Stochastic Configuration Based Fuzzy Inference System with Interpretable Fuzzy Rules and Intelligence Search Process

In this study, we introduce a novel framework for Deep Fuzzy Rule-Based System (DFRBS) and its extensions and demonstrate its capability in the medical prognostic, brain connectivity estimation and depression severity staging tasks. This model benefits from a hierarchical fuzzy rule-based system and is capable of fusing heterogeneous decisions in an interpretable manner utilizing a stacked approach. The hidden layer in each unit is represented by interpretable fuzzy rules and fuzzy rules are generated by means of the soft partitioning approach, i.e., a modified FCM clustering. According to the stacked method, the same input space is kept in all layers of DFRBS. The inputs of the middle units are constructed from the training set and additive random shifts, obtained from random projections of predictions of the previous layer. As a result, DFRBS can properly handle heterogeneous, imbalanced multivariate inputs. DFRBS is applied to Electronic Health Records (EHRs) for in-hospital mortality prediction. In addition, its modified version with first-order TSK fuzzy rules as the cores of the network is applied to EEG signals for calculation of brain effective connectivity in four-fold consciousness states. Another extended version of DFRBS is employed for multiclass classification of depression severity staging. In the cases of mortality prediction and depression severity staging, our results are demonstrated that DFRBS outperforms various common methods while maintaining interpretable rule bases and our results in case of connectivity estimation demonstrate that the proposed non-linear connectivity estimator is capable of detecting novel correlates of consciousness.KeywordsFuzzy modelDeep learningTSKMortality predictionConnectivity network

We examine the performance of compact fuzzy rule-based classification systems that consist of a small number of simple fuzzy rules with high comprehensibility. Those fuzzy systems are designed in a heuristic manner using rule selection criteria. We first describe fuzzy rule-based classification. Next we describe heuristic rule selection criteria using the terminology in data mining: confidence and support. A small number of fuzzy rules are extracted from numerical data based on each rule selection criterion. Then we examine the classification performance of extracted fuzzy rules through computational experiments on a number of benchmark data sets from the UCI ML Repository. Our results should be viewed as the lowest benchmark performance of fuzzy rule-based classification systems because fuzzy rules are extracted using a simple heuristic method with no optimization or tuning procedures. Nevertheless our results on some data sets are comparable to reported results by the C4.5 algorithm in the literature.

Interpretability improvements to find the balance interpretability-accuracy in fuzzy modeling: an overview.- Regaining comprehensibility of approximative fuzzy models via the use of linguistic hedges.- Identifying flexible structured premises for mining concise fuzzy knowledge.- A multiobjective genetic learning process for joint feature selection and granularity and contexts learning in fuzzy rule-based classification systems.- Extracting linguistic fuzzy models from numerical data-AFRELI algorithm.- Constrained optimization of fuzzy decision trees.- A new method for inducing a set of interpretable fuzzy partitions and fuzzy inference systems from data.- A Feature Ranking Algorithm for Fuzzy Modelling Problems.- Interpretability in multidimensional classification.- Interpretable semi-mechanistic fuzzy models by clustering, OLS and FIS model reduction.- Trade-off between approximation accuracy and complexity: TS controller design via HOSVD based complexity minimization.- Simplification and reduction of fuzzy rules.- Effect of rule representation in rule base reduction.- Singular value-based fuzzy reduction with relaxed normalization condition.- Interpretability, complexity, and modular structure of fuzzy systems.- Hierarchical genetic fuzzy systems: accuracy, interpretability and design autonomy.- About the trade-off between accuracy and interpretability of Takagi-Sugeno models in the context of nonlinear time series forecasting.- Accurate, transparent and compact fuzzy models by multi-objective evolutionary algorithms.- Transparent fuzzy systems in modeling and control.- Uniform fuzzy partitions with cardinal splines and wavelets: getting interpretable linguistic fuzzy models.- Relating the theory of partitions in MV-logic to the design of interpretable fuzzy systems.- A formal model of interpretability of linguistic variables.- Expressing relevance and interpretability of rule-based systems.- Conciseness of fuzzy models.- Exact trade-off between approximation accuracy and interpretability: solving the saturation problem for certain FRBSs.- Interpretability improvement of RBF-based neurofuzzy systems using regularized learning.- Extracting fuzzy classification rules from fuzzy clusters on the basis of separating hyperplanes.

