Fuzzy model based recognition of handwritten numerals

This paper presents the recognition of handwritten Hindi and English numerals by representing them in the form of exponential membership functions which serve as a fuzzy model. The recognition is carried out by modifying the exponential membership functions fitted to the fuzzy sets. These fuzzy sets are derived from features consisting of normalized distances obtained using the Box approach. The membership function is modified by two structural parameters that are estimated by optimizing the entropy subject to the attainment of membership function to unity. The overall recognition rate is found to be 95% for Hindi numerals and 98.4% for English numerals.     

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.     

基于密度峰值的加权犹豫模糊聚类算法

由于人们对事物认知的局限性和信息的不确定性,在对决策问题进行聚类分析时,传统的模糊聚类不能有效解决实际场景中的决策问题,因此有学者提出了有关犹豫模糊集的聚类算法.现有的层次犹豫模糊K均值聚类算法没有利用数据集本身的信息来确定距离函数的权值,且簇中心的计算复杂度和空间复杂度都是指数级的,不适用于大数据环境.针对上述问题,...     

语言修饰集的研究现状与前景

语言修饰集作为一种刻画不确定信息的有效表达方式,用更加符合语言习惯的表达形式描述决策者对事物的评价结果.与其他语言术语相比,语言修饰集旨在修正隶属函数使其在表达专家的决策信息过程中更具有有效性、客观性,因此基于语言修饰集的研究是非常必要的.鉴于此,对语言修饰集的发展进行综述:首先回顾语言修饰集的研究背景;然后对语言修饰集在运算法则、语义量化、模糊逻辑、分类器等方面的发展进行回顾,同时介绍一些基于语言修饰集在情感分析、工程风险管理等方面的应用;最后展望语言修饰集的研究前景.     

Fast inference in SAM fuzzy systems using transition matrices

Fast inference using transition matrices (FITM) is a new fast algorithm for performing inferences in fuzzy systems. It is based on the assumption that fuzzy inputs can be expressed as a linear composition of the fuzzy sets used in the rule base. This representation let us interpret a fuzzy set as a vector, so we can just work with the coordinates of it instead of working with the whole set. The inference is made using transition matrices. The key of the method is the fact that a lot of operations can be precomputed offline to obtain the transition matrices, so actual inferences are reduced to a few online matrix additions and multiplications. The algorithm is designed for the standard additive model using the sum-product inference composition.     

Distances between fuzzy sets

Given two fuzzy subsets μ and ν of a metric space S (e.g., the Euclidean plane), we define the ‘shortest distance’ between μ and ν as a density function on the non-negative reals; our definition is applicable both when μ and ν are discrete-valued and when they are ‘smooth’ (i.e., differentiable), and it generalizes the definition of shortest distance for crisp sets in a natural way. We also define the mean distance between μ and ν, and show how it relates to the shortest distance. the relationship to earlier definitions of distance between fuzzy sets [1,3] is also discussed.     

Consensus-reaching methods for hesitant fuzzy multiple criteria group decision making with hesitant fuzzy decision making matrices

Group decision making plays an important role in various fields of management decision and economics. In this paper, we develop two methods for hesitant fuzzy multiple criteria group decision making with group consensus in which all the experts use hesitant fuzzy decision matrices (HFDMs) to express their preferences. The aim of this paper is to present two novel consensus models applied in different group decision making situations, which are composed of consensus checking processes, consensus-reaching processes, and selection processes. All the experts make their own judgments on each alternative over multiple criteria by hesitant fuzzy sets, and then the aggregation of each hesitant fuzzy set under each criterion is calculated by the aggregation operators. Furthermore, we can calculate the distance between any two aggregations of hesitant fuzzy sets, based on which the deviation between any two experts is yielded. After introducing the consensus measure, we develop two kinds of consensus-reaching procedures and then propose two step-by-step algorithms for hesitant fuzzy multiple criteria group decision making. A numerical example concerning the selection of selling ways about ‘Trade-Ins’ for Apple Inc. is provided to illustrate and verify the developed approaches. In this example, the methods which aim to reach a high consensus of all the experts before the selection process can avoid some experts’ preference values being too high or too low. After modifying the previous preference information by using our consensus measures, the result of the selection process is much more reasonable.     

Complex object comparison in a fuzzy context

The comparison concept plays a determining role in many problems related to object management in an Object-Oriented Database Model. Object comparison is appropriately managed in a crisp object-oriented context by means of the concepts of identity and value equality. However, when dealing with imprecise or imperfect objects, questions like ‘To which extent may two objects be the same one?’ or ‘How similar are two objects?’ have not a clear answer, because the equality concept becomes fuzzy. In this paper we present a set of operators that are useful when comparing objects in a fuzzy environment. In particular, we introduce a generalized resemblance degree between two fuzzy sets of imprecise objects and a generalized resemblance degree to compare complex fuzzy objects within a given class.     

