A proposal on reasoning methods in fuzzy rule-based classification systems

Fuzzy Rule-Based Systems have been succesfully applied to pattern classification problems. In this type of classification systems, the classical Fuzzy Reasoning Method (FRM) classifies a new example with the consequent of the rule with the greatest degree of association. By using this reasoning method, we lose the information provided by the other rules with different linguistic labels which also represent this value in the pattern attribute, although probably to a lesser degree. The aim of this paper is to present new FRMs which allow us to improve the system performance, maintaining its interpretability. The common aspect of the proposals is the participation, in the classification of the new pattern, of the rules that have been fired by such pattern. We formally describe the behaviour of a general reasoning method, analyze six proposals for this general model, and present a method to learn the parameters of these FRMs by means of Genetic Algorithms, adapting the inference mechanism to the set of rules. Finally, to show the increase of the system generalization capability provided by the proposed FRMs, we point out some results obtained by their integration in a fuzzy rule generation process.     

A soft computing-based approach to spatio-temporal prediction

This paper aims to incorporate intelligent mechanisms based on Soft Computing in Geographical Information Systems (GIS). The proposal here is to present a spatio-temporal prediction method of forestry evolution for a sequence of binary images by means of fuzzy inference systems (FIS), genetic algorithm (GA) and genetic programming (GP). The main inference is based on a fuzzy system which processes a set of crisp/fuzzy relations and infers a crisp relation representing the predicted image at a predefined date. The fuzzy system is formed by a fixed fuzzy rule base and a partition set that may be defined by an expert or optimized by means of a GA. Genetic programming may also be adopted to generate the size of predicted area used in the final stage of the inference process. The developed methodology is applied in regions of Venezuela, France and Guatemala to identify their forestry evolution trends. The proposed approaches are compared with other techniques to validate the system.     

Adaptive network-based fuzzy inference system with leave-one-out cross-validation approach for prediction of surface roughness

The prediction of surface roughness is a challengeable problem. In order to improve the prediction accuracy in end milling process, an improved approach is proposed to model surface roughness with adaptive network-based fuzzy inference system (ANFIS) and leave-one-out cross-validation (LOO-CV) approach. This approach focuses on both architecture and parameter optimization. LOO-CV, which is an effective measure to evaluate the generalization capability of mode, is employed to find the most suitable membership function and the optimal rule base of ANFIS model for the issue of surface roughness prediction. To find the optimal rule base of ANFIS, a new “top down” rules reduction method is suggested. Three machining parameters, the spindle speed, feed rate and depth of cut are used as inputs in the model. Based on the same experimental data, the predictive results of ANFIS with LOO-CV are compared with the results reported recently in the literature and ANFIS with clustering methods. The comparisons indicate that the presented approach outperforms the opponent methods, and the prediction accuracy can be improved to 96.38%. ANFIS with LOO-CV approach is an effective approach for prediction of surface roughness in end milling process.     

Rule generation for hierarchical collaborative fuzzy system

A new method of rule generation for the hierarchical collaborative fuzzy system, HCFS, is proposed. This HCFS is structured like various parallel fuzzy subsystems and it overcomes the dimensionality problem and the lack of interpretability of most of the traditional fuzzy systems, when dealing with complex real-world problems. An association process of different fuzzy systems is presented in this work, through the use of a relevance concept of a fuzzy system. The result of this aggregation is a collaborative structure where all sub-models have the ability to gradually improve the overall accuracy of approximation by adding their own contributions. For this structure we propose a new algorithm to be used in the procedures of the three learning phases: the structure building, the parametric identification and the division of the learning data among the various levels of the hierarchical structure. This new fuzzy modelling technique automatically generates and tunes the sets of fuzzy rules in the hierarchical collaborative structure (HCS). The effectiveness of the proposed HCFS model in handling high-dimensional and complex problems is demonstrated through various numerical simulations.     

