Uncertainty Modeling by Bilattice-Based Squares and Triangles

In this paper, Ginsberg's/Fitting's theory of bilattices, and in particular the associated constructs of bilattice-based squares and triangles, is introduced as an attractive framework for the representation of uncertain and potentially conflicting information, paralleling Goguen's L-fuzzy set theory. We recall some of the advantages of bilattice-based frameworks for handling fuzzy sets and systems, provide the related structures with adequately defined graded versions of the basic logical connectives, and study their properties and relationships     

Knowledge representation using interval-valued fuzzy formal concept lattice

Formal concept analysis (FCA) is a mathematical framework for data analysis and processing tasks. Based on the lattice and order theory, FCA derives the conceptual hierarchies from the relational information systems. From the crisp setting, FCA has been extended to fuzzy environment. This extension is aimed at handling the uncertain and vague information represented in the form of a formal context whose entries are the degrees from the scale [0, 1]. The present study analyzes the fuzziness in a given many-valued context which is transformed into a fuzzy formal context, to provide an insight into generating the fuzzy formal concepts from the fuzzy formal context. Furthermore, considering that a major problem in FCA with fuzzy setting is to reduce the number of fuzzy formal concepts thereby simplifying the corresponding fuzzy concept lattice structure, the current paper solves the problem by linking an interval-valued fuzzy graph to the fuzzy concept lattice. For this purpose, we propose an algorithm for generating the interval-valued fuzzy formal concepts. To measure the weight of fuzzy formal concepts, an algorithm is proposed using Shannon entropy. The knowledge represented by formal concepts using interval-valued fuzzy graph is compared with entropy-based-weighted fuzzy concepts at chosen threshold.     

A fuzzy Petri net-based expert system and its application to damageassessment of bridges

In this paper, a fuzzy Petri net approach to modeling fuzzy rule-based reasoning is proposed to bring together the possibilistic entailment and the fuzzy reasoning to handle uncertain and imprecise information. The three key components in our fuzzy rule-based reasoning-fuzzy propositions, truth-qualified fuzzy rules, and truth-qualified fuzzy facts-can be formulated as fuzzy places, uncertain transitions, and uncertain fuzzy tokens, respectively. Four types of uncertain transitions-inference, aggregation, duplication, and aggregation-duplication transitions-are introduced to fulfil the mechanism of fuzzy rule-based reasoning. A framework of integrated expert systems based on our fuzzy Petri net, called fuzzy Petri net-based expert system (FPNES), is implemented in Java. Major features of FPNES include knowledge representation through the use of hierarchical fuzzy Petri nets, a reasoning mechanism based on fuzzy Petri nets, and transformation of modularized fuzzy rule bases into hierarchical fuzzy Petri nets. An application to the damage assessment of the Da-Shi bridge in Taiwan is used as an illustrative example of FPNES.     

Fuzzy random chance-constrained programming

By fuzzy random programming, we mean the optimization theory dealing with fuzzy random decision problems. This paper presents a new concept of chance of fuzzy random events, and constructs a general framework of fuzzy random chance-constrained programming. We also design a spectrum of fuzzy random simulations for computing uncertain functions arising in the area of fuzzy random programming. To speed up the process of handling uncertain functions, we train a neural network to approximate uncertain functions based on the training data generated by fuzzy random simulation. Finally, we integrate the fuzzy random simulation, neural network, and genetic algorithm to produce a more powerful and effective hybrid intelligent algorithm for solving fuzzy random programming models and illustrate its effectiveness by some numerical examples     

基于直觉模糊Petri网的故障诊断

故障诊断经常受到多种不确定性和模糊性因素的影响,针对不确定性的故障诊断问题,利用直觉模糊集较好的表达不确定性信息的优势和Petri网较好的并行处理以及图形处理问题的能力,构建了直觉模糊Petri网模型。由于将直觉模糊推理转化为矩阵运算的过程中有非隶属度参数的参与,因此推理结果可提供更多的信息。根据实际故障诊断中的模糊推理问题,给出了带有权值、阈值等参数条件下新的直觉模糊推理算法。通过获取和处理故障诊断中的不确定性和模糊性的知识,该算法将故障诊断过程转化为利用直觉模糊Petri网的直觉模糊推理过程。实际燃气轮机故障诊断模型案例表明了所给直觉模糊推理算法的有效性。     

