An interval type-2 fuzzy logic system-based method for prediction interval construction

This paper introduces a new non-parametric method for uncertainty quantification through construction of prediction intervals (PIs). The method takes the left and right end points of the type-reduced set of an interval type-2 fuzzy logic system (IT2FLS) model as the lower and upper bounds of a PI. No assumption is made in regard to the data distribution, behaviour, and patterns when developing intervals. A training method is proposed to link the confidence level (CL) concept of PIs to the intervals generated by IT2FLS models. The new PI-based training algorithm not only ensures that PIs constructed using IT2FLS models satisfy the CL requirements, but also reduces widths of PIs and generates practically informative PIs. Proper adjustment of parameters of IT2FLSs is performed through the minimization of a PI-based objective function. A metaheuristic method is applied for minimization of the non-linear non-differentiable cost function. Performance of the proposed method is examined for seven synthetic and real world benchmark case studies with homogenous and heterogeneous noise. The demonstrated results indicate that the proposed method is capable of generating high quality PIs. Comparative studies also show that the performance of the proposed method is equal to or better than traditional neural network-based methods for construction of PIs in more than 90% of cases. The superiority is more evident for the case of data with a heterogeneous noise. © 2014 Elsevier B.V.

Transfer learning using the online FMM model

In this paper, we present an analysis on transfer learning using the Fuzzy Min-Max (FMM) neural network with an online learning strategy. Transfer learning leverages information from the source domain in solving problems in the target domain. Using the online FMM model, the data samples are trained one at a time. In order to evaluate the online FMM model, a transfer learning data set, based on data samples collected from real landmines, is used. The experimental results of FMM are analyzed and compared with those from other methods in the literature. The outcomes indicate that the online FMM model is effective for undertaking transfer learning tasks.

Localized learning by emerging multinational enterprises in developed host countries: a fuzzy-set analysis of Chinese foreign direct investment in Australia

Firms learn general international management and foreign market specific knowledge in their internationalization process. Firms' strategic emphasis on generalized vs. localized learning is an important yet underexplored issue in the extant literature. Drawing on the theoretical framework of dynamic capability, and in the context of emerging multinational enterprises' FDI into developed host countries, this study examines the equifinal process-position-path configurations of firms that will motivate them to engage in localized learning (as opposed to generalized learning). Utilizing primary and secondary data of eleven Chinese foreign direct investments in Australia, collected at both headquarters and subsidiary levels, we conducted fuzzy-set qualitative comparative analysis (fsQCA) that provided substantial support to our propositions. This study contributes to the internationalization process model by identifying equifinal process-position-path configurations, as well as their core and peripheral conditions that motivate localized learning at both the headquarters and the subsidiary levels.

Condition monitoring of broken rotor bars using a hybrid FMM-GA model

A condition monitoring system for induction motors using a hybrid Fuzzy Min-Max (FMM) neural network and Genetic Algorithm (GA) is presented in this paper. Two types of experiments, one from the finite element method and another from real laboratory tests of broken rotor bars in an induction motor are conducted. The induction motor with broken rotor bars is operated under different load conditions. FMM is first used for learning and distinguishing between a healthy motor and one with broken rotor bars. The GA is then utilized for extracting fuzzy if-then rules using the don’t care approach in minimizing the number of rules. The results clearly demonstrate the effectiveness of the hybrid FMM-GA model in condition monitoring of broken rotor bars in induction motors.

Motor fault detection and diagnosis using a hybrid FMM-CART model with online learning

In this paper, a hybrid online learning model that combines the fuzzy min-max (FMM) neural network and the Classification and Regression Tree (CART) for motor fault detection and diagnosis tasks is described. The hybrid model, known as FMM-CART, incorporates the advantages of both FMM and CART for undertaking data classification (with FMM) and rule extraction (with CART) problems. In particular, the CART model is enhanced with an importance predictor-based feature selection measure. To evaluate the effectiveness of the proposed online FMM-CART model, a series of experiments using publicly available data sets containing motor bearing faults is first conducted. The results (primarily prediction accuracy and model complexity) are analyzed and compared with those reported in the literature. Then, an experimental study on detecting imbalanced voltage supply of an induction motor using a laboratory-scale test rig is performed. In addition to producing accurate results, a set of rules in the form of a decision tree is extracted from FMM-CART to provide explanations for its predictions. The results positively demonstrate the usefulness of FMM-CART with online learning capabilities in tackling real-world motor fault detection and diagnosis tasks. © 2014 Springer Science+Business Media New York.

