The Need for Fuzzy AI

Artificial intelligence (AI) is once again a topic of huge interest for computer scientists around the world. Whilst advances in the capability of machines are being made all around the world at an incredible rate, there is also increasing focus on the need for computerised systems to be able to explain their decisions, at least to some degree. It is also clear that data and knowledge in the real world are characterised by uncertainty. Fuzzy systems can provide decision support, which both handle uncertainty and have explicit representations of uncertain knowledge and inference processes. However, it is not yet clear how any decision support systems, including those featuring fuzzy methods, should be evaluated as to whether their use is permitted. This paper presents a conceptual framework of indistinguishability as the key component of the evaluation of computerised decision support systems. Case studies are presented in which it has been clearly demonstrated that human expert performance is less than perfect, together with techniques that may enable fuzzy systems to emulate human-level performance including variability. In conclusion, this paper argues for the need for " fuzzy AI” in two senses: (i) the need for fuzzy methodologies (in the technical sense of Zadeh’s fuzzy sets and systems) as knowledge-based systems to represent and reason with uncertainty; and (ii) the need for fuzziness (in the non-technical sense) with an acceptance of imperfect performance in evaluating AI systems.      

一种集成遗传算法与模糊推理的粗糙集数据分析算法

粗糙集数据分析的主要优点在于它不要求任何关于被处理数据的先验或额外的知识,文章利用其对数据库进行分析计算,自动获取数据库在各个层次上的规则集。在保证量化后的数据库具有最大一致性的前提下,利用遗传算法求取连续属性值的最优量化区间个数及各个区间分点值。同时将量化区间进行模糊化,将清晰规则集转化为模糊规则集,利用模糊推理进行决策以提高鲁棒性。通过对UCI中几个数据库的测试验证了所提出算法的有效性。     

A simple O(n log n) algorithm for finding the maximum distance between two finite planar sets

A simple O(n log n) algorithm is presented for computing the maximum Euclidean distance between two finite planar sets of n points. When the n points form the vertices of simple polygons this complexity reduces to O(n).     

Rough sets and Boolean reasoning

In this article, we discuss methods based on the combination of rough sets and Boolean reasoning with applications in pattern recognition, machine learning, data mining and conflict analysis.     

Optimal algorithms for computing the minimum distance between two finite planar sets

It is shown in this paper that the minimum distance between two finite planar sets of n points can be computer in O(n log n) worst-case running time and that this is optimal to within a constant factor. Furthermore, when the sets form a convex polygon this complexity can be reduced O(n).     

Rough Self Organizing Map

A rough self-organizing map (RSOM) with fuzzy discretization of feature space is described here. Discernibility reducts obtained using rough set theory are used to extract domain knowledge in an unsupervised framework. Reducts are then used to determine the initial weights of the network, which are further refined using competitive learning. Superiority of this network in terms of quality of clusters, learning time and representation of data is demonstrated quantitatively through experiments over the conventional SOM.     

不平衡数据分类的研究现状*

不平衡数据在实际应用中广泛存在,它们已对机器学习领域构成了一个挑战,如何有效处理不平衡数据也成为目前的一个新的研究热点.综述了这一新领域的研究现状,包括该领域最新研究内容、方法及成果.     

基于直觉模糊推理的目标识别方法

针对目标识别特征值的不确定性问题,提出一种基于直觉模糊推理的目标识别方法．首先,分析现有目标识别方法的不确定性与局限性,并对空中目标识别问题及目标特征进行描述;然后,设计系统状态属性变量的隶属度函数与非隶属度函数;最后,建立直觉模糊推理规则,设计推理合成算法和解模糊算法,并检验所建规则的合理性．仿真实例验证了所提方法的有效性与适用性．     

Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning

Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users.The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem.We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.     

粗糙集与模糊系统集成的化学模式分类方法及其应用

模糊方法是一种有效的化学模式分类方法,但模糊规则的获取和相关参数的确定较为困难。对此,本文采用粗糙集方法,无需任何先验知识,约简系统,获取最简规则集,在此基础上构建结构合理．适用于分类的模糊-神经网络系统,并根据规则的统计性质和离散化结果初始化网络参数,采用LM方法训练网络;在橄榄油模式分类建模的应用中,该方法训练收敛速度快,所建模型预测性能良好,要优于现代统计方法和前馈神经网络。     

Distinguishability of interval type-2 fuzzy sets data by analyzing upper and lower membership functions

In this paper, we deal with the problem of classification of interval type-2 fuzzy sets through evaluating their distinguishability. To this end, we exploit a general matching algorithm to compute their similarity measure. The algorithm is based on the aggregation of two core similarity measures applied independently on the upper and lower membership functions of the given pair of interval type-2 fuzzy sets that are to be compared. Based on the proposed matching procedure, we develop an experimental methodology for evaluating the distinguishability of collections of interval type-2 fuzzy sets. Experimental results on evaluating the proposed methodology are carried out in the context of classification by considering interval type-2 fuzzy sets as patterns of suitable classification problem instances. We show that considering only the upper and lower membership functions of interval type-2 fuzzy sets is sufficient to (i) accurately discriminate between them and (ii) judge and quantify their distinguishability.     