Pythagorean Uncertain Linguistic Variable Hamy Mean Operator and Its Application to Multi-attribute Group Decision Making

Pythagorean fuzzy set (PFS) can provide more flexibility than intuitionistic fuzzy set (IFS) for handling uncertain information, and PFS has been increasingly used in multi-attribute decision making problems. This paper proposes a new multi-attribute group decision making method based on Pythagorean uncertain linguistic variable Hamy mean (PULVHM) operator and VIKOR method. Firstly, we define operation rules and a new aggregation operator of Pythagorean uncertain linguistic variable (PULV) and explore some properties of the operator. Secondly, taking the decision makers' hesitation degree into account, a new score function is defined, and we further develop a new group decision making approach integrated with VIKOR method. Finally, an investment example is demonstrated to elaborate the validity of the proposed method. Sensibility analysis and comprehensive comparisons with another two methods are performed to show the stability and advantage of our method.      

Handling imprecision and uncertainty in software development effort prediction: A type-2 fuzzy logic based framework

Traditional approaches for software projects effort prediction such as the use of mathematical formulae derived from historical data, or the use of experts judgments are plagued with issues pertaining to effectiveness and robustness in their results. These issues are more pronounced when these effort prediction approaches are used during the early phases of the software development lifecycle, for example requirements development, whose effort predictors along with their relationships to effort are characterized as being even more imprecise and uncertain than those of later development phases, for example design. Recent works have demonstrated promising results using approaches based on fuzzy logic. Effort prediction systems that use fuzzy logic can deal with imprecision; they, however, can not deal with uncertainty. This paper presents an effort prediction framework that is based on type-2 fuzzy logic to allow handling imprecision and uncertainty inherent in the information available for effort prediction. Evaluation experiments have shown the framework to be promising.     

Fuzzy branching temporal logic

Intelligent systems require a systematic way to represent and handle temporal information containing uncertainty. In particular, a logical framework is needed that can represent uncertain temporal information and its relationships with logical formulae. Fuzzy linear temporal logic (FLTL), a generalization of propositional linear temporal logic (PLTL) with fuzzy temporal events and fuzzy temporal states defined on a linear time model, was previously proposed for this purpose. However, many systems are best represented by branching time models in which each state can have more than one possible future path. In this paper, fuzzy branching temporal logic (FBTL) is proposed to address this problem. FBTL adopts and generalizes concurrent tree logic (CTL*), which is a classical branching temporal logic. The temporal model of FBTL is capable of representing fuzzy temporal events and fuzzy temporal states, and the order relation among them is represented as a directed graph. The utility of FBTL is demonstrated using a fuzzy job shop scheduling problem as an example.     

On the cardinality index and attitudinal character of fuzzy measures

We briefly introduce the fuzzy measure and then discuss its use in representing information about uncertain variables. A relationship between the fuzzy measure and the Dempster-Shafer belief structure is discussed and a method for generating the family of fuzzy measures associated with a belief structure is described. We discuss the use of the Shapley index as a means for introducing an extension of the concept of entropy to fuzzy measures called the Shapley entropy. It is shown that all fuzzy measures generated from a given Dempster-Shafer belief structure have the same value for their Shapley entropy. We introduce the cardinality index of a fuzzy measure and use it to define the attitudinal character of a fuzzy measure. A semantics for this attitudinal character in the framework of using fuzzy measures to represent information about uncertain variables is suggested.     

