Improved structure optimization for fuzzy-neural networks

Fuzzy-neural-network-based inference systems are well-known universal approximators which can produce linguistically interpretable results. Unfortunately, their dimensionality can be extremely high due to an excessive number of inputs and rules, which raises the need for overall structure optimization. In the literature, various input selection methods are available, but they are applied separately from rule selection, often without considering the fuzzy structure. This paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously. First, a method is developed to select the most significant rules, along with a refinement stage to remove unnecessary correlations. An improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model, leading to a balanced tradeoff between interpretability and accuracy. Simulation results confirm the efficacy of the proposed method.

A New Gradient Descent Approach for Local Learning of Fuzzy Neural Models

The majority of reported learning methods for Takagi-Sugeno-Kang fuzzy neural models to date mainly focus on the improvement of their accuracy. However, one of the key design requirements in building an interpretable fuzzy model is that each obtained rule consequent must match well with the system local behaviour when all the rules are aggregated to produce the overall system output. This is one of the distinctive characteristics from black-box models such as neural networks. Therefore, how to find a desirable set of fuzzy partitions and, hence, to identify the corresponding consequent models which can be directly explained in terms of system behaviour presents a critical step in fuzzy neural modelling. In this paper, a new learning approach considering both nonlinear parameters in the rule premises and linear parameters in the rule consequents is proposed. Unlike the conventional two-stage optimization procedure widely practised in the field where the two sets of parameters are optimized separately, the consequent parameters are transformed into a dependent set on the premise parameters, thereby enabling the introduction of a new integrated gradient descent learning approach. A new Jacobian matrix is thus proposed and efficiently computed to achieve a more accurate approximation of the cost function by using the second-order Levenberg-Marquardt optimization method. Several other interpretability issues about the fuzzy neural model are also discussed and integrated into this new learning approach. Numerical examples are presented to illustrate the resultant structure of the fuzzy neural models and the effectiveness of the proposed new algorithm, and compared with the results from some well-known methods.

An Efficient LS-SVM-Based Method for Fuzzy System Construction

This paper proposes an efficient learning mechanism to build fuzzy rule-based systems through the construction of sparse least-squares support vector machines (LS-SVMs). In addition to the significantly reduced computational complexity in model training, the resultant LS-SVM-based fuzzy system is sparser while offers satisfactory generalization capability over unseen data. It is well known that the LS-SVMs have their computational advantage over conventional SVMs in the model training process; however, the model sparseness is lost, which is the main drawback of LS-SVMs. This is an open problem for the LS-SVMs. To tackle the nonsparseness issue, a new regression alternative to the Lagrangian solution for the LS-SVM is first presented. A novel efficient learning mechanism is then proposed in this paper to extract a sparse set of support vectors for generating fuzzy IF-THEN rules. This novel mechanism works in a stepwise subset selection manner, including a forward expansion phase and a backward exclusion phase in each selection step. The implementation of the algorithm is computationally very efficient due to the introduction of a few key techniques to avoid the matrix inverse operations to accelerate the training process. The computational efficiency is also confirmed by detailed computational complexity analysis. As a result, the proposed approach is not only able to achieve the sparseness of the resultant LS-SVM-based fuzzy systems but significantly reduces the amount of computational effort in model training as well. Three experimental examples are presented to demonstrate the effectiveness and efficiency of the proposed learning mechanism and the sparseness of the obtained LS-SVM-based fuzzy systems, in comparison with other SVM-based learning techniques.

Privacy-Protected Facial Biometric Verification via Fuzzy Forest Learning

Although visual surveillance has emerged as an effective technolody for public security, privacy has become an issue of great concern in the transmission and distribution of surveillance videos. For example, personal facial images should not be browsed without permission. To cope with this issue, face image scrambling has emerged as a simple solution for privacyrelated applications. Consequently, online facial biometric verification needs to be carried out in the scrambled domain thus bringing a new challenge to face classification. In this paper, we investigate face verification issues in the scrambled domain and propose a novel scheme to handle this challenge. In our proposed method, to make feature extraction from scrambled face images robust, a biased random subspace sampling scheme is applied to construct fuzzy decision trees from randomly selected features, and fuzzy forest decision using fuzzy memberships is then obtained from combining all fuzzy tree decisions. In our experiment, we first estimated the optimal parameters for the construction of the random forest, and then applied the optimized model to the benchmark tests using three publically available face datasets. The experimental results validated that our proposed scheme can robustly cope with the challenging tests in the scrambled domain, and achieved an improved accuracy over all tests, making our method a promising candidate for the emerging privacy-related facial biometric applications.

Fuzzy logic-based implicit authentication for mobile access control

In order to address the increasing compromise of user privacy on mobile devices, a Fuzzy Logic based implicit authentication scheme is proposed in this paper. The proposed scheme computes an aggregate score based on selected features and a threshold in real-time based on current and historic data depicting user routine. The tuned fuzzy system is then applied to the aggregated score and the threshold to determine the trust level of the current user. The proposed fuzzy-integrated implicit authentication scheme is designed to: operate adaptively and completely in the background, require minimal training period, enable high system accuracy while provide timely detection of abnormal activity. In this paper, we explore Fuzzy Logic based authentication in depth. Gaussian and triangle-based membership functions are investigated and compared using real data over several weeks from different Android phone users. The presented results show that our proposed Fuzzy Logic approach is a highly effective, and viable scheme for lightweight real-time implicit authentication on mobile devices.

Risk assessment of E-Commerce projects using evidential reasoning

The purpose of this study is to develop a decision making system to evaluate the risks in E-Commerce (EC) projects. Competitive software businesses have the critical task of assessing the risk in the software system development life cycle. This can be conducted on the basis of conventional probabilities, but limited appropriate information is available and so a complete set of probabilities is not available. In such problems, where the analysis is highly subjective and related to vague, incomplete, uncertain or inexact information, the Dempster-Shafer (DS) theory of evidence offers a potential advantage. We use a direct way of reasoning in a single step (i.e., extended DS theory) to develop a decision making system to evaluate the risk in EC projects. This consists of five stages 1) establishing knowledge base and setting rule strengths, 2) collecting evidence and data, 3) determining evidence and rule strength to a mass distribution for each rule; i.e., the first half of a single step reasoning process, 4) combining prior mass and different rules; i.e., the second half of the single step reasoning process, 5) finally, evaluating the belief interval for the best support decision of EC project. We test the system by using potential risk factors associated with EC development and the results indicate that the system is promising way of assisting an EC project manager in identifying potential risk factors and the corresponding project risks.

Possibilistic Information Fusion Using Maximal Coherent Subsets

When multiple sources provide information about the same unknown quantity, their fusion into a synthetic interpretable message is often a tedious problem, especially when sources are conicting. In this paper, we propose to use possibility theory and the notion of maximal coherent subsets, often used in logic-based representations, to build a fuzzy belief structure that will be instrumental both for extracting useful information about various features of the information conveyed by the sources and for compressing this information into a unique possibility distribution. Extensions and properties of the basic fusion rule are also studied.