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Formulating a generalized monotone fuzzy rule interpolation (MFRI) model is difficult. A complete and monotone fuzzy rule-base is essential for devising a monotone zero-order Takagi–Sugeno–Kang (TSK) fuzzy inference system (FIS) model. However, such a complete and monotone fuzzy rule-base is not always available in practice. In this article, we develop an MFRI modeling scheme for generating a monotone zero-order TSK FIS from a monotone and incomplete fuzzy rule-base. In our proposal, a monotone-ordered fuzzy rule-base that consists of the available fuzzy rules from a monotone and incomplete fuzzy rule-base and those derived from the MFRI reasoning is formed. We outline three important properties that the MFRI's deduced fuzzy rules should satisfy to ensure a monotone-ordered fuzzy rule-base. A Lagrangian function for the MFRI scheme, together with its Karush–Kuhn–Tucker optimality conditions, is formulated and analyzed. The key idea is to impose constraints that guide the MFRI inference outcomes. An iterative MFRI algorithm that adopts an augmented Lagrangian function is devised. The proposed MFRI algorithm aims to achieve an ${\boldsymbol{\varepsilon }}$ -optimality condition and to produce an ${\boldsymbol{\varepsilon }}$ -optimal solution, which is geared for practical applications. We apply the MFRI algorithm to a failure mode and effect analysis case study and a tanker ship heading regulation problem. The results indicate the effectiveness of MFRI for generating monotone TSK FRI models in tackling practical problems. [ABSTRACT FROM AUTHOR]

Despite the popularity and practical importance of the fuzzy inference system (FIS), the use of an FIS model as an n-ary aggregation function, which is characterized by both the monotonicity and boundary properties, is yet to be established. This is because research on ensuring that FIS models satisfy the monotonicity property, i.e., monotone FIS, is relatively new, not to mention the additional requirement of satisfying the boundary property. The aim of this article, therefore, is to establish the parametric conditions for the Takagi–Sugeno–Kang (TSK) FIS model to operate as an n-ary aggregation function (hereafter denoted as n-TSK-FIS) via the specifications of fuzzy membership functions and fuzzy rules. An absorption property with fuzzy rules interpretation is outlined, and the use of n-TSK-FIS as a uninorm is explained. Exploiting the established parametric conditions, a framework for which an n-TSK-FIS model can be constructed from data samples is formulated and analyzed, along with a number of remarks. Synthetic data sets and a benchmark example on education assessment are presented and discussed. To be best of the authors’ knowledge, this article serves as the first use of the TSK-FIS model as an n-ary aggregation function. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of a monotone fuzzy partition, which is useful for constructing a monotone zero-order Takagi–Sugeno–Kang Fuzzy Inference System (ZOTSK-FIS). It is known that a monotone ZOTSK-FIS model can always be produced when a consistent, complete, and monotone fuzzy rule base is used. However, such an ideal situation is not always available in practice, because a fuzzy rule base is susceptible to uncertainties, e.g., inconsistency, incompleteness, and nonmonotonicity. As a result, we devise an interval method to model these uncertainties by considering the minimum interval of acceptability of a fuzzy rule, resulting in a set of monotone interval-valued fuzzy rules. This further leads to the formulation of a Monotone Interval Fuzzy Inference System (MIFIS) with a minimized uncertainty measure. The proposed MIFIS model is analyzed mathematically and evaluated empirically for the Failure Mode and Effect Analysis (FMEA) application. The results indicate that MIFIS outperforms ZOTSK-FIS, and allows effective decision making using uncertain fuzzy rules solicited from human experts in tackling real-world FMEA problems. [ABSTRACT FROM AUTHOR]

The sufficient conditions for satisfying the monotonicity property of the Takagi-Sugeno-Kang (TSK) fuzzy inference system (FIS) have shown to be useful in many different applications. However, the related sufficient and necessary conditions are still unknown. As such, even when the sufficient conditions are violated, the TSK FIS model may still able to satisfy the monotonicity property. Therefore, the monotonicity test is used as an approximated method to determine the validness of the monotonicity property. To the best of our knowledge, the use of the monotonicity test in FIS is new. In this paper, we focus on single-input zero-order TSK FIS with Gaussian fuzzy membership functions. An algorithm to test the monotonicity property, either accepting or rejecting an TSK FIS model of being monotone, is devised and analyzed. The relationship between TSK FIS and its capability of satisfying the monotonicity property, along with the sufficient conditions and the outcome of the monotonicity test, is established through a Monte Carlo simulation. The Monte Carlo simulation is a useful necessity test for the sufficient conditions. We define a necessity measure of the sufficient conditions (NMSC) as the probability that a randomly generated monotone TSK FIS model (evaluated based on the monotonicity test algorithm) satisfies the sufficient conditions. We empirically show that the NMSC score reduces with increasing number of fuzzy rules. In addition, an application of the TSK FIS model to failure modes and effects analysis is demonstrated. As compared with the sufficient conditions, a better FIS-based model with a lower error measure can be obtained using the monotonicity test. The outcome indicates the effectiveness of the monotonicity test for designing low-dimensional TSK FIS models with large numbers of fuzzy rules. [ABSTRACT FROM AUTHOR]

