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Capturing the interdependencies between real valued time series can be achieved by finding common similar patterns. The abstraction of time series makes the process of finding similarities closer to the way as humans do. Therefore, the abstraction by means of a symbolic levels and finding the common patterns attracts researchers. One particular algorithm, Longest Common Subsequence, has been used successfully as a simila rity measure between two sequences including real valued time series. In this paper, we propose Fuzzy Longest Common Subsequence matching for time series.

Shakespeare teaches us in this Hamlet quote that reality is much more complex than our mental projections and understanding. Reality is fuzzier than we would care to think. Although introducing subjectivities to modeling seems to harm the'objectivity' for the purists, this objectivity is more of a deliberate ignorance of real life issues than a sound strategy for modeling. There is a myriad of ambiguities and uncertainties in the information we receive decode and signal which tends to limit the functionality of traditional methods that are based on crisp logic. For instance, while USD 500 premium means you will have to give USD 500 to purchase the policy, the opinion whether this premium is adequate for the insurer or not, and reasonable or too expensive for the consumer is quite subjective. Fuzzy theory is developed to overcome this insufficiency by taking account of ambiguity in information.

This paper presents the development of a hybrid learning system based on Support Vector Machines (SVM), Adaptive Neuro-Fuzzy Inference System (ANFIS) and domain knowledge to solve prediction problem. The proposed two-stage Domain Knowledge based Fuzzy Information System (DKFIS) improves the prediction accuracy attained by ANFIS alone. The proposed framework has been implemented on a noisy and incomplete dataset acquired from a hydrocarbon field located at western part of India. Here, oil saturation has been predicted from four different well logs i.e. gamma ray, resistivity, density, and clay volume. In the first stage, depending on zero or near zero and non-zero oil saturation levels the input vector is classified into two classes (Class 0 and Class 1) using SVM. The classification results have been further fine-tuned applying expert knowledge based on the relationship among predictor variables i.e. well logs and target variable - oil saturation. Second, an ANFIS is designed to predict non-zero (Class 1) oil saturation values from predictor logs. The predicted output has been further refined based on expert knowledge. It is apparent from the experimental results that the expert intervention with qualitative judgment at each stage has rendered the prediction into the feasible and realistic ranges. The performance analysis of the prediction in terms of four performance metrics such as correlation coefficient (CC), root mean square error (RMSE), and absolute error mean (AEM), scatter index (SI) has established DKFIS as a useful tool for reservoir characterization.

In this paper, we attempt to extend Multi Attributive Border Approximation area Comparison (MABAC) approach for multi-attribute decision making (MADM) problems based on type-2 fuzzy sets (IT2FSs). As a special case of IT2FSs interval type-2 trapezoidal fuzzy numbers (IT2TrFNs) are adopted here to deal with uncertainties present in many practical evaluation and selection problems. A systematic description of MABAC based on IT2TrFNs is presented in the current study. The validity and feasibility of the proposed method are illustrated by a practical example of selecting the most suitable candidate for a software company which is heading to hire a system analysis engineer based on few attributes. Finally, a comparison with two other existing MADM methods is described.

This Website contains a short introduction to Noisy Data together with the more relevant bibliography and it also contains the complementary material to the SCI2S research group papers on Noisy Data in Data Mining.

Arthur C. Clarke famously stated that "any sufficiently advanced technology is indistinguishable from magic." No current technology embodies this statement more than neural networks and deep learning. And like any good magic it not only dazzles and inspires but also puts fear into people's hearts. One known property of artificial neural networks (ANNs) is that they are universal function approximators. This means that any mathematical function can be represented by a neural network.

Abstract--In this paper we propose a novel approach for learning from data using rule based fuzzy inference systems where the model parameters are estimated using Bayesian inference and Markov Chain Monte Carlo (MCMC) techniques. We show the applicability of the method for regression and classification tasks using synthetic data-sets and also a real world example in the financial services industry. Then we demonstrate how the method can be extended for knowledge extraction to select the individual rules in a Bayesian way which best explains the given data. Finally we discuss the advantages and pitfalls of using this method over state-of-the-art techniques and highlight the specific class of problems where this would be useful. ROBABILITY theory and fuzzy logic have been shown to be complementary [1] and various works have looked at the symbiotic integration of these two paradigms [2], [3] including the recently introduced concept of Z-numbers [4]. Historically fuzzy logic has been applied to problems involving imprecision in linguistic variables, while probability theory has been used for quantifying uncertainty in a wide range of disciplines. V arious generalisations and extensions of fuzzy sets have been proposed to incorporate uncertainty and vagueness which arise from multiple sources. For example, the type-2 fuzzy [5], [6] sets and type-n fuzzy sets [5] can include uncertainty while defining the membership functions themselves. Intuitionistic fuzzy sets [7] additionally introduce the degree of non-membership of an element to take into account that there might be some hesitation degree and the degree of membership and non-membership of an element might not always add to one. Non-stationary fuzzy sets [8] can model variation of opinion over time by defining a collection of type 1 fuzzy sets and an explicit relationship between them. Fuzzy multi-sets [9] generalise crisp sets where multiple occurrences of an element are permitted. Hesitant fuzzy sets [10] have been proposed from the motivation that the problem of assigning a degree of membership to an element is not because of a margin of error (like Atanassov's intuitionistic fuzzy sets) or a possibility distribution on possibility values (e.g. Formally these can be viewed as fuzzy multi-sets but with a different interpretation.

In this paper, we take a new look at the possibilistic c-means (PCM) and adaptive PCM (APCM) clustering algorithms from the perspective of uncertainty. This new perspective offers us insights into the clustering process, and also provides us greater degree of flexibility. We analyze the clustering behavior of PCM-based algorithms and introduce parameters $\sigma_v$ and $\alpha$ to characterize uncertainty of estimated bandwidth and noise level of the dataset respectively. Then uncertainty (fuzziness) of membership values caused by uncertainty of the estimated bandwidth parameter is modeled by a conditional fuzzy set, which is a new formulation of the type-2 fuzzy set. Experiments show that parameters $\sigma_v$ and $\alpha$ make the clustering process more easy to control, and main features of PCM and APCM are unified in this new clustering framework (UPCM). More specifically, UPCM reduces to PCM when we set a small $\alpha$ or a large $\sigma_v$, and UPCM reduces to APCM when clusters are confined in their physical clusters and possible cluster elimination are ensured. Finally we present further researches of this paper.

Self-organizing maps (SOM) and neural networks of learning vector quantization (LVQ) have seen extensive use for solving different problems in Data Mining domain (clustering, classification, fault detection and compression of information etc.). This type of neural networks was proposed by T. Kohonen [1, 2] and represents, in fact, a single-layer feedforward architecture, which provides an operator for mapping of input space into the output space. Operation-wise SOM and LVQ are quite similar to each neuron is fed input signal (sample) producing output, which is used during competition stage to determine winning neuron - usually the one with maximum output signal value. Vector of synaptic weights for winning neuron is the one closest to the input sample in terms of the metric chosen (which is Euclidian metric in most cases). Next is neurons adjustment phase.