Mining fuzzy association rules from uncertain data

Association rule mining is an important data analysis method that can discover associations within data. There are numerous previous studies that focus on finding fuzzy association rules from precise and certain data. Unfortunately, real-world data tends to be uncertain due to human errors, instrument errors, recording errors, and so on. Therefore, a question arising immediately is how we can mine fuzzy association rules from uncertain data. To this end, this paper proposes a representation scheme to represent uncertain data. This representation is based on possibility distributions because the possibility theory establishes a close connection between the concepts of similarity and uncertainty, providing an excellent framework for handling uncertain data. Then, we develop an algorithm to mine fuzzy association rules from uncertain data represented by possibility distributions. Experimental results from the survey data show that the proposed approach can discover interesting and valuable patterns with high certainty.     

A new fuzzy approach for handling class labels in canonical correlation analysis

Canonical correlation analysis (CCA) can extract more discriminative features by utilizing class labels, especially the ones that can reflect the sample distribution appropriately. In this paper, a new fuzzy approach for handling class labels in the form of fuzzy membership degrees is proposed. We elaborately design a novel fuzzy membership function to represent the distribution of image samples. These fuzzy class labels promote the classification performances of CCA and kernel CCA (KCCA) through incorporating distribution information into the process of feature extraction. Comprehensive experimental results on face recognition demonstrate the effectiveness and feasibility of the proposed method.     

A narrow band interval type-2 fuzzy approach for image segmentation

Traditional fuzzy sets capture vagueness through precise numeric membership degrees. This poses a dilemma of excessive precision in describing uncertain phenomenon. Interval type-2 fuzzy sets have shown its effectiveness in handling uncertainties in comparison to the traditional fuzzy sets. In this paper, the interval type-2 fuzzy approach is introduced into the framework of active contour model, which effectively segment images with large uncertainties. However, the computational cost is largely increased by employing the interval type-2 fuzzy set. Therefore, we try to update the pixels within a narrow band region near the contour boundary for reducing the computational cost caused by employing the interval type-2 fuzzy set. Moreover, both spatial and gray constraints are taken into consideration when calculating the fuzzy membership value to retain more image details. Experimental results on synthetic and real images show that the proposed method is effective and efficient, and is relatively independent of initial conditions.     

A new interval-valued knowledge measure for interval-valued intuitionistic fuzzy sets and application in decision making

In this paper, firstly we discuss some entropy measures for the interval-valued intuitionistic fuzzy sets (IvIFSs). Then we extend the knowledge measure for the intuitionistic fuzzy sets (IFSs) to propose a new interval-valued knowledge measure for the IvIFSs. Based on the proposed knowledge measure we construct a new interval-valued information entropy measure for IvIFSs, which is an extended notion of the entropy measures for IFSs. The proposed knowledge measure is defined as an interval of amounts of knowledge measured on an IvIFS, related to the uncertain information in terms of interval membership degree and interval non-membership degree. In comparison with other existing measures, it seems to be simpler and more intuitively appealing. Several illustrative examples are performed to demonstrate the effectiveness and practicality of the proposed method in handling with the increasing complexity of the decision making problems.     

一种基于模糊融合的遥感图像目标识别方法

数据融合利用多传感器的信息,克服了单一传感器信息不完整、不精确、不确定的缺点,因此广泛应用于目标识别中,该文提出了一种基于模糊融合的遥感图像目标识别的新方法。首先在单源图像上提取可疑目标,然后根据目标在不同类型图像上的成像特点,选择合适的目标特征,充分考虑到各特征的重要程度,把模糊隶属度函数和模糊密度结合起来,最后利用特征层模糊融合对目标的身份进行判定。此方法应用在实际目标的识别中,取得了很好的效果。     

Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge

Abstract: Just like rough set theory, fuzzy set theory addresses the topic of dealing with imperfect knowledge. Recent investigations have shown how both theories can be combined into a more flexible, more expressive framework for modelling and processing incomplete information in information systems. At the same time, intuitionistic fuzzy sets have been proposed as an attractive extension of fuzzy sets, enriching the latter with extra features to represent uncertainty (on top of vagueness). Unfortunately, the various tentative definitions of the concept of an ‘intuitionistic fuzzy rough set’ that were raised in their wake are a far cry from the original objectives of rough set theory. We intend to fill an obvious gap by introducing a new definition of intuitionistic fuzzy rough sets, as the most natural generalization of Pawlak's original concept of rough sets.     

