Knowledge maps for e-learning

Maps such as concept maps and knowledge maps are often used as learning materials. These maps have nodes and links, nodes as key concepts and links as relationships between key concepts. From a map, the user can recognize the important concepts and the relationships between them. To build concept or knowledge maps, domain experts are needed. Therefore, since these experts are hard to obtain, the cost of map creation is high. In this study, an attempt was made to automatically build a domain knowledge map for e-learning using text mining techniques. From a set of documents about a specific topic, keywords are extracted using the TF/IDF algorithm. A domain knowledge map (K-map) is based on ranking pairs of keywords according to the number of appearances in a sentence and the number of words in a sentence. The experiments analyzed the number of relations required to identify the important ideas in the text. In addition, the experiments compared K-map learning to document learning and found that K-map identifies the more important ideas.     

Learning through computer-based concept mapping with scaffolding aid

Abstract Concept mapping has been applied in a variety of fields, including instruction, learning, curriculum development, and assessment. Because many empirical studies have proven the validity of concept mapping, a computer-based concept mapping system has been developed. The system provides two learning environments. In the 'construct-by-self' environment, the system provides students with the evaluation results and corresponding hints for feedback. The students construct concept maps by themselves with only the assistance of the feedback. In the 'construct-on-scaffold' environment, in addition to the feedback, the students receive an incomplete concept map, within which some nodes and links were set as blanks for the scaffold. A study comparing the effectiveness of the 'construct-by-self', 'construct-on-scaffold', and 'construct by paper-and-pencil' concept mapping showed that the 'construct-on-scaffold' had better effect for learning on biology. Both of the two computer-based procedures are helpful for students in completing their concept maps.     

Integrating fuzzy topological maps and fuzzy geometric maps for behavior‐based robots

In behavior‐based robots, planning is necessary to elaborate abstract plans that resolve complex navigational tasks. Usually maps of the environment are used to plan the robot motion and to resolve the navigational tasks. Two types of maps have been mainly used: metric and topological maps. Both types present advantages and weakness so that several integration approaches have been proposed in literature. However, in many approaches the integration is conducted to build a global representation model, and the planning and navigational techniques have not been fitted to profit from both kinds of information. We propose the integration of topological and metric models into a hybrid deliberative‐reactive architecture through a path planning algorithm based on A^* and a hierarchical map with two levels of abstraction. The hierarchical map contains the required information to take advantage of both kinds of modeling. On one hand, the topological model is based on a fuzzy perceptual model that allows the robot to classify the environment in distinguished places, and on the other hand, the metric map is built using regions of possibility with the shape of fuzzy segments, which are used later to build fuzzy grid‐based maps. The approach allows the robot to decide on the use of the most appropriate model to navigate the world depending on minimum‐cost and safety criteria. Experiments in simulation and in a real office‐like environment are shown for validating the proposed approach integrated into the navigational architecture. © 2002 Wiley Periodicals, Inc.     

Mixed-method integration and advances in fuzzy cognitive maps for computational policy simulations for natural hazard mitigation

Human systems need to be adaptive to the consequences of natural hazards. Public policy decisions on natural hazard mitigation can benefit from computational models that embody a comprehensive view of the system. Such models need to be transparent and integrate both expert and lay expert knowledge and experience in an efficient manner. By integrating hard and soft sciences within an overall systems framework, scientists, policy makers and communities can better understand how to improve adaptive capacity. We present a fuzzy cognitive map based Auto-Associative Neural Networks framework generated from a development mixed method integration (triangulation) for adaptive policy formulations. The specific policies relate to preparation for, response to, and recovery from earthquakes in mountainous ski-field environments – a case study chosen to highlight the framework. Three different data collection techniques – expert geomorphic assessments, semi-structured qualitative interviews with three stakeholder groups (experts and lay experts), and fuzzy cognitive maps (FCM) (node and arc maps of stakeholder perceptions) were employed. FCM were first analysed using Graph theory indices to determine map structure. Special attention was paid to subsequent processing of fuzzy cognitive maps (e.g., condensation and aggregation) with qualitative followed by quantitative means to simplify the FCM from the original total of 300 variables to 5 high-level themes to improve the efficacy of subsequent policy simulations. Specifically, the use of Self Organising Maps (SOM) to group concepts (condensation) and individual stakeholders (aggregation) into social group FCMs is a novel contribution to advancing FCM. In the process, SOM also enabled the embedment of nonlinear relationships inherent in the system in the simplified FCM allowing a platform for realistic and meaningful policy simulations based on collective perceptions. Specifically, each of the three simplified stakeholder group FCM and a total social group FCM was represented by Auto-Associative Neural Networks (AANN) which converts an FCM into a dynamical system that allows policy scenario simulations based on input from both expert and lay expert stakeholders. A policy scenario is the level of importance given to a set of concepts and their effects on the system behaviour as revealed by the simulations. We present the results from one of several policy simulations to highlight the effectiveness of the mixed-method integration leading to simplified-FCM based ANNN simulations. Results revealed the similarities and differences between stakeholder group responses in relation to the scenario analysed and how these formed collective responses in the total social group map. Furthermore, outcomes of group and total social group simulations could be interpreted from individual and group stakeholder FCMs giving credibility to the mixed-method approach.     

