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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]