In this paper, we propose a particle swarm optimization method incorporating quantum qubit operation to construct and optimize fuzzy rule-based classifiers. The proposed algorithm, denoted as QiQPSO, is inspired by the quantum computing principles. It employs quantum rotation gates to update the probability of each qubit with the corresponding quantum angle updating according to the update equation of the quantum-behaved particle swarm optimization (QPSO). After description of the principle of QiQPSO, we show how to apply QiQPSO to establish a fuzzy classifier through two procedures. The QiQPSO algorithm is first used to construct the initial fuzzy classification system based on the sample data and the grid method of partitioning the feature space, and then the fuzzy rule base of the initial fuzzy classifier is optimized further by QiQPSO in order to reduce the number of the fuzzy rules and thus improve its interpretability. In order to verify the effectiveness of the proposed method, QiQPSO is tested on various real-world classification problems. The experimental results show that the QiQPSO is able to effectively select feature variables and fuzzy rules of the fuzzy classifiers with high classification accuracies. The performance comparison with other methods also shows that the fuzzy classifier optimized by QiQPSO has higher interpretability as well as comparable or even better classification accuracies.

Fuzzy systems (FSs) have been extensively applied to automatic control, pattern recognition, and decision analysis. However, a common bottleneck is encountered in the derivation of fuzzy rules, which is often difficult, time consuming, and relies on expert knowledge. To automate the design of FSs, many metaheuristic learning algorithms have been proposed. One major optimization category uses Swarm Intelligence (SI) model (Kennedy et al., 2001). The SI technique studies collective behavior in decentralized systems. Its development was based on mimicking the social behavior of animals or insects in an effort to find the optima in the problem space. SI models are initialized with a population of random solutions. One well-known SI model is particle swarm optimization (PSO) (Kennedy & Eberhart, 1995). Many modified PSO models have been proposed and successfully applied to different optimization problems (Clerc & Kennedy, 2002; Bergh & Engelbrecht, 2004; Ratnaweera et al., 2004; Juang, 2004; Kennedy & Mendes, 2006; Parrott & Li, 2006; Chen & Li, 2007). FS design using PSO has also been proposed in several studies (Juang, 2004; Chatterjee et al., 2005; Juang et al., 2007; Araujo & Coelho, 2008; Sharma et al., 2009). Another well-known SI is ant colony optimization (ACO) (Dorigo & Stutzle, 2004). The ACO technique is inspired by real ant colony observations. It is a multi-agent approach that was originally proposed to solve difficult discrete combinatorial optimization problems, such as the traveling salesman problem (TSP) (Dorigo et al., 1996; Dorigo & Gambardella, 1997). In the original ACO meta-heuristic, artificial ant colonies cooperate to find good solutions for difficult discrete optimization problems. Different ACO models have been applied to FS design problems (Cassillas et al., 2000; Cassillas et al., 2005; Mucientes & Casillas; 2007; Juang & Lo, 2007; Juang et al., 2008; Juang & Lu; 2009). In (Cassillas et al.,2000; Mucientes & Casillas; 2007; Juang et al., 2008; Juang & Lu; 2009), the FS input space was partitioned in grid type with antecedent part parameters of an FS manually assigned in advance. In (Juang & Lo, 2007), the FS input space was flexibly partitioned using a fuzzy clustering-like algorithm in order to reduce the total number of rules. For all of these studies, the consequent part parameters were optimized in discrete space using ACO. Since only the consequent part parameters are optimized, and the optimization space is restricted to be discrete, the designed FSs are unsuitable for problems where high accuracy is a major concern. Source: Fuzzy Systems, Book edited by: Ahmad Taher Azar, ISBN 978-953-7619-92-3, pp. 216, February 2010, INTECH, Croatia, downloaded from SCIYO.COM