模糊处理变结构神经网络日负荷预测方法研究

对于受不确定因素影响的日电力负荷,首次提出了基于模糊分类规则的变结构神经网络负荷预测模型,考虑从两方面改进预测精度,一个方面是通过模糊分类规则,使过去的负荷数据分为不同气候特征,选用同类特征数据进行预测,另一方面是通过神经网络变结构优化,确定最优网络和最优拟合逼近,从而得到最优的预测结果,这种新方法同时考虑了天气因素的影响和神经网络的最优确定,因此,较大提高了日负荷预测的精度。     

An interpretability improvement for fuzzy rule bases obtained by the iterative rule learning approach

Interpretability is one of the key concepts in many of the applications using the fuzzy rule-based approach. It is well known that there are many different criteria around this concept, the complexity being one of them. In this paper, we focus our efforts in reducing the complexity of the fuzzy rule sets. One of the most interesting approaches for learning fuzzy rules is the iterative rule learning approach. It is mainly characterized by obtaining rules covering few examples in final stages, being in most cases useless to represent the knowledge. This behavior is due to the specificity of the extracted rules, which eventually creates more complex set of rules. Thus, we propose a modified version of the iterative rule learning algorithm in order to extract simple rules relaxing this natural trend. The main idea is to change the rule extraction process to be able to obtain more general rules, using pruned searching spaces together with a knowledge simplification scheme able to replace learned rules. The experimental results prove that this purpose is achieved. The new proposal reduces the complexity at both, the rule and rule base levels, maintaining the accuracy regarding to previous versions of the algorithm.     

Combining boosting and evolutionary algorithms for learning of fuzzy classification rules

This paper presents a novel boosting algorithm for genetic learning of fuzzy classification rules. The method is based on the iterative rule learning approach to fuzzy rule base system design. The fuzzy rule base is generated in an incremental fashion, in that the evolutionary algorithm optimizes one fuzzy classifier rule at a time. The boosting mechanism reduces the weight of those training instances that are classified correctly by the new rule. Therefore, the next rule generation cycle focuses on fuzzy rules that account for the currently uncovered or misclassified instances. The weight of a fuzzy rule reflects the relative strength the boosting algorithm assigns to the rule class when it aggregates the casted votes. The approach is compared with other classification algorithms for a number problem sets from the UCI repository.     

A new hybrid algorithm based on optimal fuzzy controller in multimachine power system

In this article, a new methodology based on fuzzy proportional‐integral‐derivative (PID) controller is proposed to damp low frequency oscillation in multimachine power system where the parameters of proposed controller are optimized offline automatically by hybrid genetic algorithm (GA) and particle swarm optimization (PSO) techniques. This newly proposed method is more efficient because it cope with oscillations and different operating points. In this strategy, the controller is tuned online from the knowledge base and fuzzy interference. In the proposed method, for achieving the desired level of robust performance exact tuning of rule base and membership functions (MF) are very important. The motivation for using the GA and PSO as a hybrid method are to reduce fuzzy effort and take large parametric uncertainties in to account. This newly developed control strategy mixed the advantage of GA and PSO techniques to optimally tune the rule base and MF parameters of fuzzy controller that leads to a flexible controller with simple structure while is easy to implement. The proposed method is tested on three machine nine buses and 16 machine power systems with different operating conditions in present of disturbance and nonlinearity. The effectiveness of proposed controller is compared with robust PSS that tune using PSO and the fuzzy controller which is optimized rule base by GA through figure of demerit and integral of the time multiplied absolute value of the error performance indices. The results evaluation shows that the proposed method achieves good robust performance for a wide range of load change in the presents of disturbance and system nonlinearities and is superior to the other controllers. © 2014 Wiley Periodicals, Inc. Complexity 21: 78–93, 2015     

