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In this paper, we propose a cascade AdaBoost neural network (CANN) based on concepts and construct of AdaBoost neurons and cascade structure. Compared with AdaBoost, CANN can represent complex relationships between features. In CANN, representation learning is performed through AdaBoost, and the method of random selection features is utilized to encourage the diversity of AdaBoost neurons. Through the cascade structure, CANN has the context structure for complex feature representation. At the same time, in order to avoid the problem of feature disappearance, shortcut connection is used to add the previous information to the later nodes. Furthermore, particle swarm optimization (PSO) algorithm is utilized to optimize the structure of CANN, it can obtain the number of iterations to achieve better performance. Two types of CANN are proposed based — binary-classification CANN (BCANN) or multi-classification CANN (MCANN). The performance of CANN is evaluated with two kinds of data sets: machine learning data sets and atrial fibrillation data set. A comparative analysis illustrates that the proposed CANN leads to better performance than the models reported in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we relax the definition of Rényi information dimension. The power law of the Entropy-Layer in the Galton board is discovered and we calculate its information fractal dimension. When the Galton board is extended to bias or three-dimensional space, we get the same fractal features. In addition, according to the connection between Pascal's triangle and the Poisson distribution, we find constrained Poisson distribution groups with the same information dimension. This is the first time the information entropy is utilized to explore the fractal features of the Galton board and Pascal's triangle. [ABSTRACT FROM AUTHOR]

Eigenvalues and eigenvectors are widely used in various applications. Particularly, these concepts underlie analysis of consistency of a decision maker's (DMs) preference knowledge. In real-world problems, DMs knowledge is inherently associated with imprecision and partial reliability. This involves combination of fuzzy and probabilistic information. The concept of a Z-number is a formal construct to describe such kind of information. In this study, we formulate the concepts of Z-number valued eigenvalue and eigenvector for matrices components of which are Z-numbers. A formal statement of the problem and a solution method for computation of Z-number valued eigensolutions are proposed. Numerical examples and an application devoted to foreign market selection problem are provided to show the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

Distributivity between two operations is a property posed many years ago — that is especially interesting in the framework of logical connectives because of its applications to fuzzy logic and approximate reasoning as their applications. Since semi-uninorms have been used in these topics, the study of the distributivity between two semi-uninorms becomes of particular interest that calls for thorough studies. The distributivity between two semi-uninorms, which are non-commutative and non-associative uninorms, has been developed only in the cases when both semi-uninorms are examples of very special classes of semi-uninorms. On the other hand, in general, the distributivity does not rely on the commutativity and associativity. The objective of this work is twofold. The first one is to show new solutions to distributivity equations for semi-uninorms. The second one is to check whether the results concerning the distributivity between two uninorms are valid for semi-uninorms. We investigate the distributivity involving two semi-uninorms when only one semi-uninrom lies in the most studied classes of semi-uninorms, achieving the above two objectives simultaneously. [ABSTRACT FROM AUTHOR]

Behavioral decision making is an area of multidisciplinary research attracting growing interest of scientists and practitioners, economists, and business people. A wide spectrum of successful theories is present now, including Prospect theory, multiple priors models, studies on altruism, trust and fairness. However, these theories are developed for precise and complete information, whereas real information concerning a decision maker's (DM) behavior and environment is imperfect, qualitative, and, as a result, often described in natural language (NL). We suggest an approach based on modeling a DM's behavior by a set of states. Each state represents a certain principal behavior. In our approach, states of nature and DM's states constitute a single space of combined states. For formalizing relevant information described in NL, we use fuzzy set theory. The utility model is based on Choquet-like integration over combined states. The investigations show that Expected Utility, Choquet Expected Utility and Cumulative Prospect Theory are special cases of the suggested approach. We apply the suggested approach to solving a benchmark and a real-life decision problem. The obtained results show validity of the suggested approach. [ABSTRACT FROM AUTHOR]

In this study, we highlight some fundamental issues of knowledge management and cast them in the setting of Granular Computing (GrC). We show how its formal constructs - information granules are instrumental in knowledge representation and specification of its level of abstraction. [ABSTRACT FROM AUTHOR]

We develop a new approach to the design of neural networks, which utilizes a collaborative framework of knowledge-driven experience. In contrast to the "standard" way of developing neural networks, which explicitly exploits experimental data, this approach incorporates a mechanism of knowledge-driven experience. The essence of the proposed scheme of learning is to take advantage of the parameters (connections) of neural networks built in the past for the same phenomenon (which might also exhibit some variability over time or space) for which are interested to construct the network on a basis of currently available data. We establish a conceptual and algorithmic framework to reconcile these two essential sources of information (data and knowledge) in the process of the development of the network. To make a presentation more focused and come up with a detailed quantification of the resulting architecture, we concentrate on the experience-based design of radial basis function neural networks (RBFNNs). We introduce several performance indexes to quantify an effect of utilization of the knowledge residing within the connections of the networks and establish an optimal level of their use. Experimental results are presented for low-dimensional synthetic data and selected datasets available at the Machine Learning Repository. [ABSTRACT FROM AUTHOR]