A clustering-based failure mode and effect analysis model and its application to the edible bird nest industry

Failure mode and effect analysis (FMEA) is a popular safety and reliability analysis tool in examining potential failures of products, process, designs, or services, in a wide range of industries. While FMEA is a popular tool, the limitations of the traditional Risk Priority Number (RPN) model in FMEA have been highlighted in the literature. Even though many alternatives to the traditional RPN model have been proposed, there are not many investigations on the use of clustering techniques in FMEA. The main aim of this paper was to examine the use of a new Euclidean distance-based similarity measure and an incremental-learning clustering model, i.e., fuzzy adaptive resonance theory neural network, for similarity analysis and clustering of failure modes in FMEA; therefore, allowing the failure modes to be analyzed, visualized, and clustered. In this paper, the concept of a risk interval encompassing a group of failure modes is investigated. Besides that, a new approach to analyze risk ordering of different failure groups is introduced. These proposed methods are evaluated using a case study related to the edible bird nest industry in Sarawak, Malaysia. In short, the contributions of this paper are threefold: (1) a new Euclidean distance-based similarity measure, (2) a new risk interval measure for a group of failure modes, and (3) a new analysis of risk ordering of different failure groups. © 2014 The Natural Computing Applications Forum.

A new fuzzy ratio and its application to the single input rule modules connected fuzzy inference system

The principle of ratios has been applied to many real world problems, e.g. the part-to-part and part-to-whole ratio formulations. As it is difficult for humans to provide an exact ratio in many real situations, we introduce a fuzzy ratio in this paper. We use some notions from fuzzy arithmetic to analyze fuzzy ratios captured from humans. An application of the formulated fuzzy ratio to a Single Input Rule Modules connected Fuzzy Inference System (SIRMs-FIS) is demonstrated. Instead of using a precise weight, fuzzy sets are employed to represent the relative importance of each rule module. The resulting fuzzy weights are explained as a fuzzy ratio on a weight domain. In addition, a new SIRMs-FIS model with fuzzy weights and part-to-whole fuzzy ratio is devised. A simulated example is presented to clarify the proposed SIRM-FIS model.

A new monotonicity index for fuzzy rule-based systems

A search in the literature reveals that mathematical conditions (usually sufficient conditions) for the Fuzzy Inference System (FIS) models to satisfy the monotonicity property have been developed. A monotonically-ordered fuzzy rule base is important to maintain the monotonicity property of an FIS. However, it may difficult to obtain a monotonically-ordered fuzzy rule base in practice. We have previously introduced the idea of fuzzy rule relabeling to tackle this problem. In this paper, we further propose a monotonicity index for the FIS system, which serves as a metric to indicate the degree of a fuzzy rule base fulfilling the monotonicity property. The index is useful to provide an indication whether a fuzzy rule base should (or should not) be used in practice, even with fuzzy rule relabeling. To illustrate the idea, the zero-order Sugeno FIS model is exemplified. We add noise as errors into the fuzzy rule base to formulate a set of non-monotone fuzzy rules. As such, the metric also acts as a measure of noise in the fuzzy rule base. The results show that the proposed metric is useful to indicate the degree of a fuzzy rule base fulfilling the monotonicity property.

Building fuzzy inference systems with similarity reasoning : NSGAII-based fuzzy rule selection and evidential functions

In our previous investigations, two Similarity Reasoning (SR)-based frameworks for tackling real-world problems have been proposed. In both frameworks, SR is used to deduce unknown fuzzy rules based on similarity of the given and unknown fuzzy rules for building a Fuzzy Inference System (FIS). In this paper, we further extend our previous findings by developing (1) a multi-objective evolutionary model for fuzzy rule selection; and (2) an evidential function to facilitate the use of both frameworks. The Non-Dominated Sorting Genetic Algorithms-p (NSGA-p) is adopted for fuzzy rule selection, in accordance with the Pareto optimal criterion. Besides that, two new evidential functions are developed, whereby given fuzzy rules are considered as evidence. Simulated and benchmark examples are included to demonstrate the applicability of these suggestions. Positive results were obtained.

A novel fuzzy multi-objective framework to construct optimal prediction intervals for wind power forecast

The forecasting behavior of the high volatile and unpredictable wind power energy has always been a challenging issue in the power engineering area. In this regard, this paper proposes a new multi-objective framework based on fuzzy idea to construct optimal prediction intervals (Pis) to forecast wind power generation more sufficiently. The proposed method makes it possible to satisfy both the PI coverage probability (PICP) and PI normalized average width (PINAW), simultaneously. In order to model the stochastic and nonlinear behavior of the wind power samples, the idea of lower upper bound estimation (LUBE) method is used here. Regarding the optimization tool, an improved version of particle swam optimization (PSO) is proposed. In order to see the feasibility and satisfying performance of the proposed method, the practical data of a wind farm in Australia is used as the case study.

An enhanced fuzzy min-max neural network for pattern classification

An enhanced fuzzy min-max (EFMM) network is proposed for pattern classification in this paper. The aim is to overcome a number of limitations of the original fuzzy min-max (FMM) network and improve its classification performance. The key contributions are three heuristic rules to enhance the learning algorithm of FMM. First, a new hyperbox expansion rule to eliminate the overlapping problem during the hyperbox expansion process is suggested. Second, the existing hyperbox overlap test rule is extended to discover other possible overlapping cases. Third, a new hyperbox contraction rule to resolve possible overlapping cases is provided. Efficacy of EFMM is evaluated using benchmark data sets and a real medical diagnosis task. The results are better than those from various FMM-based models, support vector machine-based, Bayesian-based, decision tree-based, fuzzy-based, and neural-based classifiers. The empirical findings show that the newly introduced rules are able to realize EFMM as a useful model for undertaking pattern classification problems.