具有模糊属性的关联产生式发掘算法及应用

本文通过不确定性推理的分析，提出了模糊关联的概念，用模糊概念表示事务数据之间的关联关系，研究了模糊关联的性质，给出了模糊关联产生式的发掘算法及应用的实例．     

基于三角模糊集划分的MISO Mamdani模糊系统参数关联性分析

基于三角模糊集划分的MISO Mamdani模糊系统是模糊规则获取研究领域的一类重点研究对象。在这种划分下，系统的输入空间被划分成若干个超立方体，在每个超立方体内系统的输出与2^p条模糊规则中的参数相关。本文将每个超立方体分成若干个区域，并且严格论证了在每个区域内系统输出仅与其中2^p-1条模糊规则及另2^p-1条模糊规则中相应参数平均值相关。这个结论使得可以根据样本误差的区域分布情况优化参数的选取。对于该类系统的参数优化过程中的参数选取具有积极的意义。     

A learning process for fuzzy control rules using genetic algorithms

The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable genetic algorithms.     

Chaos synchronization using fuzzy logic controller

The design of a rule-based controller for a class of master-slave chaos synchronization is presented in this paper. In traditional fuzzy logic control (FLC) design, it takes a long time to obtain the membership functions and rule base by trial-and-error tuning. To cope with this problem, we directly construct the fuzzy rules subject to a common Lyapunov function such that the master–slave chaos systems satisfy stability in the Lyapunov sense. Unlike conventional approaches, the resulting control law has less maximum magnitude of the instantaneous control command and it can reduce the actuator saturation phenomenon in real physic system. Two examples of Duffing–Holmes system and Lorenz system are presented to illustrate the effectiveness of the proposed controller.     

Improving the accuracy while preserving the interpretability of fuzzy function approximators by means of multi-objective evolutionary algorithms

The identification of a model is one of the key issues in the field of fuzzy system modeling and function approximation theory. An important characteristic that distinguishes fuzzy systems from other techniques in this area is their transparency and interpretability. Especially in the construction of a fuzzy system from a set of given training examples, little attention has been paid to the analysis of the trade-off between complexity and accuracy maintaining the interpretability of the final fuzzy system. In this paper a multi-objective evolutionary approach is proposed to determine a Pareto-optimum set of fuzzy systems with different compromises between their accuracy and complexity. In particular, two fundamental and competing objectives concerning fuzzy system modeling are addressed: fuzzy rule parameter optimization and the identification of system structure (i.e. the number of membership functions and fuzzy rules), taking always in mind the transparency of the obtained system. Another key aspect of the algorithm presented in this work is the use of some new expert evolutionary operators, specifically designed for the problem of fuzzy function approximation, that try to avoid the generation of worse solutions in order to accelerate the convergence of the algorithm.     

Fuzzy rough sets and multiple-premise gradual decision rules

We propose a new fuzzy rough set approach which, differently from most known fuzzy set extensions of rough set theory, does not use any fuzzy logical connectives (t-norm, t-conorm, fuzzy implication). As there is no rationale for a particular choice of these connectives, avoiding this choice permits to reduce the part of arbitrary in the fuzzy rough approximation. Another advantage of the new approach is that it is based on the ordinal properties of fuzzy membership degrees only. The concepts of fuzzy lower and upper approximations are thus proposed, creating a base for induction of fuzzy decision rules having syntax and semantics of gradual rules. The proposed approach to rule induction is also interesting from the viewpoint of philosophy supporting data mining and knowledge discovery, because it is concordant with the method of concomitant variations by John Stuart Mill. The decision rules are induced from lower and upper approximations defined for positive and negative relationships between credibility degrees of multiple premises, on one hand, and conclusion, on the other hand.     

Extracting compact and information lossless sets of fuzzy association rules

Applying classical association rule extraction framework on fuzzy datasets leads to an unmanageably highly sized association rule sets. Moreover, the discretization operation leads to information loss and constitutes a hamper towards an efficient exploitation of the mined knowledge. To overcome such a drawback, this paper proposes the extraction and the exploitation of compact and informative generic basis of fuzzy association rules. The presented approach relies on the extension, within the fuzzy context, of the notion of closure and Galois connection, that we introduce in this paper. In order to select without loss of information a generic subset of all fuzzy association rules, we define three fuzzy generic basis from which remaining (redundant) FARs are generated. This generic basis constitutes a compact nucleus of fuzzy association rules, from which it is possible to informatively derive all the remaining rules. In order to ensure a sound and complete derivation process, we introduce an axiomatic system allowing the complete derivation of all the redundant rules. The results obtained from experiments carried out on benchmark datasets are very encouraging. They highlight a very important reduction of the number of the extracted fuzzy association rules without information loss.     