New hesitation-based distance and similarity measures on intuitionistic fuzzy sets and their applications

In this paper, we present new definitions on distance and similarity measures between intuitionistic fuzzy sets (IFSs) by combining with hesitation degree. First, we discuss the limitations in traditional distance and similarity measures, which are caused by the neglect of hesitation degree's influence. Even though a vector-valued similarity measure was proposed, which has two components indicating similarity and hesitation aspects, it still cannot perform well in practical applications because hesitation works only when the values of similarity measures are equal. In order to overcome the limitations, we propose new definitions on hesitation, distance and similarity measures, and research some theorems which satisfy the requirements of the proposed definitions. Meanwhile, we investigate the relationships among hesitation, distance, similarity and entropy of IFSs to verify the consistency of our work and previous research. Finally, we analyse and discuss the advantages and disadvantages of the proposed similarity measure in detail, and then we apply the proposed measures (dH and SH) to deal with pattern recognition problems, and demonstrate that they outperform state-of-the-art distance and similarity measures.     

Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications

In this paper, we presented 10 similarity measures between Pythagorean fuzzy sets (PFSs) based on the cosine function by considering the degree of membership, degree of nonmembership and degree of hesitation in PFSs. Then, we applied these similarity measures and weighted similarity measures between PFSs to pattern recognition and medical diagnosis. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for pattern recognition and medical diagnosis.     

基于模糊推理的环境监测识别系统设计

首先提取反映烟尘特性的烟尘图像特征参数,对图像特征参数使用基于参数正态分布的模糊化方法进行模糊归一化处理;然后进行K均值模糊聚类分析;最后使用基于灰色补偿理论的径向基函数神经网络进行模式识别,判断出烟尘污染等级.系统实际运行中取得了良好的识别结果.     

COMBINED QUALITATIVE/QUANTITATIVE SIMULATION MODELS OF CONTINUOUS-TIME PROCESSES USING FUZZY INDUCTIVE REASONING TECHNIQUES

Abstract

A new mixed quantitative and qualitative simulation methodology based on fuzzy inductive reasoning is presented. The feasibility of this methodology is demonstrated by means of a simple hydraulic control system. The mechanical and electrical parts of the control system are modeled using differential equations, whereas the hydraulic part is modeled using fuzzy inductive reasoning. The technique is described in detail in the first part of this paper. The example is shown in the second part of the paper. The mixed quantitative and qualitative model is simulated in ACSL, and the simulation results are compared with those obtained from a fully quantitative model. The example was chosen as a simple to describe, yet numerically demanding process whose sole purpose is to prove the concept. Several practical applications of this mixed modeling technique are mentioned in the paper. but their realization has not yet been completed     

The Variable Precision Rough Set Inductive Logic Programming Model and Strings

The Variable Precision Rough Set Inductive Logic Programming model (VPRSILP model) extends the Variable Precision Rough Set (VPRS) model to Inductive Logic Programming (ILP). The generic Rough Set Inductive Logic Programming (gRS-ILP) model provides a framework for ILP when the setting is imprecise and any induced logic program will not be able to distinguish between certain positive and negative examples. The gRS-ILP model is extended in this paper to the VPRSILP model by including features of the VPRS model. The VPRSILP model is applied to strings and an illustrative experiment on transmembrane domains in amino acid sequences is presented.     

Optimization of fuzzy partitions for inductive reasoning using genetic algorithms

Fuzzy Inductive Reasoning (FIR) is a data-driven methodology that uses fuzzy and pattern recognition techniques to infer system models and to predict their future behavior. It is well known that variations on fuzzy partitions have a direct effect on the performance of the fuzzy-rule-based systems. The FIR methodology is not an exception. The performance of the model identification and prediction processes of FIR is highly influenced by the discretization parameters of the system variables, i.e. the number of classes of each variable and the membership functions that define its semantics. In this work, we design two new genetic fuzzy systems (GFSs) that improve this modeling and simulation technique. The main goal of the GFSs is to learn the fuzzification parameters of the FIR methodology. The new approaches are applied to two real modeling problems, the human central nervous system and an electrical distribution problem.     

一个基于模糊神经网络的模式分类系统

目前,基于神经网络的分类系统在许多领域得到了越来越广泛的应用。但是,该系统大多采用的是离线自适应机制,即神经网络需学习新的分类知识时,要重新训练神经网络,从而大大增加神经网络的训练时间;对于重叠分类,一般是构成一个贝叶斯分类器。然而,贝叶斯分类器的构成需要关于分类数据的概率密度函数的先验知识,而这些知识常常在模式分类前是难以获得的。为了解决这些问题,文中根据模糊集合理论,提出了一种基于模糊神经网络