A hybrid FAM–CART model and its application to medical data classification

In this paper, a hybrid model consisting of the fuzzy ARTMAP (FAM) neural network and the classification and regression tree (CART) is formulated. FAM is useful for tackling the stability–plasticity dilemma pertaining to data-based learning systems, while CART is useful for depicting its learned knowledge explicitly in a tree structure. By combining the benefits of both models, FAM–CART is capable of learning data samples stably and, at the same time, explaining its predictions with a set of decision rules. In other words, FAM–CART possesses two important properties of an intelligent system, i.e., learning in a stable manner (by overcoming the stability–plasticity dilemma) and extracting useful explanatory rules (by overcoming the opaqueness issue). To evaluate the usefulness of FAM–CART, six benchmark medical data sets from the UCI repository of machine learning and a real-world medical data classification problem are used for evaluation. For performance comparison, a number of performance metrics which include accuracy, specificity, sensitivity, and the area under the receiver operation characteristic curve are computed. The results are quantified with statistical indicators and compared with those reported in the literature. The outcomes positively indicate that FAM–CART is effective for undertaking data classification tasks. In addition to producing good results, it provides justifications of the predictions in the form of a decision tree so that domain users can easily understand the predictions, therefore making it a useful decision support tool.

A modified fuzzy min-max neural network for data clustering and its application to power quality monitoring

When no prior knowledge is available, clustering is a useful technique for categorizing data into meaningful groups or clusters. In this paper, a modified fuzzy min-max (MFMM) clustering neural network is proposed. Its efficacy for tackling power quality monitoring tasks is demonstrated. A literature review on various clustering techniques is first presented. To evaluate the proposed MFMM model, a performance comparison study using benchmark data sets pertaining to clustering problems is conducted. The results obtained are comparable with those reported in the literature. Then, a real-world case study on power quality monitoring tasks is performed. The results are compared with those from the fuzzy c-means and k-means clustering methods. The experimental outcome positively indicates the potential of MFMM in undertaking data clustering tasks and its applicability to the power systems domain.

Fuzzy portfolio allocation models through a new risk measure and fuzzy sharpe ratio

A new portfolio risk measure that is the uncertainty of portfolio fuzzy return is introduced in this paper. Beyond the well-known Sharpe ratio (i.e., the reward-to-variability ratio) in modern portfolio theory, we initiate the so-called fuzzy Sharpe ratio in the fuzzy modeling context. In addition to the introduction of the new risk measure, we also put forward the reward-to-uncertainty ratio to assess the portfolio performance in fuzzy modeling. Corresponding to two approaches based on TM and TW fuzzy arithmetic, two portfolio optimization models are formulated in which the uncertainty of portfolio fuzzy returns is minimized, while the fuzzy Sharpe ratio is maximized. These models are solved by the fuzzy approach or by the genetic algorithm (GA). Solutions of the two proposed models are shown to be dominant in terms of portfolio return uncertainty compared with those of the conventional mean-variance optimization (MVO) model used prevalently in the financial literature. In terms of portfolio performance evaluated by the fuzzy Sharpe ratio and the reward-to-uncertainty ratio, the model using TW fuzzy arithmetic results in higher performance portfolios than those obtained by both the MVO and the fuzzy model, which employs TM fuzzy arithmetic. We also find that using the fuzzy approach for solving multiobjective problems appears to achieve more optimal solutions than using GA, although GA can offer a series of well-diversified portfolio solutions diagrammed in a Pareto frontier.

Hierarchical gene selection and genetic fuzzy system for cancer microarray data classification

This paper introduces a novel approach to gene selection based on a substantial modification of analytic hierarchy process (AHP). The modified AHP systematically integrates outcomes of individual filter methods to select the most informative genes for microarray classification. Five individual ranking methods including t-test, entropy, receiver operating characteristic (ROC) curve, Wilcoxon and signal to noise ratio are employed to rank genes. These ranked genes are then considered as inputs for the modified AHP. Additionally, a method that uses fuzzy standard additive model (FSAM) for cancer classification based on genes selected by AHP is also proposed in this paper. Traditional FSAM learning is a hybrid process comprising unsupervised structure learning and supervised parameter tuning. Genetic algorithm (GA) is incorporated in-between unsupervised and supervised training to optimize the number of fuzzy rules. The integration of GA enables FSAM to deal with the high-dimensional-low-sample nature of microarray data and thus enhance the efficiency of the classification. Experiments are carried out on numerous microarray datasets. Results demonstrate the performance dominance of the AHP-based gene selection against the single ranking methods. Furthermore, the combination of AHP-FSAM shows a great accuracy in microarray data classification compared to various competing classifiers. The proposed approach therefore is useful for medical practitioners and clinicians as a decision support system that can be implemented in the real medical practice.