Fuzzy Cognitive Maps (FCMs) are considered a soft computing technique combining elements of fuzzy logic and recurrent neural networks. They found multiple application in such domains as modeling of system behavior, prediction of time series, decision making and process control. Less attention, however, has been turned towards using them in pattern classification. In this work we propose an FCM based classifier with a fully connected map structure. In contrast to methods that expect reaching a steady system state during reasoning, we chose to execute a few FCM iterations (steps) before collecting output labels. Weights were learned with a gradient algorithm and logloss or cross-entropy were used as the cost function. Our primary goal was to verify, whether such design would result in a descent general purpose classifier, with performance comparable to off the shelf classical methods. As the preliminary results were promising, we investigated the hypothesis that the performance of $d$-step classifier can be attributed to a fact that in previous $d-1$ steps it transforms the feature space by grouping observations belonging to a given class, so that they became more compact and separable. To verify this hypothesis we calculated three clustering scores for the transformed feature space. We also evaluated performance of pipelines built from FCM-based data transformer followed by a classification algorithm. The standard statistical analyzes confirmed both the performance of FCM based classifier and its capability to improve data. The supporting prototype software was implemented in Python using TensorFlow library.

Artificial intelligence systems, which are designed with a capability to learn from the data presented to them, are used throughout society. These systems are used to screen loan applicants, make sentencing recommendations for criminal defendants, scan social media posts for disallowed content and more. Because these systems don't assign meaning to their complex learned correlation network, they can learn associations that don't equate to causality, resulting in non-optimal and indefensible decisions being made. In addition to making decisions that are sub-optimal, these systems may create legal liability for their designers and operators by learning correlations that violate anti-discrimination and other laws regarding what factors can be used in different types of decision making. This paper presents the use of a machine learning expert system, which is developed with meaning-assigned nodes (facts) and correlations (rules). Multiple potential implementations are considered and evaluated under different conditions, including different network error and augmentation levels and different training levels. The performance of these systems is compared to random and fully connected networks.

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent similar function spaces without a costly training phase. However, for accuracy, random feature methods require more measurements than trainable parameters, limiting their use for data-scarce applications or problems in scientific machine learning. This paper introduces the sparse random feature method that learns parsimonious random feature models utilizing techniques from compressive sensing. We provide uniform bounds on the approximation error for functions in a reproducing kernel Hilbert space depending on the number of samples and the distribution of features. The error bounds improve with additional structural conditions, such as coordinate sparsity, compact clusters of the spectrum, or rapid spectral decay.

Human emotion recognition has become a need for more realistic and interactive machines and computer systems. The greatest challenge is the availability of high-performance algorithms to effectively manage individual differences and nonstationarities in physiological data streams, i.e., algorithms that self-customize to a user with no subject-specific calibration data. We describe an evolving Gaussian Fuzzy Classifier (eGFC), which is supported by an online semi-supervised learning algorithm to recognize emotion patterns from electroencephalogram (EEG) data streams. We extract features from the Fourier spectrum of EEG data. The data are provided by 28 individuals playing the games 'Train Sim World', 'Unravel', 'Slender The Arrival', and 'Goat Simulator' - a public dataset. Different emotions prevail, namely, boredom, calmness, horror and joy. We analyze the effect of individual electrodes, time window lengths, and frequency bands on the accuracy of user-independent eGFCs. We conclude that both brain hemispheres may assist classification, especially electrodes on the frontal (Af3-Af4), occipital (O1-O2), and temporal (T7-T8) areas. We observe that patterns may be eventually found in any frequency band; however, the Alpha (8-13Hz), Delta (1-4Hz), and Theta (4-8Hz) bands, in this order, are the highest correlated with emotion classes. eGFC has shown to be effective for real-time learning of EEG data. It reaches a 72.2% accuracy using a variable rule base, 10-second windows, and 1.8ms/sample processing time in a highly-stochastic time-varying 4-class classification problem.

Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent similar function spaces without a costly training phase. However, for accuracy, random feature methods require more measurements than trainable parameters, limiting their use for data-scarce applications or problems in scientific machine learning. This paper introduces the sparse random feature method that learns parsimonious random feature models utilizing techniques from compressive sensing. We provide uniform bounds on the approximation error for functions in a reproducing kernel Hilbert space depending on the number of samples and the distribution of features. The error bounds improve with additional structural conditions, such as coordinate sparsity, compact clusters of the spectrum, or rapid spectral decay. We show that the sparse random feature method outperforms shallow networks for well-structured functions and applications to scientific machine learning tasks.

Network models provide an efficient way to represent many real life problems mathematically. In the last few decades, the field of network optimization has witnessed an upsurge of interest among researchers and practitioners. The network models considered in this thesis are broadly classified into four types including transportation problem, shortest path problem, minimum spanning tree problem and maximum flow problem. Quite often, we come across situations, when the decision parameters of network optimization problems are not precise and characterized by various forms of uncertainties arising from the factors, like insufficient or incomplete data, lack of evidence, inappropriate judgements and randomness. Considering the deterministic environment, there exist several studies on network optimization problems. However, in the literature, not many investigations on single and multi objective network optimization problems are observed under diverse uncertain frameworks. This thesis proposes seven different network models under different uncertain paradigms. Here, the uncertain programming techniques used to formulate the uncertain network models are (i) expected value model, (ii) chance constrained model and (iii) dependent chance constrained model. Subsequently, the corresponding crisp equivalents of the uncertain network models are solved using different solution methodologies. The solution methodologies used in this thesis can be broadly categorized as classical methods and evolutionary algorithms. The classical methods, used in this thesis, are Dijkstra and Kruskal algorithms, modified rough Dijkstra algorithm, global criterion method, epsilon constraint method and fuzzy programming method. Whereas, among the evolutionary algorithms, we have proposed the varying population genetic algorithm with indeterminate crossover and considered two multi objective evolutionary algorithms.

Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not conform to actual situations. In real life, everything comes in an order, so how to measure uncertainties of the dynamic process of determining sequence of propositions contained in a frame of discernment is still an open issue and no related research has been proceeded. Therefore, a novel ordinal entropy to measure uncertainties of the frame of discernment considering the order of confirmation of propositions is proposed in this paper. Compared with traditional entropies, it manifests effects on degree of uncertainty brought by orders of propositions existing in a frame of discernment. Besides, some numerical examples are provided to verify the correctness and validity of the proposed entropy in this paper.

The Intergovernmental Panel on Climate Change (IPCC) fifth assessment report states that warming of the climate system is unequivocal and notes that each of the last three decades has been successively warmer at the Earth's surface than any preceding decade since 1850. The projections of the IPCC Report regarding future global temperature change range from 1.1 to 4 C, but that temperatures increases of more than 6 C cannot be ruled out [1]. This wide range of values reflects our limitations in performing accurate projections of future climate change produced by different potential pathways of greenhouse gas (GHG) emissions. The sources of the uncertainty that prevent us from obtaining better precision are diverse. One of them is related to the computer models used to project future climate change.

We study the reinforcement learning for finite-horizon episodic Markov decision processes with adversarial reward and full information feedback, where the unknown transition probability function is a linear function of a given feature mapping. We propose an optimistic policy optimization algorithm with Bernstein bonus and show that it can achieve $\tilde{O}(dH\sqrt{T})$ regret, where $H$ is the length of the episode, $T$ is the number of interaction with the MDP and $d$ is the dimension of the feature mapping. Furthermore, we also prove a matching lower bound of $\tilde{\Omega}(dH\sqrt{T})$ up to logarithmic factors. To the best of our knowledge, this is the first computationally efficient, nearly minimax optimal algorithm for adversarial Markov decision processes with linear function approximation.

This paper describes the design and development of a prototype technique for artificial intelligence based on the fusion of genetic algorithm, neural network and fuzzy logic. It starts by establishing a relationship between the neural network and fuzzy logic. Then, it combines the genetic algorithm with them. Information fusions are at the confidence level, where matching scores can be reported and discussed. The technique is called the Genetic Neuro-Fuzzy (GNF). It can be used for high accuracy real-time environments.