A PSO-aided neuro-fuzzy classifier employing linguistic hedge concepts

The present paper proposes the development of an adaptive neuro-fuzzy classifier which employs two relatively less explored and comparatively new problem solving domains in fuzzy systems. The relatively less explored field is the domain of the fuzzy linguistic hedges which has been employed here to define the flexible shapes of the fuzzy membership functions (MFs). To achieve finer and finer adaptation, and hence control, over the fuzzy MFs, each MF is composed of several piecewise MF sections and the shape of each such MF section is varied by applying a fuzzy linguistic operator on it. The system employs a Takagi–Sugeno based neuro-fuzzy system where the rule consequences are described by zero order elements. This proposed linguistic hedge based neuro-fuzzy classifier (LHBNFC) employs a relatively new field in the area of combinatorial metaheuristics, called particle swarm optimization (PSO), for its efficient learning. PSO has been employed in this scheme to simultaneously tune the shape of the fuzzy MFs as well as the rule consequences for the entire fuzzy rule base. The performance of the proposed system is demonstrated by implementing it for two classical benchmark data sets: (i) the iris data and (ii) the thyroid data. Performance comparison vis-à-vis other available algorithms shows the effectiveness of our proposed algorithm.     

一种基于粒子群算法的分类器设计

将粒子群算法应用于数据分类,给出了适用于粒子群算法的分类规则编码,构造了新的分类规则适应度函数来更准确的提取规则集,并通过修改粒子位置更新方程使粒子群算法适于解决分类规则挖掘问题,进而实现了基于粒子群算法的分类器设计。该文进一步用UCI基准数据集对作者提出的粒子群分类器进行了测试,并将几种不同速度与位置更新策略的粒子群算法分类器与遗传算法分类器进行对比,实验结果表明,这种粒子群分类器是一种有效、可行的分类器设计方案。     

Geno-fuzzy classification trees

Making the non-terminal nodes of a binary tree classifier fuzzy can mitigate tree brittleness. Using a genetic algorithm, two optimization techniques are explored. In one case, each generation minimizes classification error by optimizing a common fuzzy percent, p_T, used to determine parameters at every node. In the other case, each generation yields a sequence of minimized node-specific parameters. The output value is determined through defuzzification after input vectors, in general, take both paths at each node with a weighting factor determined by the node membership functions. Experiments conducted using this geno-fuzzy approach yield an improvement compared with other classical algorithms.     

A fast recursive algorithm based on fuzzy 2-partition entropy approach for threshold selection

The fuzzy c-partition entropy approach for threshold selection is an effective approach for image segmentation. The approach models the image with a fuzzy c-partition, which is obtained using parameterized membership functions. The ideal threshold is determined by searching an optimal parameter combination of the membership functions such that the entropy of the fuzzy c-partition is maximized. It involves large computation when the number of parameters needed to determine the membership function increases. In this paper, a recursive algorithm is proposed for fuzzy 2-partition entropy method, where the membership function is selected as S-function and Z-function with three parameters. The proposed recursive algorithm eliminates many repeated computations, thereby reducing the computation complexity significantly. The proposed method is tested using several real images, and its processing time is compared with those of basic exhaustive algorithm, genetic algorithm (GA), particle swarm optimization (PSO), ant colony optimization (ACO) and simulated annealing (SA). Experimental results show that the proposed method is more effective than basic exhaustive search algorithm, GA, PSO, ACO and SA.     

AGFS: Adaptive Genetic Fuzzy System for medical data classification

A Genetic Fuzzy System (GFS) is basically a fuzzy system augmented by a learning process based on a genetic algorithm (GA). Fuzzy systems have demonstrated their ability to solve different kinds of problems in various application domains. Currently, there is an increasing interest to augment fuzzy systems with learning and adaptation capabilities. Two of the most successful approaches to hybridize fuzzy systems with learning and adaptation methods have been made in the realm of soft computing. The GA can be merged with Fuzzy system for different purposes like rule selection, membership function optimization, rule generation, co-efficient optimization, for data classification. Here we propose an Adaptive Genetic Fuzzy System (AGFS) for optimizing rules and membership functions for medical data classification process. The primary intension of the research is 1) Generating rules from data as well as for the optimized rules selection, adapting of genetic algorithm is done and to explain the exploration problem in genetic algorithm, introduction of new operator, called systematic addition is done, 2) Proposing a simple technique for scheming of membership function and Discretization, and 3) Designing a fitness function by allowing the frequency of occurrence of the rules in the training data. Finally, to establish the efficiency of the proposed classifier the presentation of the anticipated genetic-fuzzy classifier is evaluated with quantitative, qualitative and comparative analysis. From the outcome, AGFS obtained better accuracy when compared to the existing systems.     

