Rule Antecedents Research Articles

Enhancing Multiclass Classification in FARC-HD Fuzzy Classifier: On the Synergy Between $n$-Dimensional Overlap Functions and Decomposition Strategies

There are many real-world classification problems involving multiple classes, e.g., in bioinformatics, computer vision, or medicine. These problems are generally more difficult than their binary counterparts. In this scenario, decomposition strategies usually improve the performance of classifiers. Hence, in this paper, we aim to improve the behavior of fuzzy association rule-based classification model for high-dimensional problems (FARC-HD) fuzzy classifier in multiclass classification problems using decomposition strategies, and more specifically One-versus-One (OVO) and One-versus-All (OVA) strategies. However, when these strategies are applied on FARC-HD, a problem emerges due to the low-confidence values provided by the fuzzy reasoning method. This undesirable condition comes from the application of the product t -norm when computing the matching and association degrees, obtaining low values, which are also dependent on the number of antecedents of the fuzzy rules. As a result, robust aggregation strategies in OVO, such as the weighted voting obtain poor results with this fuzzy classifier. In order to solve these problems, we propose to adapt the inference system of FARC-HD replacing the product t -norm with overlap functions . To do so, we define n-dimensional overlap functions . The usage of these new functions allows one to obtain more adequate outputs from the base classifiers for the subsequent aggregation in OVO and OVA schemes. Furthermore, we propose a new aggregation strategy for OVO to deal with the problem of the weighted voting derived from the inappropriate confidences provided by FARC-HD for this aggregation method. The quality of our new approach is analyzed using 20 datasets and the conclusions are supported by a proper statistical analysis. In order to check the usefulness of our proposal, we carry out a comparison against some of the state-of-the-art fuzzy classifiers. Experimental results show the competitiveness of our method.

CCAR: An efficient method for mining class association rules with itemset constraints

Class association rules (CARs) are basically used to build a classification model for prediction; they can also be used to describe correlations between itemsets and class labels. The latter is very popular in mining medical data. For example, epidemiologists often consider rules which indicate the relations between risk factors (itemsets) and HIV test results (class labels). However, in the real world, end users are often interested in a subset of class association rules. Particularly, they may consider only rules which contain at least one itemset from a user-defined set of itemsets in the rule antecedent. For example, when classifying which populations are at high risk for HIV infection, epidemiologists often concentrate on rules that include demographic information such as sex, age, and marital status in rule antecedents. Two naive strategies are to solve this problem by applying the itemset constraints into the pre-processing or post-processing step. However, such approaches are time-intensive. This paper thus proposes an efficient method for integrating the constraints into the class association rule mining process. The experimental results show that the proposed algorithm outperforms two basic approaches in the mining time and the memory consumption. The practical benefits of our method are demonstrated by a real-life application in the HIV/AIDS domain.

Fuzzy reasoning method by optimizing the similarity of truth-tables

This paper presents a new fuzzy reasoning method by optimizing the similarity of truth-tables (OS method for short). Its basic idea is to find a fuzzy set such that the truth-tables generated by the antecedent rule and the consequent rule are as similar as possible. Based on this idea, the principle of OS method and the fuzzy reasoning with OS method are given and discussed. And then the OS methods with certain similarity measure and several fuzzy implications are investigated. Finally, numerical examples are analyzed to compare the proposed method with compositional rule of inference (CRI) method.

The Application of the Ant Colony Decision Rule Algorithm on Distributed Data Mining