Implementing fuzzy logic controllers using a neural network framework

We describe a system for implementing fuzzy logic controllers using a neural network. A significant aspect of this system is that the linguistic values associated with the fuzzy control rules can be general concave continuous fuzzy subsets. By using structures suggested by the fuzzy logic framework, we simplify the learning requirements. On the other hand the adaptive aspect of the neural framework allows for the necessary learning.     

Uncertainty analysis of transport of water and pesticide in an unsaturated layered soil profile using fuzzy set theory

Incomplete information is notoriously common in planning soil and groundwater remediation. For making decisions groundwater flow and transport models are commonly used. However, uncertainty in prediction arises due to imprecise information on flow and transport parameters like saturated/unsaturated hydraulic conductivity, water retention curve parameters, precipitation and evapo-transpiration rates as well as factors governing the fate of pollutant in soil like dispersion, diffusion, degradation and chemical transformation. Different methods exist for quantifying uncertainty, e.g. first and second order Taylor’s Series and Monte-Carlo method. In this paper, a methodology based on fuzzy set theory is presented to express imprecision of input data, in terms of fuzzy number, to quantify the uncertainty in prediction. The application of the fuzzy set theory is demonstrated through pesticide (endosulfan) transport in an unsaturated layered soil profile. The governing partial differential equation along with fuzzy inputs, results in a non-linear optimization problem. The solution gives complete membership functions for flow (suction head) and pesticide concentration in soil column.     

A Fuzzy Multi-Criteria Outranking Approach in Support of Business Angels’ Decision Analysis Process for the Assessment of Companies as Investment Opportunities

In this paper, a multi-criteria method is presented for the evaluation and ranking of a selected set of companies as investment opportunities in aid of the relevant decision analysis process of business angels. The multi-criteria methodology is based on the PROMETHEE method, which is further extended to deal with fuzzy input data in order to address the data imprecision and uncertainty of the decision process. The paper concludes by suggesting a web-based system implementation of the proposed methodology, which will significantly enhance modern business angels networks.     

Interpretation of fuzzy data by means of fuzzy rules with applications to speech recognition

Recently, a speech recognition methodology has been proposed which has as one of its main principles the explicit assumption of intrinsic uncertainty of the data (speech signals) and inexactness of the knowledge (acoustic phonetic, etc…) available to interpret them. The main problem presented by this methodology is that of parsing ‘fuzzy data’ by means of ‘fuzzy rules’. To solve this problem, an appropriate fuzzy parsing and interpretation scheme has been proposed. It assumes the data to be represented as strings of ‘fuzzy symbols’, defined as fuzzy sets over the appropriate set of categories, and knowledge as finite-state networks with the arcs labelled by fuzzy symbols of the same type. A formal presentation of this scheme is the main topic of this paper. Included is a brief discussion of the application to Automatic Speech Recognition, and a summary of some results obtained from an implementation example.     

A Fuzzy Multi-criteria Outranking Approach in Support of Business Angels’ Decision-Analysis Process for the Assessment of Companies as Investment Opportunities

In this paper, a multi-criteria method is presented for the evaluation and ranking of a selected set of companies as investment opportunities in aid of the relevant decision-analysis process of business angels. The multi-criteria methodology is based on the PROMETHEE method, which is further extended to deal with fuzzy input data in order to address the data imprecision and uncertainty of the decision process. The paper concludes by suggesting a web-based system implementation of the proposed methodology, which will significantly enhance modern business angels networks.