基于区间二型模糊粗糙集的连续属性约简算法

一型模糊粗糙集可以直接处理连续属性集,但不能处理高度不确定性数据,而区间二型模糊集可以增强系统处理不确定性的能力。为了提高处理噪声数据的精确度,在一型模糊粗糙集的基础上,定义区间二型模糊粗糙集。基于区间二型模糊粗糙集模型研究了连续域决策信息系统的属性约简,通过紧计算域给出了新的约简算法。由于拒绝变量集合的存在,提出的约简算法可在有限时间内收敛,并且得到了更加合理的结果。数值仿真验证了约简算法的可行性与有效性。     

对区间二型模糊集的EKM降型法的改进

二型模糊集的质心计算称为降型,目前的降型方法大多计算成本较高,其中EKM (Enhanced Karnik-Mendel)法可计算区间二型模糊集的质心。然而,由于EKM算法中求取切换点的初始化方法还不完善,计算时间较长,使其在实际应用中受到一定限制。对此,提出一种新的改进EKM法,对原有方法进行了两处改进：更改切换点的初始化条件和改进查找切换点的方法。所提出的方法可实现向上和向下搜索,计算量大大减小,降型更有效。仿真结果验证了新的改进EKM法的有效性。     

图像分割质量评价的二型模糊集方法

图像分割质量的评价是图像分割技术和算法研究的重要环节,在图像分析和计算机视觉中有着重要应用。依据二型模糊集在不精确性描述方面的独特优势,提出一种图像分割评判指标的二型模糊集表示方法,引入两种二型模糊集的模糊性度量作为图像分割质量的评判标准,构建图像分割质量评价模型。模拟实验验证了该模型的有效性和实用性。     

二型模糊集的模糊熵研究

研究基于质心的二型模糊集的模糊熵和加权模糊熵,构造了两个二型模糊集的模糊熵度量.针对二型模糊集的特殊情形,提出一种新的区间值模糊集的模糊熵度量,既弥补了现有区间值模糊集退化为普通模糊集时熵为零的不足,又克服了两个明显不同的区间值模糊集熵相等的缺点.数值实例和仿真实验表明了所提出模糊熵的合理性和实用性.     

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.     

General type-2 fuzzy rough sets based on \alpha -plane Representation theory

Rough sets theory and fuzzy sets theory are mathematical tools to deal with uncertainty, imprecision in data analysis. Traditional rough set theory is restricted to crisp environments. Since theories of fuzzy sets and rough sets are distinct and complementary on dealing with uncertainty, the concept of fuzzy rough sets has been proposed. Type-2 fuzzy set provides additional degree of freedom, which makes it possible to directly handle highly uncertainties. Some researchers proposed interval type-2 fuzzy rough sets by combining interval type-2 fuzzy sets and rough sets. However, there are no reports about combining general type-2 fuzzy sets and rough sets. In addition, the $\alpha $ -plane representation method of general type-2 fuzzy sets has been extensively studied, and can reduce the computational workload. Motivated by the aforementioned accomplishments, in this paper, from the viewpoint of constructive approach, we first present definitions of upper and lower approximation operators of general type-2 fuzzy sets by using $\alpha $ -plane representation theory and study some basic properties of them. Furthermore, the connections between special general type-2 fuzzy relations and general type-2 fuzzy rough upper and lower approximation operators are also examined. Finally, in axiomatic approach, various classes of general type-2 fuzzy rough approximation operators are characterized by different sets of axioms.     

基于区间二型模糊决策粗糙集的三支决策方法

考虑到区间二型模糊数在描述高度不确定性信息方面的优势,将区间二型模糊数拓展到决策粗糙集中,提出两种区间二型模糊三支决策方法.在没有类标签的区间二型模糊信息系统中,解释损失函数与确定条件概率是需要解决的两个关键问题.首先,根据区间二型模糊数的性质,将其引入决策粗糙集中,为损失函数提供一种新的解释.其次,基于贝叶斯决策过程...     

Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets

In this paper, we present a new method to deal with fuzzy multiple attributes group decision-making problems based on ranking interval type-2 fuzzy sets. First, we propose a new method for ranking interval type-2 fuzzy sets. Then, we propose a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of interval type-2 fuzzy sets. We also use some examples to illustrate the fuzzy multiple attributes group decision-making process of the proposed method. The proposed method is simpler than the methods presented in [Chen and Lee, 2010a] and [Lee and Chen, 2010b] for fuzzy multiple attributes group decision-making based on interval type-2 fuzzy sets. It provides us with a useful way for dealing with fuzzy multiple attributes group decision-making problems based on interval type-2 fuzzy sets.     

Similarity measures for type-2 fuzzy sets and application in MCDM

Neural Computing and Applications - Type-2 fuzzy set theory is extensively used for decision making, pattern recognition and word computing due to exceptional expression of uncertain information....     

Fuzzy rule interpolation based on the ratio of fuzziness of interval type-2 fuzzy sets

In recent years, some fuzzy rule interpolation methods have been presented for sparse fuzzy rule-based systems based on interval type-2 fuzzy sets. However, the existing methods have the drawbacks that they cannot guarantee the convexity of the fuzzy interpolated result and may generate the same fuzzy interpolated results with respect to different observations. Moreover, they also cannot deal with fuzzy rule interpolation with bell-shaped interval type-2 fuzzy sets. In this paper, we present a new method for fuzzy rule interpolation for sparse fuzzy rule-based systems based on the ratio of fuzziness of interval type-2 fuzzy sets. The proposed method can overcome the drawbacks of the existing methods. First, it calculates the weights of the closest fuzzy rules with respect to the observation to obtain an intermediate consequence fuzzy set. Then, it uses the ratio of fuzziness of interval type-2 fuzzy sets to infer the fuzzy interpolated result based on the intermediate consequence fuzzy set. We also use some examples to compare the fuzzy interpolated results of the proposed method with the results by the existing methods. The experimental results show that the proposed fuzzy rule interpolation method gets more reasonable results than the existing methods.     

直觉模糊集相似度遗传算法求解多目标车间调度问题

为了提高高维多目标置换流水车间调度问题的求解质量,提出基于直觉模糊集相似度的遗传算法(similarity of intuitionistic fuzzy sets GA,SIFS_GA).算法中分别将参考解和Pareto解映射为参考解直觉模糊集和Pareto解直觉模糊集.计算两个集合之间的直觉模糊相似度,用以判断Pareto解的优劣.以直觉模糊集相似度值引导多目标遗传算法进化.对6个CEC标准测试集与10个流水车间调度测试实例进行仿真实验,结果表明SIFS_GA算法性能优于常用的多目标优化算法,且可以有效解决多目标置换流水车间调度问题,尤其在解决规模较大的问题上是一种有效方法.     

基于SVD 方法的简约型区间二型模糊模型构建

针对奇异值-QR分解方法存在有效奇异值难以确定的问题,采用奇异值分解方法分析从区间二型模糊模型抽取的两个激活强度矩阵,提出了奇异值归一化差值的概念以描述相邻奇异值的变化情况,从而反映了重要规则和冗余规则在奇异值变化上的本质差异;进而根据其临界点确定有效奇异值个数,并利用QR分解得到有效奇异值所对应的重要规则构建简约型区间二型模糊结构。仿真实例验证了所提出方法的有效性和可行性。     

Investment project evaluation by a decision making methodology based on type-2 fuzzy sets