ABSTRACT Based on the deep research of Ant Colony Algorithm, an Ant Colony decision rule Algorithm is proposed for rules mining based on the thought of ant colony and rule mining of decision tree. Then the algorithm is compared with C4.5 and applied on the rules mining and the results are showed by simulation. INTRODUCTION In general, the goal of data mining is to extract knowledge from data. Data mining is an inter-disciplinary field, whose core is at the intersection of machine learning, statistics and databases (Quinlan, 1986). There are several data mining tasks, including classification, regression, clustering, dependence modeling, etc. (Quinlan, 1993). Each of these tasks can be regarded as a kind of problem to be solved by a data mining algorithm. Therefore, the first step in designing a data mining algorithm is to define which task the algorithm will address. In recent, there are many mining tools, such as neutral network, gene algorithm, decision trees, rule referring, to predict the future development[1], and they are able to help people to make good decisions. But there are some shortcomings in these methods, such as incomprehensive results, over-fit rules and difficulties in being applied on distributed simulation. In this paper we propose an Ant Colony Optimization (ACO) algorithm (Dorigo, Maniezzo & Colorni, 1996; Stutzle & Hoos, 1997; and de A. Silla & Ramalho, 2001) for the classification task of data mining. In this task the goal is to assign each case (object, record, or instance) to one class, out of a set of predefined classes, based on the values of some attributes (called predictor attributes) for the case. In the context of the classification task of data mining, discovered knowledge is often expressed in the form of IF-THEN rules, as follows: IF THEN . The rule antecedent (IF part) contains a set of conditions, usually connected by a logical conjunction operator (AND). In this paper we will refer to each rule condition as a term, so that the rule antecedent is a logical conjunction of terms in the form: IF term1 AND term2 AND ... Each term is a triple, such as . The rule consequent (THEN part) specifies the class predicted for cases whose predictor attributes satisfy all the terms specified in the rule antecedent. From a data mining viewpoint, this kind of knowledge representation has the advantage of being intuitively comprehensible for the user, as long as the number of discovered rules and the number of terms in rule antecedents are not large. In this paper, the ACDR is applied for resolving the distributed database mining. The simulation results show that the ACDR is an available and correct algorithm for distributed mining. THE ANT COLONY OPTIMIZATION ALGORITHM The ant colony optimization technique has emerged recently as a novel meta-heuristic belongs to the class of problem-solving strategies derived from natural (other categories include neural networks, simulated annealing, and evolutionary algorithms). The ant system optimization algorithm is basically a multi-agent system where low level interactions between single agents (i.e., artificial ants) result in a complex behavior of the whole ant colony. Ant system optimization algorithms have been inspired by colonies of real ants, which deposit a chemical substance (called pheromone) on the ground. It was found that the medium used to communicate information among individuals regarding paths, and used to decide where to go, consists of pheromone trails. A moving ant lays some pheromone (in varying quantities) on the ground, thus making the path by a trail of this substance. While an isolated ant moves essentially at random, an ant encountering a previously laid trail can detect it and decide with high probability to follow it, thus reinforcing the trail with its own pheromone. …

Top-Down Approach for a Linguistic Fuzzy Logic Model

A top-down approach is introduced for processing nonlinear linguistic fuzzy logic within the Mamdani model itself in order to reduce the computational efforts. The top-down approach is composed of three steps: (1) directly obtain the best set of linguistic terms, (2) find the matching rule antecedents and their output values, and (3) visit the neighbor terms. A numerical example is provided along with detailed analysis of the approach. In addition, the approach is applied to a simplified aircraft conflict detection task. The results show that the top-down approach is effective at reducing the amount of computation compared to the classical search approach.

Generating fuzzy rule base classifier for highly imbalanced datasets using a hybrid of evolutionary algorithms and subtractive clustering

In this paper, a design methodology is proposed for generating a fuzzy rule-based classifier for highly imbalanced datasets (only binary classification problems). The classifier is based on sugeno-type fuzzy inference system (FIS) and is generated using subtractive clustering, differential evolution (DE) and multi-gene genetic programming (MGGP) to obtain fuzzy rules. Subtractive clustering and DE are utilized for producing antecedents of rules and MGGP is employed for generating the functions in the consequence parts of rules. Feature selection is utilized as an important pre-processing step for dimension reduction. Performance of the proposed method is compared with some fuzzy rule-based classification approaches taken from the literature. The experiments are performed over 22 highly imbalanced datasets from KEEL dataset repository; the classification results are evaluated using AUC as a performance measure. Some statistical non-parametric tests are used to compare classification performance of different methods in different datasets. The obtained results reveal that the proposed classifier outperforms other methods in terms of AUC values.

Takagi–Sugeno Fuzzy Models in the Framework of Orthonormal Basis Functions

An approach to obtain Takagi-Sugeno (TS) fuzzy models of nonlinear dynamic systems using the framework of orthonormal basis functions (OBFs) is presented in this paper. This approach is based on an architecture in which local linear models with ladder-structured generalized OBFs (GOBFs) constitute the fuzzy rule consequents and the outputs of the corresponding GOBF filters are input variables for the rule antecedents. The resulting GOBF-TS model is characterized by having only real-valued parameters that do not depend on any user specification about particular types of functions to be used in the orthonormal basis. The fuzzy rules of the model are initially obtained by means of a well-known technique based on fuzzy clustering and least squares. Those rules are then simplified, and the model parameters (GOBF poles, GOBF expansion coefficients, and fuzzy membership functions) are subsequently adjusted by using a nonlinear optimization algorithm. The exact gradients of an error functional with respect to the parameters to be optimized are computed analytically. Those gradients provide exact search directions for the optimization process, which relies solely on input-output data measured from the system to be modeled. An example is presented to illustrate the performance of this approach in the modeling of a complex nonlinear dynamic system.