An improved Fuzzy Min-Max (FMM) neural network with a K -nearest hyperbox expansion rule is proposed in this paper. The aim is to reduce the FMM network complexity for undertaking pattern classification tasks. In the proposed model, a useful modification to overcome a number of identified limitations of the original FMM network and to improve its classification performance is derived. In particular, the K -nearest hyperbox expansion rule is formulated to reduce the network complexity by avoiding the creation of too many small hyperboxes within the vicinity of the winning hyperbox during the FMM learning stage. The effectiveness of the proposed model is evaluated using a number of benchmark data sets. The results compare favorably with those from various FMM variants and other existing classifiers. [ABSTRACT FROM AUTHOR]

In this paper, we extend our previous work on the Enhanced Fuzzy Min–Max (EFMM) neural network by introducing a new hyperbox selection rule and a pruning strategy to reduce network complexity and improve classification performance. Specifically, a new k-nearest hyperbox expansion rule (for selection of a new winning hyperbox) is first introduced to reduce the network complexity by avoiding the creation of too many small hyperboxes within the vicinity of the winning hyperbox. A pruning strategy is then deployed to further reduce the network complexity in the presence of noisy data. The effectiveness of the proposed network is evaluated using a number of benchmark data sets. The results compare favorably with those from other related models. The findings indicate that the newly introduced hyperbox winner selection rule coupled with the pruning strategy are useful for undertaking pattern classification problems. [ABSTRACT FROM AUTHOR]

To maintain the monotonicity property of a fuzzy inference system, a monotonically ordered and complete set of fuzzy rules is necessary. However, monotonically ordered fuzzy rules are not always available, e.g., errors in human judgments lead to nonmonotone fuzzy rules. The focus of this paper is on a new monotone fuzzy rule relabeling (MFRR) method that is able to relabel a set of nonmonotone fuzzy rules to meet the monotonicity property with reduced computation. Unlike the brute-force approach, which is susceptible to the combinatorial explosion problem, the proposed MFRR method explores within a reduced search space to find the solutions, therefore decreasing the computational requirements. The usefulness of the proposed method in undertaking failure mode and effect analysis problems is demonstrated using publicly available information. The results indicate that the MFRR method can produce optimal solutions with reduced computational time. [ABSTRACT FROM PUBLISHER]

In this paper, a new fuzzy peer assessment methodology that considers vagueness and imprecision of words used throughout the evaluation process in a cooperative learning environment is proposed. Instead of numerals, words are used in the evaluation process, in order to provide greater flexibility. The proposed methodology is a synthesis of perceptual computing (Per-C) and a fuzzy ranking algorithm. Per-C is adopted because it allows uncertainties of words to be considered in the evaluation process. Meanwhile, the fuzzy ranking algorithm is deployed to obtain appropriate performance indices that reflect a student's contribution in a group, and subsequently rank the student accordingly. A case study to demonstrate the effectiveness of the proposed methodology is described. Implications of the results are analyzed and discussed. The outcomes clearly demonstrate that the proposed fuzzy peer assessment methodology can be deployed as an effective evaluation tool for cooperative learning of students. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: A study on the pedestrian’s steering behaviour through a built environment in normal circumstances is presented in this paper. The study focuses on the relationship between the environment and the pedestrian’s walking trajectory. Owing to the ambiguity and vagueness of the relationship between the pedestrians and the surrounding environment, a genetic fuzzy system is proposed for modelling and simulation of the pedestrian’s walking trajectory confronting the environmental stimuli. We apply the genetic algorithm to search for the optimum membership function parameters of the fuzzy model. The proposed system receives the pedestrian’s perceived stimuli from the environment as the inputs, and provides the angular change of direction in each step as the output. The environmental stimuli are quantified using the Helbing social force model. Attractive and repulsive forces within the environment represent various environmental stimuli that influence the pedestrian’s walking trajectory at each point of the space. To evaluate the effectiveness of the proposed model, three experiments are conducted. The first experimental results are validated against real walking trajectories of participants within a corridor. The second and third experimental results are validated against simulated walking trajectories collected from the AnyLogic® software. Analysis and statistical measurement of the results indicate that the genetic fuzzy system with optimised membership functions produces more accurate and stable prediction of heterogeneous pedestrians’ walking trajectories than those from the original fuzzy model. [Copyright &y& Elsevier]