Although investment projects supported by the state are extremely important in terms of national policy the projects to be transferred from the common public funds brings with it many problems. Highly transparent and comprehensive evaluation model are required to transfer the public resources to the right investment projects. It is necessary to consider many criteria for the evaluation of an investment project. These criteria are generally subjective and extremely difficult to express in numbers. However, using the fuzzy sets provide huge facilities to decision makers in project evaluation process with linguistic variables and measurement challenges. In this study, a new evaluation model for investment projects have been proposed for development agencies operating in Turkey. To address ambiguities and relativities in real world scenarios more conveniently, type-2 fuzzy sets and crisp sets have been simultaneously used. The proposed model for the investment project evaluation problem composed of type-2 fuzzy AHP and type-2 fuzzy TOPSIS methods. The proposed fuzzy MCDM method consists of three phases: (1) identify the criteria to be used in the model, (2) type-2 fuzzy AHP computations, (3) evaluation of investment projects with type-2 fuzzy TOPSIS and determination of the final rank. To perceive proposed model better, an application with real case data have been performed in Middle Black Sea Development Agency in Turkey. As a consequence of this application, it has been observed that the proposed model have proved effective in evaluation of alternatives in multi-criteria group decision making problems in a broader perspective and flexible fashion.     

Development of an interval type-2 fuzzy sets based hierarchical MADM model by combining DEMATEL and TOPSIS

In this study, a new interval type-2 fuzzy multiple-attribute decision making model is developed by integrating Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Decision Making Trial and Evaluation Laboratory (DEMATEL). The proposed model utilizes hierarchical decomposition approach for reducing inherent complexity of the decision making problems. Additionally, interdependencies among problem attributes are taken into consideration by using interval type-2 fuzzy DEMATEL method. Finally, ranking orders of the alternatives are obtained by hierarchical interval type-2 fuzzy TOPSIS method. As there are several forms of interactions among criteria in real life settings, decision makers should be provided with the expert and intelligent systems which can overcome the preferential independence assumption. The proposed method is able to model causal dependencies by using interval type-2 trapezoidal fuzzy sets. The proposed method is implemented in a Strengths, Weaknesses, Opportunities, and Threats (SWOT)-based strategy selection problem.     

Switching between type-2 fuzzy sets and intuitionistic fuzzy sets: an application in medical diagnosis

When dealing with vagueness, there are situations when there is insufficient information available, making it impossible to satisfactorily evaluate membership. The intuitionistic fuzzy set theory is more suitable than fuzzy sets to deal with such problem. In 1996, Atanassov proposed the mapping from intuitionistic fuzzy sets to fuzzy sets. Furthermore, intuitionistic fuzzy sets are isomorphic to interval valued fuzzy sets, and interval valued fuzzy sets are regarded as the special cases of type-2 fuzzy sets in recently studies. However, their discussions are not only hardly comprehending but also lacking the reliable applications. In this study, the advantage of type-2 fuzzy sets is employed, and the switching relation between type-2 fuzzy sets and intuitionistic fuzzy sets is defined axiomatically. The switching results are applied to show the usefulness of the proposed method in pattern recognition and medical diagnosis reasoning.     

基于模糊集截集的模糊粗糙集模型

基于L.A.Zadeh模糊集的截集的概念给出了论域U上任意模糊子集的上、下近似的刻画,得到了基于模糊集的截集的粗糙集模型,亦即模糊粗糙集,实现了用论域U中的模糊集近似论域上的任意模糊集,进一步推广了Z.Pawlak粗糙集模型,扩展了粗糙集的应用范围。最后,研究了其基本性质以及其与其他粗糙集模型的关系。     

基于最优搜索的足球机器人射门算法

机器人足球比赛中,小球的运动状态因受到碰撞和摩擦变化剧烈,所以大多数情况下不存在全局意义上的最佳射门路径,或者规划的路径机器人在给定的时间内根本无法完成。基于目标函数的足球机器人射门算法,通过在机器人运动能力范围内的最优搜索,能够找出当前状态下机器人按要求逼近球的最佳路径。该算法能够适应各种速度状态,明显提高机器人射门命中率,并迅速对小球状态突变做出响应。在比赛中,常常需要根据场上态势对机器人进行控制算法切换,但由于不同控制算法速度输出的跳跃性,机器人会出现相对球位置的抖动。针对以距离作为切换条件的情况下,不同控制算法切换时产生的“抖动”现象,分析了现象产生的原因,并通过S-曲线加权算法,有效避免了“抖动”的产生,实现了不同控制算法在切换边界的平滑过渡。