A multi-swarm optimizer based fuzzy modeling approach for dynamic systems processing

Inspired by the phenomenon of symbiosis in natural ecosystems a multi-swarm cooperative particle swarm optimizer (MCPSO) is proposed as a new fuzzy modeling strategy for identification and control of non-linear dynamical systems. In MCPSO, the population consists of one master swarm and several slave swarms. The slave swarms execute particle swarm optimization (PSO) or its variants independently to maintain the diversity of particles, while the particles in the master swarm enhance themselves based on their own knowledge and also the knowledge of the particles in the slave swarms. With four benchmark functions, MCPSO is proved to have better performance than PSO and its variants. MCPSO is then used to automatically design the fuzzy identifier and fuzzy controller for non-linear dynamical systems. The proposed algorithm (MCPSO) is shown to outperform PSO and some other methods in identifying and controlling dynamical systems.     

A fuzzy genetic algorithm for the discovery of process parameter settings using knowledge representation

In this paper, we propose a fuzzy genetic algorithm (Fuzzy-GA) approach integrating fuzzy rule sets and their membership function sets, in a chromosome. The proposed approach consists of two processes: knowledge representation and knowledge assimilation. The knowledge of process parameter setting is encoded as a string with a fuzzy rule set and the associated membership functions. The historical process data forming a combined string is used as the initial knowledge population, which is then ready for knowledge assimilation. A genetic algorithm is used to generate an optimal or nearly optimal fuzzy set and membership functions for the process parameters. The originality of this research is that the proposed system is equipped with the ability to take advantage of assessing the loss which is caused by discrepancy with a process target, thereby enabling the identification of the best set of process parameters. The approach is demonstrated by the use of an experimental example drawn from a semiconductor manufacturer and the results show us that the suggested approach is able to achieve an optimal solution for a process parameter setting problem.     

Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO

In this paper the optimization of type-2 fuzzy inference systems using genetic algorithms (GAs) and particle swarm optimization (PSO) is presented. The optimized type-2 fuzzy inference systems are used to estimate the type-2 fuzzy weights of backpropagation neural networks. Simulation results and a comparative study among neural networks with type-2 fuzzy weights without optimization of the type-2 fuzzy inference systems, neural networks with optimized type-2 fuzzy weights using genetic algorithms, and neural networks with optimized type-2 fuzzy weights using particle swarm optimization are presented to illustrate the advantages of the bio-inspired methods. The comparative study is based on a benchmark case of prediction, which is the Mackey-Glass time series (for τ = 17) problem.     

Strategic bidding using fuzzy adaptive gravitational search algorithm in a pool based electricity market

A novel stochastic optimization approach to solve optimal bidding strategy problem in a pool based electricity market using fuzzy adaptive gravitational search algorithm (FAGSA) is presented. Generating companies (suppliers) participate in the bidding process in order to maximize their profits in an electricity market. Each supplier will bid strategically for choosing the bidding coefficients to counter the competitors bidding strategy. The gravitational search algorithm (GSA) is tedious to solve the optimal bidding strategy problem because, the optimum selection of gravitational constant (G). To overcome this problem, FAGSA is applied for the first time to tune the gravitational constant using fuzzy “IF/THEN” rules. The fuzzy rule-based systems are natural candidates to design gravitational constant, because they provide a way to develop decision mechanism based on specific nature of search regions, transitions between their boundaries and completely dependent on the problem. The proposed method is tested on IEEE 30-bus system and 75-bus Indian practical system and compared with GSA, particle swarm optimization (PSO) and genetic algorithm (GA). The results show that, fuzzification of the gravitational constant, improve search behavior, solution quality and reduced computational time compared against standard constant parameter algorithms.     