基于粗糙集与差分免疫模糊聚类算法的图像分割

提出了基于粗糙集模糊聚类与差分免疫克隆聚类的图像分割算法。该算法在差分免疫克隆聚类算法的基础上,通过引入粗糙集模糊聚类,将差分免疫克隆聚类算法中的硬聚类变成模糊聚类,从而获得更丰富的聚类信息。具体来说,由于粗糙集的优势是处理不确定的数据,因此,加入粗糙集模糊聚类后更有利于算法解决不确定性问题。通过对9幅图像分割实验结果与4种算法的对比,验证了该算法在聚类性能稳定性方面的优越性,结果还同时证明了该算法具有更高的分割正确率和更好的分割结果。     

A fuzzy logic system for the detection and recognition ofhandwritten street numbers

Fuzzy logic is applied to the problem of locating and reading street numbers in digital images of handwritten mail. A fuzzy rule-based system is defined that uses uncertain information provided by image processing and neural network-based character recognition modules to generate multiple hypotheses with associated confidence values for the location of the street number in an image of a handwritten address. The results of a blind test of the resultant system are presented to demonstrate the value of this new approach. The results are compared to those obtained using a neural network trained with backpropagation. The fuzzy logic system achieved higher performance rates     

Balanced fuzzy sets

The paper presents a new approach to fuzzy sets and uncertain information based on an observation of asymmetry of classical fuzzy operators. Parallel is drawn between symmetry and negativity of uncertain information. The hypothesis is raised that classical theory of fuzzy sets concentrates the whole negative information in the value 0 of membership function, what makes fuzzy operators asymmetrical. This hypothesis could be seen as a contribution to a broad range discussion on unification of aggregating operators and uncertain information processing rather than an opposition to other approaches. The new approach “spreads” negative information from the point 0 into the interval [−1, 0] making scale and operators symmetrical. The balanced counterparts of classical operators are introduced. Relations between classical and balanced operators are discussed and then developed to the hierarchies of balanced operators of higher ranks. The relation between balanced norms, on one hand, and uninorms and nullnorms, on the other, are quite close: balanced norms are related to equivalence classes of some equivalence relation build on linear dependency in the spaces of uninorms and nullnorms. It is worth to stress that this similarity is raised by two entirely different approaches to generalization of fuzzy operators. This observation validates the generalized hierarchy of fuzzy operators to which both approaches converge. The discussion in this paper is aimed at presenting the idea and does not aspire to detailed exploration of all related aspects of uncertainty and information processing.     

Fuzzy decision trees: issues and methods

Decision trees are one of the most popular choices for learning and reasoning from feature-based examples. They have undergone a number of alterations to deal with language and measurement uncertainties. We present another modification, aimed at combining symbolic decision trees with approximate reasoning offered by fuzzy representation. The intent is to exploit complementary advantages of both: popularity in applications to learning from examples, high knowledge comprehensibility of decision trees, and the ability to deal with inexact and uncertain information of fuzzy representation. The merger utilizes existing methodologies in both areas to full advantage, but is by no means trivial. In particular, knowledge inferences must be newly defined for the fuzzy tree. We propose a number of alternatives, based on rule-based systems and fuzzy control. We also explore capabilities that the new framework provides. The resulting learning method is most suitable for stationary problems, with both numerical and symbolic features, when the goal is both high knowledge comprehensibility and gradually changing output. We describe the methodology and provide simple illustrations.     

Answers to queries concerning uncertain and imprecise information in fuzzy relational databases

A model of an extended fuzzy relational database was proposed to accommodate uncertain and imprecise information. We use two supplementary measurements, satisfactory degree and extra degree, for determining the quality of answers to Select‐Project‐Join (SPJ) queries. The method of measurement determines how much satisfactory information is provided and how much truth information is required for a query. The answers to the query thus contain sure answers and maybe answers. The core of this study is the detailed discussion on the quality of answers in an extended fuzzy relation to query processing. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 647–668, 2005.