101,178 research outputs found

    Geometric Defuzzification Revisited

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    The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.In this paper the Geometric Defuzzification strategy for type-2 fuzzy sets is reappraised. For both discretised and geometric fuzzy sets the techniques for type-1, interval type-2, and generalised type-2 defuzzification are presented in turn. In the type-2 case the accuracy of Geometric Defuzzification is assessed through a series of test runs on interval type-2 fuzzy sets, using Exhaustive Defuzzification as the benchmark method. These experiments demonstrate the Geometric Defuzzifier to be wildly inaccurate. The test sets take many shapes; they are not confined to those type-2 sets with rotational symmetry that have previously been acknowledged by the technique’s developers to be problematic as regards accuracy. Type-2 Geometric Defuzzification is then examined theoretically. The defuzzification strategy is demonstrated to be built upon a fallacious application of the concept of centroid. This explains the markedly inaccurate experimental results. Thus the accuracy issues of type-2 Geometric Defuzzification are revealed to be inevitable, fundamental and significant

    The Collapsing Defuzzifier for discretised generalised type-2 fuzzy sets

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    The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.The Greenfield–Chiclana Collapsing Defuzzifier is an established efficient accurate technique for the defuzzification of the interval type-2 fuzzy set. This paper reports on the extension of the Collapsing Defuzzifier to the generalised type-2 fuzzy set. Existing techniques for the defuzzification of generalised type-2 fuzzy sets are presented after which the interval Collapsing Defuzzifier is summarised. The collapsing technique is then extended to generalised type-2 fuzzy sets, giving the Generalised Greenfield–Chiclana Collapsing Defuzzifier. This is contrasted experimentally with both the benchmark Exhaustive Defuzzifier and the α-Planes/Karnik–Mendel Iterative Procedure approach in relation to efficiency and accuracy. The GGCCD is demonstrated to be many times faster than the Exhaustive Defuzzifier and its accuracy is shown to be excellent. In relation to the α-Planes/Karnik–Mendel Iterative Procedure approach it is shown to be comparable in accuracy, but faster

    Exploration of Subjective Color Perceptual-Ability by EEG-Induced Type-2 Fuzzy Classifiers

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    Perceptual-ability informally refers to the ability of a person to recognize a stimulus. This paper deals with color perceptual-ability measurement of subjects using brain response to basic color (red, green and blue) stimuli. It also attempts to determine subjective ability to recognize the base colors in presence of noise tolerance of the base colors, referred to as recognition tolerance. Because of intra- and inter-session variations in subjective brain signal features for a given color stimulus, there exists uncertainty in perceptual-ability. In addition, small variations in the color stimulus result in wide variations in brain signal features, introducing uncertainty in perceptual-ability of the subject. Type-2 fuzzy logic has been employed to handle the uncertainty in color perceptual-ability measurements due to a) variations in brain signal features for a given color, and b) the presence of colored noise on the base colors. Because of limited power of uncertainty management of interval type-2 fuzzy sets and high computational overhead of its general type-2 counterpart, we developed a semi-general type-2 fuzzy classifier to recognize the base color. It is important to note that the proposed technique transforms a vertical slice based general type-2 fuzzy set into an equivalent interval type-2 counterpart to reduce the computational overhead, without losing the contributions of the secondary memberships. The proposed semi-general type-2 fuzzy sets induced classifier yields superior performance in classification accuracy with respect to existing type-1, type-2 and other well-known classifiers. The brain-understanding of a perceived base or noisy base colors is also obtained by exact low resolution electromagnetic topographic analysis (e-LORETA) software. This is used as the reference for our experimental results of the semi-general type-2 classifier in color perceptual-ability detection. Statistical tests undertaken confirm the superiority of the proposed classifier over its competitors. The proposed technique is expected to have interesting applications in identifying people with excellent color perceptual-ability for chemical, pharmaceutical and textile industries

    Improving risk-adjusted performance in high frequency trading using interval type-2 fuzzy logic

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    In this paper, we investigate the ability of higher order fuzzy systems to handle increased uncertainty, mostly induced by the market microstructure noise inherent in a high frequency trading (HFT) scenario. Whilst many former studies comparing type-1 and type-2 Fuzzy Logic Systems (FLSs) focus on error reduction or market direction accuracy, our interest is predominantly risk-adjusted performance and more in line with both trading practitioners and upcoming regulatory regimes. We propose an innovative approach to design an interval type-2 model which is based on a generalisation of the popular type-1 ANFIS model. The significance of this work stems from the contributions as a result of introducing type-2 fuzzy sets in intelligent trading algorithms, with the objective to improve the risk-adjusted performance with minimal increase in the design and computational complexity. Overall, the proposed ANFIS/T2 model scores significant performance improvements when compared to both standard ANFIS and Buy-and-Hold methods. As a further step, we identify a relationship between the increased trading performance benefits of the proposed type-2 model and higher levels of microstructure noise. The results resolve a desirable need for practitioners, researchers and regulators in the design of expert and intelligent systems for better management of risk in the field of HFT