Soft sets combined with fuzzy sets and rough sets: a tentative approach

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft–rough fuzzy sets, which extends Dubois and Prade’s rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.     

Reduction method based on a new fuzzy rough set in fuzzy information system and its applications to scheduling problems

In this paper, we present the concept of fuzzy information granule based on a relatively weaker fuzzy similarity relation called fuzzy T_L-similarity relation for the first time. Then, according to the fuzzy information granule, we define the lower and upper approximations of fuzzy sets and a corresponding new fuzzy rough set. Furthermore, we construct a kind of new fuzzy information system based on the fuzzy T_L-similarity relation and study its reduction using the fuzzy rough set. At last, we apply the reduction method based on the defined fuzzy rough set in the above fuzzy information system to the reduction of the redundant multiple fuzzy rule in the scheduling problems, and numerical computational results show that the reduction method based on the new fuzzy rough set is more suitable for the reduction of multiple fuzzy rules in the scheduling problems compared with the reduction methods based on the existing fuzzy rough set.     

A fuzzy approach for the reviewer assignment problem

Assignment of experts to project proposals is a significant task for funding agencies which have to assess the potential value of the research and development (R&D) projects through peer review. The problem is known as reviewer assignment problem and has real-world applications in funding agencies, conferences and research journals. Given a set of experts and a set of proposals; the problem can be defined as assigning the most suitable experts to the proposals under some constraints, which are generally encountered by funding agencies. In this study, a fuzzy model is offered to solve the reviewer assignment problem. The objective of the model is to maximize the total matching degree of assigned experts under some constraints such as cost of forming a panel and the size of a panel. The matching degrees are defined using linguistic variables to denote the expertise of each expert with respect to each proposal. The fuzzy mathematical model, which also takes into account different constraints related to the problem, is solved via the selected fuzzy ranking methods namely; the signed distance method and the method of ranking fuzzy numbers with integral value. The solution of an example problem – inspired from a real-life situation – with both of the mentioned methods revealed the effectiveness of the solution approach. It is believed that the use of the offered fuzzy approach could improve the accuracy of the decisions made by funding agencies.     

Optimality conditions for linear programming problems with fuzzy coefficients

The optimality conditions for linear programming problems with fuzzy coefficients are derived in this paper. Two solution concepts are proposed by considering the orderings on the set of all fuzzy numbers. The solution concepts proposed in this paper will follow from the similar solution concept, called the nondominated solution, in the multiobjective programming problem. Under these settings, the optimality conditions will be naturally elicited.     

A dynamic fuzzy cognitive map applied to chemical process supervision

This work develops an intelligent tool based on fuzzy cognitive maps to supervisory process control. Fuzzy cognitive maps are a neuro-fuzzy methodology that can accurate model complexly system using a causal-effect fuzzy reasoning. In the proposed approach, new types of concept and relation, not restricted to cause–effect ones, are added to the model resulting in a dynamic fuzzy cognitive map (D-FCM). In this sense, a supervisory system is developed in order to control a fermentation process. This process has a non-linear behavior and presents several problems, such as non-minimum phase and large accommodation time. The supervisor goal is to operate the process in normal and critical conditions. The expert knowledge about the process behavior in both conditions is used to build the D-FCM supervisor. Simulation results are presented in order to validate the proposed intelligent supervisor.     

Quantization effects on the equilibrium behavior of combined fuzzy cognitive maps

Fuzzy cognitive maps (FCMs) allow experts to express their knowledge by drawing weighted causal digraphs. Experts can pool or fuse their knowledge by adding the underlying FCM causal matrices. This naturally extends the ordered‐weighted‐averaging (OWA) technique to averaging dynamical systems and can create complex dynamical systems from several simpler ones. Edge quantization allows experts to state their knowledge in the simpler terms of causal increase (1), decrease (?1), or absence (0). We model the expert FCMs as a sequence of random fields to study the small‐sample effects of quantizing both the causal edges and the fuzzy‐set concept nodes. The averaged quantized random matrices exhibit large‐sample convergence to the population means of the unquantized matrices in accordance with the Strong Law of Large Numbers. But the small‐sample averages can show substantial diversity of equilibrium attractors (fixed points or limit cycles). We use statistical tests—chi‐square tests, Spearman's rank coefficient, the Kolmogorov–Smirnov test, and the fuzzy equality of limit cycle histograms—to show that this small‐sample equilibrium diversity increases as the node multivalence or fuzzy‐set quantization increases. The appendix presents a new probabilistic convergence theorem that shows that edge quantization or thresholding does not affect FCM combination for large expert sample sizes: the sample mean of quantized expert causal edge values converges with probability one to the population mean causal edge values. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 181–202, 2007.     

