the concept for quasi interval type-2 trapezoidal fuzzy priority weight are developed to derive the interval type-2 trapezoidal fuzzy priority weight vector (IT2TrFPW) and obtain the final ranking result of alternatives. Finally, the effectiveness of the proposed decision-making method is demonstrated by a numerical example of selecting the most crucial fog-haze influence factor. Meanwhile, we also conduct a comparative analysis by comparing our method with the existing methods to show some merits of the proposed method.

     

An interval number distance- and ranking-based method for remotely sensed image fuzzy clustering

ABSTRACT

Fuzzy c-means clustering is an important non-supervised classification method for remote-sensing images and is based on type-1 fuzzy set theory. Type-1 fuzzy sets use singleton values to express the membership grade; therefore, such sets cannot describe the uncertainty of the membership grade. Interval type-2 fuzzy c-means (IT2FCM) clustering and relevant methods are based on interval type-2 fuzzy sets. Real vectors are used to describe the clustering centres, and the average values of the upper and lower membership grades are used to determine the classification of each pixel. Thus, the width information for interval clustering centres and interval membership grades are ignored. The main contribution of this article is to propose an improved IT2FCM* algorithm by adopting interval number distance (IND) and ranking methods, which use the width information of interval clustering centres and interval membership grades, thus distinguishing this method from existing fuzzy clustering methods. Three different IND definitions are tested, and the distance definition proposed by Li shows the best performance. The second contribution of this work is that two fuzzy cluster validity indices, FS- and XB-, are improved using the IND. Three types of multi/hyperspectral remote-sensing data sets are used to test this algorithm, and the experimental results show that the IT2FCM* algorithm based on the IND proposed by Li performs better than the IT2FCM algorithm using four cluster validity indices, the confusion matrix, and the kappa coefficient (κ). Additionally, the improved FS- index has more indicative ability than the original FS- index.     

Conceptual design evaluation using interval type-2 fuzzy information axiom

Concept selection is the most critical part of the design process as it determines the direction of subsequent design stages. In addition, it is a difficult task because available information for decision-making at this stage is imprecise and subjective. This necessitates the need for fuzzy decision models for selecting the best conceptual design among a set of alternatives. Although ordinary fuzzy sets cover uncertainties of linguistic words to some extent, it is recommended to use interval type-2 fuzzy sets (IT2FS) to capture potential uncertainties of words. This paper presents a new concept selection methodology that extends the fuzzy information axiom (FIA) approach to incorporate IT2FSs. The proposed methodology is called interval-type-2 fuzzy information axiom (IT2-FIA). IT2-FIA method is also enriched by using ordered weighted geometric aggregation operator to include the decision maker's attitude during the aggregation process. A case study is given to demonstrate the potential of the methodology.