    Comparison Uncertainty of Different Types of Membership Functions in T2FLS: Case of International Financial Market

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    This article deals with the determination and comparison of different types of functions of the type-2 interval of fuzzy logic, using a case study on the international financial market. The model is demonstrated on the time series of the leading stock index DJIA of the US market. Type-2 Fuzzy Logic membership features are able to include additional uncertainty resulting from unclear, uncertain or inaccurate financial data that are selected as inputs to the model. Data on the financial situation of companies are prone to inaccuracies or incomplete information, which is why the type-2 fuzzy logic application is most suitable for this type of financial analysis. This paper is primarily focused on comparing and evaluating the performance of different types of type-2 fuzzy membership functions with integrated additional uncertainty. For this purpose, several model situations differing in shape and level or degree of uncertainty of membership functions are constructed. The results of this research show that type-2 fuzzy sets with dual membership functions is a suitable expert system for highly chaotic and unstable international stock markets and achieves higher accuracy with the integration of a certain level of uncertainty compared to type-1 fuzzy logic

    Novel Intuitionistic Based Interval Type-2 Fuzzy Similarity Measures with Application to Clustering

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    Similarity measures have been widely used in applications dealing with reasoning, classification and information retrieval. In this paper, we first propose three new Interval Type-2 Fuzzy Similarity measures (IT-2 FSMs) as a dual concept of some semi-metric distances between Intuitionistic Fuzzy Sets (IFSs). We also prove that the extended IT-2 FSMs satisfy many common properties (i.e. reflexivity, transivity, symmetry and overlapping). Experiments are carried out on a variety of datasets including UCI Learning Machine and real data. Comparative studies between the proposed IT-2 FSMs and the other well-known existing similarity measures (Gorzalczany, Bustince, Mitchell, Zeng and Li as well as VSM and Jaccard) are performed. Obviously, the best results are obtained with the IT-2 FSMs being resilient to the high levels of uncertainty noise. We also prove that our IT-2 FSMs can overcome the drawbacks of some existing similarity measures based on the accuracy rate measure. In addition, the proposed IT-2 FSMs are joined with Fuzzy cmeans algorithm as a clustering method and the proposed system is compared against the existing clustering algorithms (Type- 1 Fuzzy k-means, Type-1 and Type-2 Fuzzy c-means, Cluster Forest, Bagged Clustering, Evidence Accumulation and Random Projection). Relying on the clustering quality parameters R and C (equivalent to the standard classification accuracy), the advanced IT-2FSMs show higher classification accuracy of about 86% which outperforms nearly the other classifiers

    General and Interval Type-2 Fuzzy Face-Space Approach to Emotion Recognition

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    Facial expressions of a person representing similar emotion are not always unique. Naturally, the facial features of a subject taken from different instances of the same emotion have wide variations. In the presence of two or more facial features, the variation of the attributes together makes the emotion recognition problem more complicated. This variation is the main source of uncertainty in the emotion recognition problem, which has been addressed here in two steps using type-2 fuzzy sets. First a type-2 fuzzy face space is constructed with the background knowledge of facial features of different subjects for different emotions. Second, the emotion of an unknown facial expression is determined based on the consensus of the measured facial features with the fuzzy face space. Both interval and general type-2 fuzzy sets (GT2FS) have been used separately to model the fuzzy face space. The interval type-2 fuzzy set (IT2FS) involves primary membership functions for m facial features obtained from n-subjects, each having l-instances of facial expressions for a given emotion. The GT2FS in addition to employing the primary membership functions mentioned above also involves the secondary memberships for individual primary membership curve, which has been obtained here by formulating and solving an optimization problem. The optimization problem here attempts to minimize the difference between two decoded signals: the first one being the type-1 defuzzification of the average primary membership functions obtained from the n-subjects, while the second one refers to the type-2 defuzzified signal for a given primary membership function with secondary memberships as unknown. The uncertainty management policy adopted using GT2FS has resulted in a classification accuracy of 98.333% in comparison to 91.667% obtained by its interval type-2 counterpart. A small improvement (approximately 2.5%) in classification accuracy by IT2FS has been attained by pre-processing measurements using - he well-known interval approach