In this paper, an application of the motor current signature analysis (MCSA) method and the fuzzy min–max (FMM) neural network to detection and classification of induction motor faults is described. The finite element method is employed to generate simulated data pertaining to changes in the stator current signatures under different motor conditions. The MCSA method is then used to process the stator current signatures. Specifically, the power spectral density is employed to extract harmonics features for fault detection and classification with the FMM network. Various types of induction motor faults, which include stator winding faults and eccentricity problems, under different load conditions are experimented. The results are analyzed and compared with those from other methods. The outcomes indicate that the proposed technique is effective for fault detection and diagnosis of induction motors under different conditions. [ABSTRACT FROM AUTHOR]

An important and difficult issue in designing a Fuzzy Inference System (FIS) is the specification of fuzzy sets and fuzzy rules. In this paper, two useful qualitative properties of the FIS model, i.e., the monotonicity and sub-additivity properties, are studied. The monotonic sufficient conditions of the FIS model with Gaussian membership functions are further analyzed. The aim is to incorporate the sufficient conditions into the FIS modeling process, which serves as a simple (which can be easily understood by domain users), easy-to-use (which can be easily applied to or can be a part of the FIS model), and yet reliable (which has a sound mathematical foundation) method to preserve the monotonicity property of the FIS model. Another aim of this paper is to demonstrate how these additional qualitative information can be exploited and extended to be part of the FIS designing procedure (i.e., for fuzzy sets and fuzzy rules design) via the sufficient conditions (which act as a set of useful governing equations for designing the FIS model). The proposed approach is able to avoid the "trial and error" procedure in obtaining a monotonic FIS model. To assess the applicability of the proposed approach, two practical problems are examined. The first is an FIS-based model for water level control, while the second is an FIS-based Risk Priority Number (RPN) model in Failure Mode and Effect Analysis (FMEA). To further illustrate the importance of the sufficient conditions as the governing equations, an analysis on the consequences of violating the sufficient conditions of the FIS-based RPN model is presented. [ABSTRACT FROM AUTHOR]

Abstract: The main aim of criterion-referenced assessment (CRA) is to report students’ achievements in accordance with a set of references. In practice, a score is given to each test item (or task). The scores from different test items are added together and then projected or aggregated, usually linearly, to produce a total score. Each component score can be weighted before being added together in order to reflect the relative importance of each test item. In this paper, the use of a fuzzy inference system (FIS) as an alternative to the conventional addition or weighted addition in CRA is investigated. A novel FIS-based CRA model is presented, and two important properties, i.e., the monotonicity and sub-additivity properties, of the FIS-based CRA model are investigated. A case study relating to assessment of laboratory projects in a university is conducted. The results indicate the usefulness of the FIS-based CRA model in comparing and assessing students’ performances with human linguistic terms. Implications of the importance of the monotonicity and sub-additivity properties of the FIS-based CRA model in undertaking general assessment problems are discussed. [Copyright &y& Elsevier]

In this paper, an Evolutionary Artificial Neural Network (EANN) that combines the Fuzzy ARTMAP (FAM) network and a Hybrid Evolutionary Programming (HEP) model is introduced. The proposed FAM-HEP model, which combines the strengths of FAM and HEP, is able to construct its network structure autonomously as well as to perform learning and evolutionary search and adaptation concurrently. The effectiveness of the proposed FAM-HEP network is assessed empirically using several benchmark data sets and a real medical diagnosis problem. The performance of FAM-HEP is analyzed, and the results are compared with those of FAM-EP, FAM, and other classification models. In general, the results of FAM-HEP are better than those of FAM-EP and FAM, and are comparable with those from other classification models. The study also reveals the potential of FAM-HEP as an innovative EANN model for undertaking pattern classification problems in general, and a promising computerized decision support tool for tackling medical diagnosis tasks in particular. [ABSTRACT FROM AUTHOR]

We investigate robust fault-tolerant control pertaining to Takagi–Sugeno (TS) fuzzy nonlinear systems with bounded disturbances, actuator failures, and time delays. A new fault model based on a sampled-data scheme that is able to satisfy certain criteria in relation to actuator fault matrix is introduced. Specifically, we formulate a reliable controller with state feedback, such that the resulting closed-loop-fuzzy system is robust, asymptotically stable, and able to satisfy a prescribed H ∞ performance constraint. Linear matrix inequality (LMI) together with a proper construction of the Lyapunov–Krasovskii functional is leveraged to derive delay-dependent sufficient conditions with respect to the existence of robust H ∞ controller. It is straightforward to obtain the solution by using the MATLAB LMI toolbox. We demonstrate the effectiveness of the control law and less conservativeness of the results through two numerical simulations. [ABSTRACT FROM AUTHOR]