Intelligent modeling with agent‐based fuzzy cognitive map

This article presents an agent‐based fuzzy cognitive map (ABFCM) developed injecting the concept of multi‐agent system (MAS) into the fuzzy cognitive map (FCM). Fuzzy cognitive map is used for qualitative modeling and simulation. Compared to the FCM, the ABFCM enables different inference algorithms in each node enabling simulation of systems with diverse behavior concepts. Each map node can exhibit individual, more or less intelligent, behavior and still can interact with other nodes to conclude on system behavior. Resulting method also enables automatic results interpretation adding additional intelligence to a classic FCM. Explanation of the obtained system architecture with FCM and MAS integration is presented in the article. The experimental results in the article are obtained with the ABFCM prototype, developed on the basis of ABFCM structure given in the article. Multi‐agent technology can bring new properties into existing fields and methods, like in the ABFCM case. © 2010 Wiley Periodicals, Inc.     

Type-2 fuzzy variables and their arithmetic

This paper proposes an axiomatic framework from which we develop the theory of type-2 (T2) fuzziness, called fuzzy possibility theory. First, we introduce the concept of a fuzzy possibility measure in a fuzzy possibility space (FPS). The fuzzy possibility measure takes on regular fuzzy variable (RFV) values, so it generalizes the scalar possibility measure in the literature. One of the interesting consequences of the FPS is that it leads to a new definition of T2 fuzzy set on the Euclidean space $\Re^m,This paper proposes an axiomatic framework from which we develop the theory of type-2 (T2) fuzziness, called fuzzy possibility theory. First, we introduce the concept of a fuzzy possibility measure in a fuzzy possibility space (FPS). The fuzzy possibility measure takes on regular fuzzy variable (RFV) values, so it generalizes the scalar possibility measure in the literature. One of the interesting consequences of the FPS is that it leads to a new definition of T2 fuzzy set on the Euclidean space ?^m,\Re^m, which we call T2 fuzzy vector, as a map to the space instead of on the space. More precisely, we define a T2 fuzzy vector as a measurable map from an FPS to the space ?^m\Re^m of real vectors. In the current development, we are suggesting that T2 fuzzy vector is a more appropriate definition for a T2 fuzzy set on ?^m.\Re^m. In the literature, a T2 fuzzy set is usually defined via its T2 membership function, whereas in this paper, we obtain the T2 possibility distribution function as the transformation of a fuzzy possibility measure from a universe to the space ?^m\Re^m via T2 fuzzy vector. Second, we develop the product fuzzy possibility theory. In this part, we give a general extension theorem about product fuzzy possibility measure from a class of measurable atom-rectangles to a product ample field, and discuss the relationship between a T2 fuzzy vector and T2 fuzzy variables. We also prove two useful theorems about the existence of an FPS and a T2 fuzzy vector based on the information from a finite number of RFV-valued maps. The two results provide the possible interpretations for the concepts of the FPS and the T2 fuzzy vector, and thus reinforce the credibility of the approach developed in this paper. Finally, we deal with the arithmetic of T2 fuzzy variables in fuzzy possibility theory. We divide our discussion into two cases according to whether T2 fuzzy variables are defined on single FPS or on different FPSs, and obtain two theorems about T2 fuzzy arithmetic.     

A fuzzy ontology and its application to news summarization.

In this paper, a fuzzy ontology and its application to news summarization are presented. The fuzzy ontology with fuzzy concepts is an extension of the domain ontology with crisp concepts. It is more suitable to describe the domain knowledge than domain ontology for solving the uncertainty reasoning problems. First, the domain ontology with various events of news is predefined by domain experts. The document preprocessing mechanism will generate the meaningful terms based on the news corpus and the Chinese news dictionary defined by the domain expert. Then, the meaningful terms will be classified according to the events of the news by the term classifier. The fuzzy inference mechanism will generate the membership degrees for each fuzzy concept of the fuzzy ontology. Every fuzzy concept has a set of membership degrees associated with various events of the domain ontology. In addition, a news agent based on the fuzzy ontology is also developed for news summarization. The news agent contains five modules, including a retrieval agent, a document preprocessing mechanism, a sentence path extractor, a sentence generator, and a sentence filter to perform news summarization. Furthermore, we construct an experimental website to test the proposed approach. The experimental results show that the news agent based on the fuzzy ontology can effectively operate for news summarization.     