In this study, we introduce an advanced architecture of genetically optimized Hybrid Fuzzy Neural Networks (gHFNN) and develop a comprehensive design methodology supporting their construction. A series of numeric experiments is included to illustrate the performance of the networks. The construction of gHFNN exploits fundamental technologies of Computational Intelligence (CI), namely fuzzy sets, neural networks, and genetic algorithms (GAs). The architecture of the gHFNNs results from a synergistic usage of the genetic optimization-driven hybrid system generated by combining Fuzzy Neural Networks (FNN) with Polynomial Neural Networks (PNN). In this tandem, a FNN supports the formation of the condition part of the rule-based structure of the gHFNN. The conclusion part of the gHFNN is designed using PNNs. We distinguish between two types of the simplified fuzzy inference rule-based FNN structures showing how this taxonomy depends upon the type of a fuzzy partition of input variables. As to the conclusion part of the gHFNN, the development of the PNN dwells on two general optimization mechanisms: the structural optimization is realized via GAs whereas in case of the parametric optimization we proceed with a standard least square method-based learning. To evaluate the performance of the gHFNN, we experimented with three representative numerical examples. A comparative analysis demonstrates that the proposed gHFNN come with higher accuracy as well as superb predictive capabilities when compared with other neurofuzzy models. [ABSTRACT FROM AUTHOR]

We introduce and study a new concept of fuzzy computing units. This construct is is aimed at coping with "negative" (inhibitory) information and accommodating it in the language of fuzzy sets. The essential concept developed in this study deals with computing units exploiting the concept of balanced fuzzy sets. We recall how the membership notion of fuzzy sets can be extended to the [-1,1] range giving rise to balanced fuzzy sets and then summarize properties of augmented (extended) logic operations for these constructs. We show that this idea is particularly appealing in neurocomputing as the "negative" information captured through balanced fuzzy sets exhibits a straightforward correspondence with inhibitory processing mechanisms encountered in neural networks. This gives rise to interesting properties of balanced computing units when compared with fuzzy and logic neurons developed on the basis of classical logic and classical fuzzy sets. Illustrative examples concerning topologies and properties and learning of balanced fuzzy computing units are included. A number of illustrative examples concerning topologies, properties and learning of balanced fuzzy fuzzy computing units are included. [ABSTRACT FROM AUTHOR]

In our study we presented an effective method for clustering of Web pages. From flat HTML files we extracted keywords, formed feature vectors as representation of Web pages and applied them to a clustering method. We took advantage of the Fuzzy C-Means clustering algorithm (FCM), We demonstrated an organized and schematic manner of data collection. Various categories of Web pages were retrieved from ODP (Open Directory Project) in order to create our datasets. The results of clustering proved that the method performs well for all datasets. Finally, we presented a comprehensive experimental study examining: the behavior of the algorithm for different input parameters, internal structure of datasets and classification experiments. [ABSTRACT FROM AUTHOR]

We firstly review some fundamentals of fuzzy relation calculus and, by recalling some known results, we improve the mathematical contents of our previous papers by using the properties of a triangular norm over [0, 1]. We make wide use of the theory of fuzzy relation equations for getting lossy compression and decompression of images interpreted as two-argument fuzzy matrices. The same scope is achieved by decomposing a fuzzy matrix using the concept of Schein rank. We illustrate two algorithms with a few examples. [ABSTRACT FROM AUTHOR]

In this study, we introduce a notion of stability of information granules. Granulation of information results in a series of chunks of information usually referred to as information granules. Information granules are basic building entities involved in the formation of a broad class of systems. Information granules are percepts — entities being perceived by humans as being essential when working with some real-world phenomena, especially describing and interacting with them. The percepts need to be comprehensible. They should also reflect the experimental evidence. All in all, they should be stable meaning that they are conceptual entities that reconcile experimental reality with the subjective and ultimately observerbased judgment about the environment. Once being stable, information granules could be viewed as architecture-independent. The proposed algorithmic environment supporting this concept dwells on the ideas of statistical inference that helps quantify stability through a nonparametric testing. The Χ² goodness-of-fit test is used here as a validation mechanism. First, the study elaborates on the formation of information granules and concentrates on the descriptive and prescriptive ways of their design. In the sequel, it is revealed how these two ways interact with the construction of stable information granules. A number of experimental studies are also included. [ABSTRACT FROM AUTHOR]

We propose a hybrid architecture based on a combination of fuzzy systems and polynomial neural networks. The resulting Hybrid Fuzzy Polynomial Neural Networks (HFPNN) dwells on the ideas of fuzzy rule-based computing and polynomial neural networks. The structure of the network comprises of fuzzy polynomial neurons (FPNs) forming the nodes of the first (input) layer of the HFPNN and polynomial neurons (PNs) that are located in the consecutive layers of the network. In the FPN (that forms a fuzzy inference system), the generic rules assume the form "if A then y = P(x)" where A is a fuzzy relation in the condition space while P(x) is a polynomial standing in the conclusion part of the rule. The conclusion part of the rules, especially the regression polynomial uses several types of high-order polynomials such as constant, linear, quadratic, and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are considered. Each PN of the network realizes a polynomial type of partial description (PD) of the mapping between input and out variables. HFPNN is a flexible neural architecture whose structure is based on the Group Method of Data Handling (GMDH) and developed through learning. In particular, the number of layers of the PNN is not fixed in advance but is generated in a dynamic way. The experimental part of the study involves two representative numerical examples such as chaotic time series and Box-Jenkins gas furnace data. [ABSTRACT FROM AUTHOR]

In this study, we revisit the well-known notion of fuzzy state machines and discuss their development through learning. The systematic development of fuzzy state machines has not been pursued as intensively as it could have been expected from the breadth of the possible usage of them as various modelling platforms. We concentrate on the generalization of the well known architectures exploited in Boolean system synthesis, namely Moore and Mealy machines and show how these can be implemented in terms of generic functional modules such as fuzzy JK flip-flops and fuzzy logic neurons (AND and OR neurons) organized in the form of logic processors. It is shown that the design of the fuzzy state machines can be accomplished through their learning. The detailed learning algorithm is presented and illustrated with a series of numeric examples. The study reveals an interesting option of constructing digital systems through learning: the original problem is solved in the setting of fuzzy state machines and afterwards "binarised" into the two-valued format realized via the standard digital hardware. [ABSTRACT FROM AUTHOR]