改进的粒子群模糊聚类方法

针对基于粒子群的模糊聚类算法以隶属度编码时对噪音敏感,以及处理样本数小于样本维数的数据集效果较差等问题,通过改进其中的模糊聚类约束方法,提出一种改进的基于粒子群的模糊聚类方法.当样本对各类的隶属度之和不为1时,新方法在粒子群优化得出的隶属度基础上,根据样本与各类之间的距离对隶属度进一步分配,以使隶属度满足模糊聚类约束条件.新方法显著地改善了在隶属度编码下使用粒子群进行模糊聚类的效果,并通过典型的数据集进行了验证.     

Parallel machine scheduling with fuzzy processing times using a robust genetic algorithm and simulation

This paper addresses parallel machine scheduling problems with fuzzy processing times. A robust genetic algorithm (GA) approach embedded in a simulation model is proposed to minimize the maximum completion time (makespan). The results are compared with those obtained by using the “longest processing time” rule (LPT), which is known as the most appropriate dispatching rule for such problems. This application illustrates the need for efficient and effective heuristics to solve such fuzzy parallel machine scheduling problems (FPMSPs). The proposed GA approach yields good results quickly and several times in one run. Moreover, because it is a search algorithm, it can explore alternative schedules providing the same results. Thanks to the simulation model, several robustness tests are conducted using different random number sets, and the robustness of the proposed approach is demonstrated.     

An improved hybrid particle swarm optimization algorithm for fuzzy p-hub center problem

The p-hub center problem is useful for the delivery of perishable and time-sensitive system such as express mail service and emergency service. In this paper, we propose a new fuzzy p-hub center problem, in which the travel times are uncertain and characterized by normal fuzzy vectors. The objective of our model is to maximize the credibility of fuzzy travel times not exceeding a predetermined acceptable efficient time point along all paths on a network. Since the proposed hub location problem is too complex to apply conventional optimization algorithms, we adapt an approximation approach (AA) to discretize fuzzy travel times and reformulate the original problem as a mixed-integer programming problem subject to logic constraints. After that, we take advantage of the structural characteristics to develop a parametric decomposition method to divide the approximate p-hub center problem into two mixed-integer programming subproblems. Finally, we design an improved hybrid particle swarm optimization (PSO) algorithm by combining PSO with genetic operators and local search (LS) to update and improve particles for the subproblems. We also evaluate the improved hybrid PSO algorithm against other two solution methods, genetic algorithm (GA) and PSO without LS components. Using a simulated data set of 10 nodes, the computational results show that the improved hybrid PSO algorithm achieves the better performance than GA and PSO without LS in terms of runtime and solution quality.     

Hierarchical aggregation of multiple fuzzy controllers for global complex control problems

In this paper, we illustrate a proposed method for control that combines the outputs of several individual controllers to improve global control of complex nonlinear plants. In the first part of this paper, we illustrate the proposed method that consists of two levels, where in the top level a fuzzy system represents a superior control that is designed for adjusting the behavior of the individual fuzzy controllers at the lower level. To test the approach, we consider the problem of flight control because it requires several individual controllers. Also a comparison is performed, where the hierarchical control strategy is compared with a simple control approach using the t student test. In this paper, we show that the proposed method outperforms the conventional fuzzy control approach. In the optimal design of the proposed control architecture a genetic algorithm was also applied to tune the parameters of the fuzzy systems in an optimal fashion.     

Medical diagnosis of cardiovascular diseases using an interval-valued fuzzy rule-based classification system