The fuzzy geometry of image subsets

In pattern recognition we often want to measure geometric properties of regions in an image, but these regions are not always ‘crisply’ defined; it is sometimes more appropriate to regard them as fuzzy subsets of the image. Many of the basic geometric properties of and relationships among regions can be generalized to fuzzy sets; these include connectedness, adjacency and surroundedness, starshapedness and convexity, area and perimeter, extent and diameter. This paper summarizes past work on such fuzzy geometric concepts, and also includes some new results.     

Sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets

This paper presents a new method for sensor dynamic reliability evaluation based on evidence theory and intuitionistic fuzzy sets when the prior knowledge is unknown. The dynamic reliability of sensors is evaluated based on supporting degree between basic probability assignments (BPAs) provided by sensors. First, the concept of asymmetric supporting degree is proposed. By transforming BPAs to intuitionistic fuzzy sets, supporting degree between BPAs is calculated based on intuitionistic fuzzy operations and similarity measure. Then the relationship between dynamic reliability and supporting degree is analyzed. The process of dynamic reliability evaluation is proposed. Finally, the proposed dynamic reliability evaluation is applied to evidence combination. A new evidence combination rule is proposed based on evidence discounting operation and Dempster’s rule. Comparative analysis on the performance of the proposed reliability evaluation method and evidence combination rule is carried out based on numerical examples. The proposed method for data fusion is also applied in target recognition to show its feasibility and validity.     

On Fuzzy-Mathematical Programming

In problems of system analysis, it is customary to treat imprecision by the use of probability theory. It is becoming increasingly clear, however, that in the case of many real world problems involving large scale systems such as economic systems, social systems, mass service systems, etc., the major source of imprecision should more properly be labeled ‘fuzziness’ rather than ‘randomness.’ By fuzziness, we mean the type of imprecision which is associated with the lack of sharp transition from membership to nonmembership, as in tall men, small numbers, likely events, etc. In this paper our main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh [1]. However, in our approach, the emphasis is on mathematical programming and the use of the concept of a level set to extend some of the classical results to problems involving fuzzy constraints and objective functions.     

Design of adaptive fuzzy logic controller based on linguistic-hedgeconcepts and genetic algorithms

In this paper, we propose a novel fuzzy logic controller, called linguistic hedge fuzzy logic controller, to simplify the membership function constructions and the rule developments. The design methodology of linguistic hedge fuzzy logic controller is a hybrid model based on the concepts of the linguistic hedges and the genetic algorithms. The linguistic hedge operators are used to adjust the shape of the system membership functions dynamically, and ran speed up the control result to fit the system demand. The genetic algorithms are adopted to search the optimal linguistic hedge combination in the linguistic hedge module, According to the proposed methodology, the linguistic hedge fuzzy logic controller has the following advantages: 1) it needs only the simple-shape membership functions rather than the carefully designed ones for characterizing the related variables; 2) it is sufficient to adopt a fewer number of rules for inference; 3) the rules are developed intuitionally without heavily depending on the endeavor of experts; 4) the linguistic hedge module associated with the genetic algorithm enables it to be adaptive; 5) it performs better than the conventional fuzzy logic controllers do; and 6) it can be realized with low design complexity and small hardware overhead. Furthermore, the proposed approach has been applied to design three well-known nonlinear systems. The simulation and experimental results demonstrate the effectiveness of this design.     

Effect of retroflex sounds on the recognition of Hindi voiced and unvoiced stops

As development of the speech recognition system entirely depends upon the spoken language used for its development, and the very fact that speech technology is highly language dependent and reverse engineering is not possible, there is an utmost need to develop such systems for Indian languages. In this paper we present the implementation of a time delay neural network system (TDNN) in a modular fashion by exploiting the hidden structure of previously phonetic subcategory network for recognition of Hindi consonants. For the present study we have selected all the Hindi phonemes for srecognition. A vocabulary of 207 Hindi words was designed for the task-specific environment and used as a database. For the recognition of phoneme, a three-layered network was constructed and the network was trained using the back propagation learning algorithm. Experiments were conducted to categorize the Hindi voiced, unvoiced stops, semi vowels, vowels, nasals and fricatives. A close observation of confusion matrix of Hindi stops revealed maximum confusion of retroflex stops with their non-retroflex counterparts.     

