This article explores the concepts of ocean wave multivariate multistep forecasting, reconstruction and feature selection. We introduce recurrent neural network frameworks, integrated with Bayesian hyperparameter optimization and Elastic Net methods. We consider both short- and long-term forecasts and reconstruction, for significant wave height and output power of the ocean waves. Sequence-to-sequence neural networks are being developed for the first time to reconstruct the missing characteristics of ocean waves based on information from nearby wave sensors. Our results indicate that the Adam and AMSGrad optimization algorithms are the most robust ones to optimize the sequence-to-sequence network. For the case of significant wave height reconstruction, we compare the proposed methods with alternatives on a well-studied dataset. We show the superiority of the proposed methods considering several error metrics. We design a new case study based on measurement stations along the east coast of the United States and investigate the feature selection concept. Comparisons substantiate the benefit of utilizing Elastic Net. Moreover, case study results indicate that when the number of features is considerable, having deeper structures improves the performance.

We show that deep networks are better than shallow networks at approximating functions that can be expressed as a composition of functions described by a directed acyclic graph, because the deep networks can be designed to have the same compositional structure, while a shallow network cannot exploit this knowledge. Thus, the blessing of compositionality mitigates the curse of dimensionality. On the other hand, a theorem called good propagation of errors allows to `lift' theorems about shallow networks to those about deep networks with an appropriate choice of norms, smoothness, etc. We illustrate this in three contexts where each channel in the deep network calculates a spherical polynomial, a non-smooth ReLU network, or another zonal function network related closely with the ReLU network.

Graph neural networks (GNNs) have achieved lots of success on graph-structured data. In the light of this, there has been increasing interest in studying their representation power. One line of work focuses on the universal approximation of permutation-invariant functions by certain classes of GNNs, and another demonstrates the limitation of GNNs via graph isomorphism tests. Our work connects these two perspectives and proves their equivalence. We further develop a framework of the representation power of GNNs with the language of sigma-algebra, which incorporates both viewpoints. Using this framework, we compare the expressive power of different classes of GNNs as well as other methods on graphs. In particular, we prove that order-2 Graph G-invariant networks fail to distinguish non-isomorphic regular graphs with the same degree. We then extend them to a new architecture, Ring-GNNs, which succeeds on distinguishing these graphs and provides improvements on real-world social network datasets.

ABSTRACT-An investigation of deep fuzzy systems is presented in this paper. A deep fuzzy system is represented by recursive fuzzy systems from an input terminal to output terminal. Recursive fuzzy systems are sequences of fuzzy grade memberships obtained using fuzzy transmition functions and recursive calls to fuzzy systems. A recursive fuzzy system which calls a fuzzy system times includes fuzzy chains to evaluate the final grade membership of this recursive system. A connection matrix which includes recursive calls are used to represent recursive fuzzy systems.

Field canals improvement projects (FCIPs) are one of the ambitious projects constructed to save fresh water. To finance this project, Conceptual cost models are important to accurately predict preliminary costs at the early stages of the project. The first step is to develop a conceptual cost model to identify key cost drivers affecting the project. Therefore, input variables selection remains an important part of model development, as the poor variables selection can decrease model precision. The study discovered the most important drivers of FCIPs based on a qualitative approach and a quantitative approach. Subsequently, the study has developed a parametric cost model based on machine learning methods such as regression methods, artificial neural networks, fuzzy model and case-based reasoning.

In recent years, descriptive evaluation has been introduced as a new model for educational evaluation of Iranian students. The current descriptive evaluation method is based on four-valued logic. Assessing all students with only four values is led to a lack of relative justice and the creation of unrealistic equality. Also, the complexity of the evaluation process in the current method increases teacher errors likelihood. As a suitable solution, in this paper, a fuzzy descriptive evaluation system has been proposed. The proposed method is based on fuzzy logic, which is an infinite-valued logic and it can perform approximate reasoning on natural language propositions. By the proposed fuzzy system, student assessment is performed over the school year with infinite values instead of four values. But to eliminate the diversity of assigned values to students, at the end of the school year, the calculated values for each student will be rounded to the nearest value of the four standard values of the current descriptive evaluation system. It can be implemented easily in an appropriate smartphone app, which makes it much easier for the teachers to evaluate the evaluation process. In this paper, the evaluation process of the elementary third-grade mathematics course in Iran during the period from the beginning of the MEHR (The Seventh month of Iran) to the end of BAHMAN (The Eleventh Month of Iran) is examined by the proposed system. To evaluate the validity of this system, the proposed method has been simulated in MATLAB software.

Abstract--In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. In [12] a novel RBF network with the multi-kernel is proposed to obtain an optimized and I. INTRODUCTION The unknown centres of the multikernels The RBF neural networks have shown excellent performance are determined by an improved k-means clustering in a number of problems of practical interest. An orthogonal least squares (OLS) algorithm is reservoirs of brine are analyzed for physicochemical properties used to determine the remaining parameters. The convergence of the ACA is analyzed by the [3] the RBF kernel is used to predict the pressure gradient Lyapunov criterion. In the context of nuclear physics, RBF Cognitive Radial Basis Function network (McRBFN) and its has been effectively used to model the stopping power data Projection based Learning (PBL) referred to as PBL-McRBFN of materials as in [4].

This paper discusses the trapezoidal fuzzy number(TrFN); Interval-valued intuitionistic fuzzy number(IVIFN); neutrosophic set and its operational laws; and, trapezoidal neutrosophic set(TrNS) and its operational laws. Based on the combination of IVIFN and TrNS, an Interval Valued Trapezoidal Neutrosophic Set (IVTrNS) is proposed followed by its operational laws. The paper also presents the score and accuracy functions for the proposed Interval Valued Trapezoidal Neutrosophic Number (IVTrNN). Then, an interval valued trapezoidal neutrosophic weighted arithmetic averaging (IVTrNWAA) operator is introduced to combine the trapezoidal information which is neutrosophic and in the unit interval of real numbers. Finally, a method is developed to handle the problems in the multi attribute decision making(MADM) environment using IVTrNWAA operator followed by a numerical example of NFRs prioritization to illustrate the relevance of the developed method.

This survey samples from the ever-growing family of adaptive resonance theory (ART) neural network models used to perform the three primary machine learning modalities, namely, unsupervised, supervised and reinforcement learning. It comprises a representative list from classic to modern ART models, thereby painting a general picture of the architectures developed by researchers over the past 30 years. The learning dynamics of these ART models are briefly described, and their distinctive characteristics such as code representation, long-term memory and corresponding geometric interpretation are discussed. Useful engineering properties of ART (speed, configurability, explainability, parallelization and hardware implementation) are examined along with current challenges. Finally, a compilation of online software libraries is provided. It is expected that this overview will be helpful to new and seasoned ART researchers.

In this paper, we propose an intelligence approach based on fuzzy logic to modeling human intelligence in washing clothes. At first, an intelligent feedback loop is designed for perception-based sensing of dirt inspired by human color understanding. Then, when color stains leak out of some colored clothes the human probabilistic decision making is computationally modeled to detect this stain leakage and thus the problem of recognizing dirt from stain can be considered in the washing process. Finally, we discuss the fuzzy control of washing clothes and design and simulate a smart controller based on the fuzzy intelligence feedback loop.