ObjectiveTo develop a classifier that tackles the problem of determining the risk of a patient of suffering from a cardiovascular disease within the next 10 years. The system has to provide both a diagnosis and an interpretable model explaining the decision. In this way, doctors are able to analyse the usefulness of the information given by the system.MethodsLinguistic fuzzy rule-based classification systems are used, since they provide a good classification rate and a highly interpretable model. More specifically, a new methodology to combine fuzzy rule-based classification systems with interval-valued fuzzy sets is proposed, which is composed of three steps: (1) the modelling of the linguistic labels of the classifier using interval-valued fuzzy sets; (2) the use of the K_α operator in the inference process and (3) the application of a genetic tuning to find the best ignorance degree that each interval-valued fuzzy set represents as well as the best value for the parameter α of the K_α operator in each rule.ResultsThe suitability of the new proposal to deal with this medical diagnosis classification problem is shown by comparing its performance with respect to the one provided by two classical fuzzy classifiers and a previous interval-valued fuzzy rule-based classification system. The performance of the new method is statistically better than the ones obtained with the methods considered in the comparison. The new proposal enhances both the total number of correctly diagnosed patients, around 3% with respect the classical fuzzy classifiers and around 1% vs. the previous interval-valued fuzzy classifier, and the classifier ability to correctly differentiate patients of the different risk categories.ConclusionThe proposed methodology is a suitable tool to face the medical diagnosis of cardiovascular diseases, since it obtains a good classification rate and it also provides an interpretable model that can be easily understood by the doctors.     

A multi-objective genetic optimization of interpretability-oriented fuzzy rule-based classifiers

The paper presents a multi-objective genetic approach to design interpretability-oriented fuzzy rule-based classifiers from data. The proposed approach allows us to obtain systems with various levels of compromise between their accuracy and interpretability. During the learning process, parameters of the membership functions, as well as the structure of the classifier's fuzzy rule base (i.e., the number of rules, the number of rule antecedents, etc.) evolve simultaneously using a Pittsburgh-type genetic approach. Since there is no particular coding of fuzzy rule structures in a chromosome (it reduces computational complexity of the algorithm), original crossover and mutation operators, as well as chromosome-repairing technique to directly transform the rules are also proposed. To evaluate both the accuracy and interpretability of the system, two measures are used. The first one – an accuracy measure – is based on the root mean square error of the system's response. The second one – an interpretability measure – is based on the arithmetic mean of three components: (a) the average length of rules (the average number of antecedents used in the rules), (b) the number of active fuzzy sets and (c) the number of active inputs of the system (an active fuzzy set or input means a set or input used by at least one fuzzy rule). Both measures are used as objectives in multi-objective (2-objective in our case) genetic optimization approaches such as well-known SPEA2 and NSGA-II algorithms. Moreover, for the purpose of comparison with several alternative approaches, the experiments are carried out both considering the so-called strong fuzzy partitions (SFPs) of attribute domains and without them. SFPs provide more semantically meaningful solutions, usually at the expense of their accuracy. The operation of the proposed technique in various classification problems is tested with the use of 20 benchmark data sets and compared to 11 alternative classification techniques. The experiments show that the proposed approach generates classifiers of significantly improved interpretability, while still characterized by competitive accuracy.     

A hybrid coevolutionary algorithm for designing fuzzy classifiers

Rule learning is one of the most common tasks in knowledge discovery. In this paper, we investigate the induction of fuzzy classification rules for data mining purposes, and propose a hybrid genetic algorithm for learning approximate fuzzy rules. A novel niching method is employed to promote coevolution within the population, which enables the algorithm to discover multiple rules by means of a coevolutionary scheme in a single run. In order to improve the quality of the learned rules, a local search method was devised to perform fine-tuning on the offspring generated by genetic operators in each generation. After the GA terminates, a fuzzy classifier is built by extracting a rule set from the final population. The proposed algorithm was tested on datasets from the UCI repository, and the experimental results verify its validity in learning rule sets and comparative advantage over conventional methods.     

Building contextual classifiers by integrating fuzzy rule based classification technique and k-nn method for credit scoring

Credit-risk evaluation is a very challenging and important problem in the domain of financial analysis. Many classification methods have been proposed in the literature to tackle this problem. Statistical and neural network based approaches are among the most popular paradigms. However, most of these methods produce so-called “hard” classifiers, those generate decisions without any accompanying confidence measure. In contrast, “soft” classifiers, such as those designed using fuzzy set theoretic approach; produce a measure of support for the decision (and also alternative decisions) that provides the analyst with greater insight. In this paper, we propose a method of building credit-scoring models using fuzzy rule based classifiers. First, the rule base is learned from the training data using a SOM based method. Then the fuzzy k-nn rule is incorporated with it to design a contextual classifier that integrates the context information from the training set for more robust and qualitatively better classification. Further, a method of seamlessly integrating business constraints into the model is also demonstrated.     