Selecting feature subset for high dimensional data via the propositional FOIL rules

Feature interaction is an important issue in feature subset selection. However, most of the existing algorithms only focus on dealing with irrelevant and redundant features. In this paper, a propositional FOIL rule based algorithm FRFS, which not only retains relevant features and excludes irrelevant and redundant ones but also considers feature interaction, is proposed for selecting feature subset for high dimensional data. FRFS first merges the features appeared in the antecedents of all FOIL rules, achieving a candidate feature subset which excludes redundant features and reserves interactive ones. Then, it identifies and removes irrelevant features by evaluating features in the candidate feature subset with a new metric CoverRatio, and obtains the final feature subset. The efficiency and effectiveness of FRFS are extensively tested upon both synthetic and real world data sets, and it is compared with other six representative feature subset selection algorithms, including CFS, FCBF, Consistency, Relief-F, INTERACT, and the rule-based FSBAR, in terms of the number of selected features, runtime and the classification accuracies of the four well-known classifiers including Naive Bayes, C4.5, PART and IB1 before and after feature selection. The results on the five synthetic data sets show that FRFS can effectively identify irrelevant and redundant features while reserving interactive ones. The results on the 35 real world high dimensional data sets demonstrate that compared with other six feature selection algorithms, FRFS cannot only efficiently reduce the feature space, but also can significantly improve the performance of the four well-known classifiers.

A meta-cognitive sequential learning algorithm for neuro-fuzzy inference system

In this paper, we present a meta-cognitive sequential learning algorithm for a neuro-fuzzy inference system, referred to as, ‘Meta-Cognitive Neuro-Fuzzy Inference System’ (McFIS). McFIS has two components, viz., a cognitive component and a meta-cognitive component. The cognitive component employed is a Takagi–Sugeno–Kang type-0 neuro-fuzzy inference system. A self-regulatory learning mechanism that controls the learning process of the cognitive component, by deciding what-to-learn, when-to-learn and how-to-learn from sequential training data, forms the meta-cognitive component. McFIS realizes the above decision by employing sample deletion, sample reserve and sample learning strategy, respectively. The meta-cognitive component use the instantaneous error of the sample and spherical potential of the rule antecedents to select the best training strategy for the current sample. Also, in sample learning strategy, when a new rule is added the rule consequent is assigned such that the localization property of Gaussian rule is fully exploited. The performance of McFIS is evaluated on four regression and eight classification problems. The performance comparison shows the superior generalization performance of McFIS compared to existing algorithms.

Optimal Fuzzy Model Construction With Statistical Information Using Genetic Algorithm

Fuzzy rule based models have a capability to approximate any continuous function to any degree of accuracy on a compact domain. The majority of FLC design process relies on heuristic knowledge of experience operators. In order to make the design process automatic we present a genetic approach to learn fuzzy rules as well as membership function parameters. Moreover, several statistical information criteria such as the Akaike information criterion (AIC), the Bhansali-Downham information criterion (BDIC), and the Schwarz-Rissanen information criterion (SRIC) are used to construct optimal fuzzy models by reducing fuzzy rules. A genetic scheme is used to design Takagi-Sugeno-Kang (TSK) model for identification of the antecedent rule parameters and the identification of the consequent parameters. Computer simulations are presented confirming the performance of the constructed fuzzy logic controller.

Special Issue on Fuzzy Rule Interpolation

Fuzzy Rule Interpolation (FRI) methods are well known tools for reasoning in case of insufficient knowledge expressed as sparse fuzzy rule-bases. It also provides a simple way to define fuzzy functions. Despite these advantages, FRI techniques are relatively rarely applied in practice. Enabling sparse fuzzy rule-bases, FRI dramatically simplifies rule-base creation. Regardless of whether the rule-base is generated by a human expert, or automatically from input-output data, the ability to provide reasonable interpolated conclusions even if no rule fires for a given observation, help to concentrate on cardinal actions alone. This reduces the number of rules needed, speeds up parameter optimization and validation steps, and hence simplifies rule-base creation itself. This special issuefs six papers take six different directions in current FRI research. The first introduces the FRI concept and sets up a unified criteria and evaluation system. This work collects the main properties an FRI method generally has to fulfill. The next two papers are related to the constantly important mainstream research on the more and more sophisticated FRI methods, the endeavor of finding the best way for defining a fuzzy valued fuzzy function based on data given in the form of the relation of fuzzy sets, i.e., in fuzzy rules. The second paper introduces a novel FRI method that is able to handle fuzzy observations activating multiple rule antecedents applying the concept of nonlinear fuzzy-valued function. The third paper presents a novel ganalogical-basedh FRI method that rather fits into the traditional FRI research line, improving the n-rule-based gscale and move transformationh FRI to ensure continuous approximate functions. The fourth paper addresses the issue of defining a distance function between fuzzy sets on a domain that is not necessarily Euclidean metric space. In FRI, this takes on the importance if antecedent or consequent domains are non-Euclidean metric spaces. The last two papers discuss direct FRI control applications. One is an example proving that the sparse fuzzy rule-base is an efficient knowledge representation in intelligent control solutions. The last deals with the computational efficiency of implemented FRI methods applied to direct control area, clearly showing that the sparse fuzzy rule-base is not only a convenient way for knowledge representation, but also makes FRI methods possible devices for direct embedded control applications.