    Fuzzy Decision Support Applied to Machine Maintenance

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    This research work focuses on the optimal algorithms of decision making and forecasting respectively, in order to achieve a better prediction. Decision making techniques and forecasting methods are investigated due to the poor accuracy of forecasting in comparison with real world data. The uncertainty of real world data leads to the use of type-1 fuzzy sets, type-2 fuzzy sets, fuzzy decision tree and fuzzy time-series for fuzzy data-mining - to which they are applied for the look-ahead based interval-valued fuzzy decision tree with optimal perimeter of the neighbourhood (LAIVFDT-OPN) model, and high-order type-2 fuzzy time series (HO-T2FTS) model. In the experiment with a real world business, a ‘computerised maintenance integration management system’ (CMIMS) is constructed as a simulation model for a case study. The CMIMS model consists of the LAIVFDT-OPN and HO-T2FTS models. It is also applied to a set of real world data from a factory in Thailand. Due to the significant uncertainty involved in machine maintenance, most tasks in machine diagnosis are still carried out manually by technicians. In this research, a prototype of CMIMS employing fuzzy data mining to diagnose machine maintenance is constructed. Considering the special features of machine maintenance data, fuzzy decision trees and fuzzy time series are adopted in the proposal method. To represent the uncertain fuzzy memberships, interval-valued fuzzy decision trees are proposed and an optimal neighbourhood perimeter is defined for look-ahead fuzzy decision trees. Based on the existing first-order type-2 time-series and high-order type-1 fuzzy time series, an improved high-order type-2 fuzzy time series method is put forward. In this case study, the CMIMS model can be used to analyse and evaluate uncertain data. It also can be employed to facilitate decision making in machine equipment status, and forecast machine maintenance plan in the future in stead of technicians. Our results demonstrated that the proposal method is effective in fuzzy decision support for machine maintenance

    Multiobjective Evolutionary Optimization of Type-2 Fuzzy Rule-Based Systems for Financial Data Classification

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    Classification techniques are becoming essential in the financial world for reducing risks and possible disasters. Managers are interested in not only high accuracy, but in interpretability and transparency as well. It is widely accepted now that the comprehension of how inputs and outputs are related to each other is crucial for taking operative and strategic decisions. Furthermore, inputs are often affected by contextual factors and characterized by a high level of uncertainty. In addition, financial data are usually highly skewed toward the majority class. With the aim of achieving high accuracies, preserving the interpretability, and managing uncertain and unbalanced data, this paper presents a novel method to deal with financial data classification by adopting type-2 fuzzy rule-based classifiers (FRBCs) generated from data by a multiobjective evolutionary algorithm (MOEA). The classifiers employ an approach, denoted as scaled dominance, for defining rule weights in such a way to help minority classes to be correctly classified. In particular, we have extended PAES-RCS, an MOEA-based approach to learn concurrently the rule and data bases of FRBCs, for managing both interval type-2 fuzzy sets and unbalanced datasets. To the best of our knowledge, this is the first work that generates type-2 FRBCs by concurrently maximizing accuracy and minimizing the number of rules and the rule length with the objective of producing interpretable models of real-world skewed and incomplete financial datasets. The rule bases are generated by exploiting a rule and condition selection (RCS) approach, which selects a reduced number of rules from a heuristically generated rule base and a reduced number of conditions for each selected rule during the evolutionary process. The weight associated with each rule is scaled by the scaled dominance approach on the fuzzy frequency of the output class, in order to give a higher weight to the minority class. As regards the data base learning, the membership function parameters of the interval type-2 fuzzy sets used in the rules are learned concurrently to the application of RCS. Unbalanced datasets are managed by using, in addition to complexity, selectivity and specificity as objectives of the MOEA rather than only the classification rate. We tested our approach, named IT2-PAES-RCS, on 11 financial datasets and compared our results with the ones obtained by the original PAES-RCS with three objectives and with and without scaled dominance, the FRBCs, fuzzy association rule-based classification model for high-dimensional dataset (FARC-HD) and fuzzy unordered rules induction algorithm (FURIA), the classical C4.5 decision tree algorithm, and its cost-sensitive version. Using nonparametric statistical tests, we will show that IT2-PAES-RCS generates FRBCs with, on average, accuracy statistically comparable with and complexity lower than the ones generated by the two versions of the original PAES-RCS. Further, the FRBCs generated by FARC-HD and FURIA and the decision trees computed by C4.5 and its cost-sensitive version, despite the highest complexity, result to be less accurate than the FRBCs generated by IT2-PAES-RCS. Finally, we will highlight how these FRBCs are easily interpretable by showing and discussing one of them

    Performance Analysis of Extracted Rule-Base Multivariable Type-2 Self-Organizing Fuzzy Logic Controller Applied to Anesthesia

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    We compare type-1 and type-2 self-organizing fuzzy logic controller (SOFLC) using expert initialized and pretrained extracted rule-bases applied to automatic control of anaesthesia during surgery. We perform experimental simulations using a nonfixed patient model and signal noise to account for environmental and patient drug interaction uncertainties. The simulations evaluate the performance of the SOFLCs in their ability to control anesthetic delivery rates for maintaining desired physiological set points for muscle relaxation and blood pressure during a multistage surgical procedure. The performances of the SOFLCs are evaluated by measuring the steady state errors and control stabilities which indicate the accuracy and precision of control task. Two sets of comparisons based on using expert derived and extracted rule-bases are implemented as Wilcoxon signed-rank tests. Results indicate that type-2 SOFLCs outperform type-1 SOFLC while handling the various sources of uncertainties. SOFLCs using the extracted rules are also shown to outperform those using expert derived rules in terms of improved control stability
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