This paper presents a method for fuzzy model reference adaptive control system design for a partially known multi-input multi-output (MIMO) linear dynamic plant. Differential or convolutional equations can describe the plant to be controlled, and the fuzzy controller is assumed to be from the MIMO sector-bounded nonstationary nonlinearities class. The task is to obtain robust adaptive stabilization. Some absolute stability theorems and integral evaluations of the state and control vectors are applied in the MIMO fuzzy adaptive controller design procedure for the first time. A method for automatically obtaining a near-optimal nonlinear dynamic reference model is described. A practical step-by-step procedure of the MIMO adaptive fuzzy controller design is proposed, resulting in highly interpretable MIMO fuzzy control rules based on triangular fuzzy sets and strong triangular fuzzy partition. An example of the fuzzy controller design according to the proposed procedure is given.

In fuzzy learning, interpretability and accuracy are often antagonistic. In many cases, this dilemma is usually overcome by the changeover from fuzzy inference systems to radial basis neural networks: the system performs well but the interpretability of fuzzy rules is lost. It is not a fatality: constrained optimization methods can both preserve interpretability and increase the accuracy of the fuzzy model.

This paper introduces an intelligent machining system (IMS) using an adaptive-network-based fuzzy inference system (ANFIS) predictor and the particle swarm optimization (PSO) algorithm with a hybrid objective function. The proposed IMS provides suitable machining parameters for the users, to satisfy different machining requirements such as accuracy, surface smoothness, and speed. First, the key computer numerical control parameters are selected, and the actual trajectories under different machining parameters obtained by linear scales are collected. These data are analyzed to obtain the machining time, contouring error, and tracking error, corresponding to the speed, milling accuracy, and surface smoothness, respectively. Second, a data-driven approach using ANFIS is established to obtain the corresponding relationship model between the machining parameters and three aforementioned performance indices. Subsequently, to establish the IMS, we combine the trained ANFIS model and establish a hybrid objective function optimization problem solved by PSO algorithm according the specific requirement of the user. Finally, the performance and effectiveness of the proposed machining system is demonstrated by experimental practical machining.

In this study, we designed a trajectory-tracking fuzzy logic controller (TTFLC) for the TRIGA Mark-II Training and Research Reactor, which is located at the Istanbul Technical University. The designed fuzzy logic controller (FLC) is based on the zeroorder Sugeno method. The parameters of the FLC membership functions and the action weights of the 15 rules in the rule base are optimised by using the particle swarm optimisation (PSO) algorithm. The objective of this study is to control the TRIGA Mark-II reactor using the designed PSO-tuning TTFLC in a simulator. We used a simulation code from the literature called `YAVCAN' for studying the non-linear behaviour of the core of the TRIGA Mark-II reactor. To select the best parameters of the PSO algorithm for this system, we conducted some experiments. After selecting the best PSO parameters, the algorithm was started a number of times to determine the optimal parameters of the designed FLC and the optimal parameters of the controller. After determining these parameters, the performance of the designed controller was tested for various initial and desired power levels and under conditions of disturbance. The simulation results showed that the proposed controller could control the reactor power successfully, and it could ensure that the reactor tracks the desired trajectory power within the acceptable error tolerance. Therefore, the PSO algorithm is suitable for finding the optimal parameters of the FLC.