Car assembly line fault diagnosis based on triangular fuzzy support vector classifier machine and particle swarm optimization

This paper presents a new version of fuzzy support vector classifier machine to diagnose the nonlinear fuzzy fault system with multi-dimensional input variables. Since there exist problems of finite samples and uncertain data in complex fuzzy fault system modeling, the input and output variables are described as fuzzy numbers. Then by integrating the fuzzy theory and v-support vector classifier machine, the triangular fuzzy v-support vector regression machine (TF v-SVCM) is proposed. To seek the optimal parameters of TF v-SVCM, particle swarm optimization (PSO) is also applied to optimize parameters of TF v-SVCM. A diagnosing method based on TF v-SVCM and PSO are put forward. The results of the application in fault system diagnosis confirm the feasibility and the validity of the diagnosing method. The results of application in fault diagnosis of car assembly line show the hybrid diagnosis model based on TF v-SVCM and PSO is feasible and effective, and the comparison between the method proposed in this paper and other ones is also given, which proves this method is better than standard v-SVCM.     

Synthesis of fuzzy logic and Dempster–Shafer Theory for the simulation of the decision-making process in stock trading systems

Modern computerized stock trading systems (mechanical trading systems) are based on the simulation of the decision-making process and generate advice for traders to buy or sell stocks or other financial tools by taking into account the price history, technical analysis indicators, accepted rules of trading and so on. Two stock trading simulating systems based on trading rules defined using fuzzy logic are developed and compared. The first is based on the so-called “Logic-Motivated Fuzzy Logic Operators” (LMFL) approach and aims to avoid certain disadvantages of the classical Mamdani’s method, which has been developed for use in fuzzy logic controllers and not for solving the decision-making problems of stock trading. The LMFL   approach is based on the modified mathematical representation of t$t$-norm and Yager’s implication rule. The second trading system combines the tools of fuzzy logic and Dempster–Shafer Theory (DST  ) to represent the features of the decision-making process more transparently. The fuzzy representation of trading rules based on the theory of technical analysis is used in these expert systems. Since the theory of technical analysis is based on the indicators used by experts to predict stock price movements, the method maps these indicators into new inputs that can be used in a fuzzy logic system. The only required inputs to calculate these indicators are past sequences (history) of stock prices. The method relies on fuzzy logic to choose an appropriate decision when certain price movements or certain price formations occur. The optimization procedure based on historical (teaching) data is used as it significantly improves the performance of such expert systems. The efficiency of the developed expert systems is measured by comparing their outputs versus stock price movements. The results obtained using real NYSE$NYSE$ data allow us to say that the developed expert system based on the synthesis of fuzzy logic and DST provides better results and is more reliable. Moreover, such a conjunction of fuzzy logic, DST and technical analysis, makes it possible to make a profit even when trading against a dominating trend.     

Particle swarm approaches using Lozi map chaotic sequences to fuzzy modelling of an experimental thermal-vacuum system

Particle Swarm Optimization (PSO) approach intertwined with Lozi map chaotic sequences to obtain Takagi–Sugeno (TS) fuzzy model for representing dynamical behaviours are proposed in this paper. The proposed method is an alternative for nonlinear identification approaches especially when dealing with complex systems that cannot always be modelled using first principles to determine their dynamical behaviour. Since modelling nonlinear systems is normally a difficult task, fuzzy models have been employed in many identification problems due its inherent nonlinear characteristics and simple structure, as well. This proposed chaotic PSO (CPSO) approach is employed here for optimizing the premise part of the IF–THEN rules of TS fuzzy model; for the consequent part, least mean squares technique is used. The proposed method is utilized in an experimental application; a thermal-vacuum system which is employed for space environmental emulation and satellite qualification. Results obtained with a variety of CPSO's are compared with traditional PSO approach. Numerical results indicate that the chaotic PSO approach succeeded in eliciting a TS fuzzy model for this nonlinear and time-delay application.