Verified stochastic methods

Markov chains provide quite attractive features for simulating a system’s behavior under consideration of uncertainties. However, their use is somewhat limited because of their deterministic transition matrices. Vague probabilistic information and imprecision appear in the modeling of real-life systems, thus causing difficulties in the pure probabilistic model set-up. Moreover, their accuracy suffers due to implementations on computers with floating point arithmetics. Our goal is to address these problems by extending the Dempster-Shafer with Intervals toolbox for MATLAB with novel verified algorithms for modeling that work with Markov chains with imprecise transition matrices, known as Markov set-chains. Additionally, in order to provide a statistical estimation tool that can handle imprecision to set up Markov chain models, we develop a new verified algorithm for computing relations between the mean and the standard deviation of fuzzy sets.     

Type-2 Fuzzy Control for Driving State and Behavioral Decisions of Unmanned Vehicle

In this paper, interval type-2 fuzzy sets, fuzzy comprehensive evaluation and the fuzzy control rules are synthesized to realize the control of unmanned vehicle in driving state and behavioral decisions. Compared to the type-1 fuzzy set, type-2 fuzzy sets have more advantages in handling the model based on uncertainties, linguistic information because the membership functions are fuzzy sets. Different membership functions are established for each factor when the unmanned vehicle is driving at different speed intervals. In addition, a new evaluation method is developed to analyze unmanned vehicle’s driving state. Finally, a set of dynamic fuzzy rules are sorted out, which can be applied to the unmanned vehicle’s behavioral decision-making and provide a new idea to related research.      

指数型犹豫模糊熵在多属性决策中的应用

提出一种指数型犹豫模糊熵,并基于熵权法给出犹豫模糊多属性决策模型.首先,给出犹豫模糊元熵的公理化定义,构造犹豫模糊元的指数型犹豫模糊熵测度公式,并证明指数型犹豫模糊熵测度公式满足犹豫模糊元熵的公理化定义基本准则.在此基础上,引入犹豫模糊集的熵定义和熵测度公式,并证明犹豫模糊集的指数型犹豫模糊熵测度公式同样满足犹豫模糊集...     

A new Chinese character recognition approach based on the fuzzy clustering analysis

In this paper, a new Chinese character recognition (CCR) approach is proposed based on the fuzzy clustering analysis theory. Chinese characters (CCs) have various similar radicals and stroke components, which make it difficult to recognize features in the CCR process. At the same time, the recognition accuracy and the efficiency are lower when the objects to be recognized are complex. In order to solve these problems, a fuzzy clustering analysis method is introduced to enhance the computing efficiency. At first, the CCs including learning samples and testing samples are transformed into binarization templates in the form of matrixes. Then, the minimum distance algorithm is applied to calculate ‘distances’ between the testing sample templates and the learning sample templates. At last, the character recognition can be achieved by searching the minimum distance from the results. The experiment results of the CCR process can prove the effectiveness and accuracy of the new method.     

Generalized score functions on interval-valued intuitionistic fuzzy sets with preference parameters for different types of decision makers and their application

In this paper, the interval-valued intuitionistic fuzzy sets (IVIFSs) are studied from the viewpoint of the decision makers’ preference. Firstly, two series of principles are proposed to guide the ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs), and two kinds of illustrative generalized score functions on IVIFSs are proposed according to the newly proposed principles. Secondly, two kinds of generalized score functions on IVIFSs are proposed based on decision-makers’ preference. The two generalized score functions are both of two parameters, which represent the decision makers’ attitudinal characters on the classical score values and the classical accuracy values on IVIFNs, respectively. Thirdly, two kinds of generalized score functions on IVIFSs, which are suitable for ranking IVIFNs when there is no information about the importance weights of the classical score values and accuracy values on IVIFNs, are proposed based on integral. Fourthly, three kinds of multi-criteria decision-making (MCDM) methods in interval-valued intuitionistic fuzzy setting are proposed. Finally, an example shows that when a novel generalized score function on IVIFSs is proposed, its suitable application environments should also be pointed out.     

基于模糊聚类和改进混合蛙跳的协同过滤推荐*

由于传统的协同过滤推荐算法存在很多缺陷,如数据稀疏性、冷启动、低推荐精度等,提出了一种基于模糊聚类和改进混合蛙跳的协同过滤推荐算法。首先利用一种构造的基于时间的指数遗忘函数对原始评分数据进行处理;然后根据得到的基于时间衰退的评分矩阵对用户进行模糊C-均值(FCM)聚类,并找出与目标用户有较高相似性的前几个类作为候选邻居集;再用改进的混合蛙跳算法找到最近邻居集;最后求出目标用户对未参与项目的预测评分。经实验证明,该算法比其他一些算法的推荐精度要高,且由于数据稀疏性引起的不良影响也得到了有效的缓解。