区间直觉模糊粗糙集

将模糊粗糙集推广到区间直觉模糊粗糙集,基于区间直觉模糊等价关系和两个论域之间的一般区间直觉模糊关系,给出了区间直觉模糊粗糙集模型的不同形式,并讨论了一些相关性质。     

A formal approach to fuzzy modeling

A formalism for coding fuzzy models of dynamical systems is presented. It is shown that the formalism is rich enough to capture the performance of arbitrary conventional discrete time dynamical systems whose transition maps are polynomials with rational coefficients. The proof of this fact provides a constructive algorithm for generating fuzzy models to arbitrarily closely approximate an arbitrary map on a compact set. Our modeling formalism highlights the similarities between fuzzy systems and hybrid control systems. We hope to be able to exploit these similarities by extending results from the area of hybrid systems to the fuzzy domain and vice versa     

基于相似粗糙集和模糊认知图的文本分类研究

阐述了基于相似粗糙集和模糊认知图的文本分类问题,提出了一种基于模糊认知图的文本分类推理算法,使文本分类成为一个基于文本特征项的权和特征项与类别的相关度构成的模糊认知图进行推理的结果,最后对该算法进行了实验,并对结果进行了分析.     

On employing fuzzy modeling algorithms for the valuation of residential premises

In this paper, we investigate fuzzy modeling techniques for predicting the prices of residential premises, based on some main drivers such as usable area of premises, age of a building, number of rooms in a flat, floor on which a flat is located, number of storeys in a building as well as the distance from the city center. Our proposed modeling techniques rely on two aspects: the first one (called SparseFIS) is a batch off-line modeling method and tries to out-sparse an initial dense rule population by optimizing the rule weights within an iterative optimization procedure subject to constrain the number of important rules; the second one (called FLEXFIS) is a single-pass incremental method which is able to build up fuzzy models in an on-line sample-wise learning context. As such, it is able to adapt former generated prediction models with new data recordings on demand and also to cope with on-line data streams. The final obtained fuzzy models provide some interpretable insight into the relations between the various features and residential prices in form of linguistically readable rules (IF-THEN conditions). Both methods will be compared with a state-of-the-art premise estimation method usually conducted by many experts and exploiting heuristic concepts such as sliding time window, nearest neighbors and averaging. The comparison is based on a two real-world data set including prices for residential premises within the years 1998-2008.     

Predicting helix pair structure from fuzzy contact maps

One approach to protein structure prediction is to first predict from sequence, a thresholded and binary 2D representation of a protein's topology known as a contact map. The predicted contact map can be used as distance constraints to construct a 3D structure. We focus on the latter half of the process for helix pairs and present an approach that aims to obtain a set of non-binary distance constraints from contacts maps. We extend the definition of “in contact” by incorporating fuzzy logic to construct fuzzy contact maps. Then, template-based retrieval and distance geometry bound smoothing were applied to obtain distance constraints in the form of a distance map. From the distance map, we can calculate the helix pair structure. Our experimental results indicate that distance constraints close to the true distance map could be predicted at various noise levels and the resulting structure was highly correlated to the predicted distance map.     

Integrating high resolution remote sensing,GIS and fuzzy set theory for identifying susceptibility areas of forest insect infestations

The use of fuzzy set theory has become common in remote sensing and geographical information system (GIS) applications to deal with issues surrounding the uncertainty of geospatial datasets. The objective of this study is to develop a model that integrates the concept of fuzzy set theory with remote sensing and GIS in order to produce susceptibility maps of insect infestations in forest landscapes. Fuzzy set theory was applied to information extracted from multiple‐year high resolution remote sensing data and integrated in a raster‐based GIS to create a map indicating the spatial variation of insect susceptibility in a landscape. Variable‐specific fuzzy membership functions were developed based on expert knowledge and existing data, and integrated through a semantic import model. The results from a case study on mountain pine beetle (Dendroctonus ponderosae Hopkins) illustrate that the model provides a method to successfully estimate areas of varying susceptibility to insect infestation from high resolution remote sensing images. It was concluded that fuzzy sets are an adequate method for dealing with uncertainty in defining susceptibility variables. The susceptibility maps can be utilized for guiding management decisions based on the spatial aspects of insect–host relationships.