Opinion Mining or Sentiment Analysis is the task of extracting people final opinion about something through their unstructured sentiments. The Opinion Mining process is as follows: first, product features which are most important to a user are extracted from his/her comments. Then, sentiments will be emotionally classified using their emotional implications. In this paper we propose an opinion classification method based on Fuzzy Logic. Up to now, a few methods have taken advantage of fuzzy logic in opinion classification and all of them have imported fuzzy rules into system as background knowledge. But the main challenge here is finding the fuzzy rules. Our contribution is to automatically extract fuzzy rules and their parameters from training data. Here we have used the Particle Swarm Optimization (PSO) algorithm to extract fuzzy rules from training data. Also, for better results we have devised a mutation-based PSO. All proposed methods have been implemented and tested on relevant data. Results confirm that our method can reach better accuracy than current state of the art methods in this domain.

In this paper, an interval type-2 Takagi-Sugeno fuzzy classification system (IT2T-SFCS) learned by particle swarm optimization (PSO) and support vector machine (SVM) for antecedent and consequent parameters optimization is proposed. The IT2T-SFCS is constructed by fuzzy if-then rules whose antecedents are interval type-2 fuzzy sets and consequents are linear state equations. The antecedents of IT2T-SFCS use the fuzzy iterative self-organizing data analysis technique (ISODATA) and PSO to learn and calculate the optimal centers and the uncertain widths of the Gaussian membership functions. Consequent parameters in IT2T-SFCS are learned through SVM for the purpose of achieving higher generalization ability. The proposed IT2T-SFCS is able to directly handle uncertainties, minimize the effects of uncertainties and get the better generalization performance, which inherits the benefits of interval type-2 T-S fuzzy system and SVM. For demonstration, IT2T-SFCS is used as a classifier in gender recognition. The experimental results show that the performance of the proposed IT2T-SFCS is superior to that of the previous mainstream classifiers.

This paper introduced the self-tuning fuzzy PID controller based on particle swarm optimization which aims to gain more precise control over the position of pneumatic proportional valve barrel, where particle swarm works to optimize the membership function, fuzzy rule and PID parameter in fuzzy control. The study fruits also include online optimization of the self-tuning fuzzy PID controller parameters. Comparing to the conventional control methodology, The self-tuning fuzzy PID controller with PSO optimization is proven to show better precision, dynamic performance index and more rapid tracking performance and robustness. To this end, step response was used to compare and analyze the results from the PSO algorithm optimization, providing a pragmatic method of better comprehensive performance for PID parameter optimization.

Fuzzy inference system with interpretable fuzzy rules: Advancing explainable artificial intelligence for disease diagnosis—A comprehensive review

In this paper improvement in voltage sag by using PSO optimized fuzzy controller is described. Dstatcom is the FACTS device used in voltage sag improvement. Particle swarm optimization (PSO) is used to optimize the if then rules of the fuzzy controller. In this system a Dstatcom is placed in a three phase system to control the voltage sag. A fuzzy controller is designed to control the output of Dstatcom. The whole system is simulated using MATLAB Simulink. The fuzzy controlled Dstatcom output is compared with a PI controlled Dstatcom output. The system without Dstatcom is also simulated using MATLAB Simulink. The fuzzy controller rules are optimized using particle swarm optimization and the results are also compared with other systems.

A novel approach applied to Particle Swarm Optimization (PSO) and Ant Colony Optimization is presented. The main contribution of this work is the use of fuzzy systems to dynamically update the parameters for the ACO and PSO algorithms. In the case of ACO, two fuzzy systems are designed for the Ant Colony System (ACS) algorithm variant. The first system adjusts the value for the pheromone evaporation parameter from the global pheromone trail update equation and the second system adjusts the values for the pheromone evaporation parameter from the local pheromone trail update equation. In the case of PSO, a fuzzy system is designed to find the values for the inertia weight parameter from the velocity equation. Fuzzy logic controllers (FLCs) are optimized with ACO and PSO, respectively, to prove the performance of the proposed approach. The particular benchmark problems considered to test the proposed methods are the water level control in a tank and temperature control in a shower. Therefore, PSO and ACO algorithms are applied in the optimization of the parameters of the FLCs. The achievement of the proposed fuzzy ACO and PSO algorithms is compared with the original results of each benchmark control problem.