Soft Computing is an interdisciplinary area that encompasses a variety of computing paradigms. Examples of some popular soft computing paradigms include fuzzy computing, neural computing, evolutionary computing, and probabilistic computing. Soft computing paradigms, in general, aim to produce computing systems/machines that exhibit some useful properties, e.g. making inference with vague and/or ambiguous information, learning from noisy and/or incomplete data, adapting to changing environments, and reasoning with uncertainties. These properties are important for the systems/machines to be useful in assisting humans in our daily activities. Indeed, soft computing paradigms have been demonstrated to be capable of tackling a wide range of problems, e.g. optimization, decision making, information processing, pattern recognition, and intelligent data analysis. A number of papers pertaining to some recent advances in theoretical development and practical application of different soft computing paradigms are highlighted in this special issue. [ABSTRACT FROM AUTHOR]

Computational Intelligence (CI) models comprise robust computing methodologies with a high level of machine learning quotient. CI models, in general, are useful for designing computerized intelligent systems/machines that possess useful characteristics mimicking human behaviors and capabilities in solving complex tasks, e.g., learning, adaptation, and evolution. Examples of some popular CI models include fuzzy systems, artificial neural networks, evolutionary algorithms, multi-agent systems, decision trees, rough set theory, knowledge-based systems, and hybrid of these models. This special issue highlights how different computational intelligence models, coupled with other complementary techniques, can be used to handle problems encountered in image processing and information reasoning. [ABSTRACT FROM AUTHOR]

• An improved multi-agent system based on Fuzzy ARTMAP (FAM) and Q-learning, i.e., IQ-MACS, is proposed. • A trust measurement using a combination of Q-learning and Bayesian formalism is added at team level. • Two real-world case studies, i.e., human motion detection and motor fault detection, with and without noise are used to evaluate the proposed model. • The outcome indicates that IQMACS is able to produce promising results. The Fuzzy ARTMAP (FAM) network is an online supervised neural network that operates by computing the similarity level between the new sample and those prototype nodes stored in its network against a threshold. In our previous study, we have developed a multi-agent system consisting of an ensemble of FAM networks and Q-learning, known as QMACS, for data classification. In this paper, an Improved QMACS (IQMACS) model with trust measurement using a combination of Q-learning and Bayesian formalism is proposed. A number of benchmark and real-world problems, i.e., motor fault detection and human motion detection, are conducted to evaluate the effectiveness of IQMACS. Statistical features are extracted from real-world case studies and utilized for classification with IQMACS, QMACS, and their constituents. The experimental results indicate that IQMACS produces better classification performance by combining the outcomes of its constituents as compared with those of QMACS and other related methods. [ABSTRACT FROM AUTHOR]

The Metacognitive Scaffolding Learning Machine (McSLM), combining the concept of metacognition—what-to-learn, how-to-learn, and when-to-learn, and the Scaffolding theory—a tutoring theory for a learner to learn a complex task, has been successfully developed to enhance the capability of Evolving Intelligent Systems (EIS) in processing non-stationary data streams. Three issues, namely uncertainty, temporal behaviour, unknown system order, are however uncharted by any existing McSLMs and all McSLMs in the literature are designed for classification problems. This paper proposes a novel McSLM, called Recurrent Interval-Valued Metacognitive Scaffolding Fuzzy Neural Network (RIVMcSFNN) and used to solve regression and time-series modelling problems from data streams. RIVMcSFNN presents a novel recurrent network architecture as a cognitive constituent, which features double local recurrent connections at both the hidden layer and the consequent layer. The new recurrent network architecture is driven by the interval-valued multivariate Gaussian function in the hidden node and the nonlinear Wavelet function in the consequent node. As with its predecessors, the RIVMcSFNN characterises an open structure, where it can automatically grow, prune, adjust, merge, recall its hidden node and can select relevant data samples on the fly using an online active learning methodology. The RIVMcSFNN is also equipped with the online dimensionality reduction technique to cope with the curse of dimensionality . All learning mechanisms are carried out in the single-pass and local learning mode and actualise the plug-and-play learning principle, which aims to minimise the use of pre-and/or post-training steps. The efficacy of our algorithm was tested using numerous data-driven modelling problems and comprehensive comparisons with its counterparts. The RIVMcSFNN demonstrated substantial improvements in both accuracy and complexity against existing variants of the McSLMs and EISs. [ABSTRACT FROM AUTHOR]