Generalisation of Scale and Move Transformation-Based Fuzzy Interpolation

Fuzzy interpolative reasoning has been extensively studied due to its ability to enhance the robustness of fuzzy systems and reduce system complexity. In particular, the scale and move transformation-based approach is able to handle interpolation with multiple antecedent rules involving triangular, complex polygon, Gaussian and bell-shaped fuzzy membership functions [1]. Also, this approach has been extended to deal with interpolation and extrapolation with multiple multi-antecedent rules [2]. However, the generalised extrapolation approach based on multiple rules may not degenerate back to the basic crisp extrapolation based on two rules. Besides, the approximate function of the extended approach may not be continuous. This paper therefore proposes a new approach to generalising the basic fuzzy interpolation technique of [1] in an effort to eliminate these limitations. Examples are given throughout the paper for illustration and comparative purposes. The result shows that the proposed approach avoids the identified problems, providing more reasonable interpolation and extrapolation.

Multivariable Gaussian Evolving Fuzzy Modeling System

This paper introduces a class of evolving fuzzy rule-based system as an approach for multivariable Gaussian adaptive fuzzy modeling. The system is an evolving Takagi-Sugeno (eTS) functional fuzzy model, whose rule base can be continuously updated using a new recursive clustering algorithm based on participatory learning. The fuzzy sets of the rule antecedents are multivariable Gaussian membership functions, which have been adopted to preserve information between input variable interactions. The parameters of the membership functions are estimated by the clustering algorithm. A weighted recursive least-squares algorithm updates the parameters of the rule consequents. Experiments considering time-series forecasting and nonlinear system identification are performed to evaluate the performance of the approach proposed. The multivariable Gaussian evolving fuzzy models are compared with alternative evolving fuzzy models and classic models with fixed structures. The results suggest that multivariable Gaussian evolving fuzzy modeling is a promising approach for adaptive system modeling.

A prototype-based rule inference system incorporating linear functions

A calculus of appropriateness measures of linguistic expressions is proposed, which is based on the prototype theory and random set theory interpretation of vague concepts. A prototype-based rule inference system is then introduced to incorporate linguistic labels in the rule antecedents and linear functions in the consequents of rules. And a rule learning algorithm is developed by combining a new clustering algorithm and a conjugate gradient algorithm. The proposed prototype-based inference system is then applied to a number of benchmark prediction problems including a nonlinear two-dimensional surface, the Mackey–Glass time series and the sunspot time-series. Results suggest that the proposed model is very robust and can perform well in high-dimensional noisy data.

Flexible rule-based inference exploiting taxonomies

Rule-based systems are widely used to implement knowledge-based systems. They are usually intuitive to use, have good performance and can be easily integrated with other software components. However, a critical problem is that the behavior of a rule-based system tends to degrade abruptly whenever the knowledge base is incomplete or not detailed enough or when operating at the borders of its expertise. Various forms of approximate reasoning have been introduced but they solve the problem only in a partial way. In the paper we propose new forms of rule inference that tackle this problem, introducing a form of flexible or common sense reasoning that can support a softer degradation of problem solving ability when knowledge is partial or incomplete. The solution we propose relies on the exploitation of semantic information associated with the concepts involved in the rules. In particular, we show how taxonomical information can be exploited to define flexible forms of match between rule antecedents and the working memory, and flexible forms of conflict resolution. In this way, even when no rule perfectly matches the working memory, the inference engine can select rules that apply to more general or to similar cases and provide some approximate solution. The approach has been motivated by work on context aware (recommender) systems where the problem of incomplete descriptions and brittle degradation of problem solving ability are particularly relevant.

Prediction of color change after tooth bleaching using fuzzy logic for Vita Classical shades identification

Tooth bleaching is becoming increasingly popular among patients and dentists since it is a relatively noninvasive approach for whitening and lightening teeth. Instruments and visual assessment with respect to commercial shade guides are currently used to evaluate tooth color. However, the association between these procedures is imprecise and the degree of color change after tooth bleaching is known to vary substantially between studies; there are currently no objective guidelines to predict the effectiveness of a tooth-bleaching treatment. We propose a new methodology based on fuzzy logic as a natural means of representing the imprecision present when modeling the color change produced by a tooth-bleaching treatment on the basis of a tooth's initial chromatic values. This system has the advantage of producing a set of interpretable fuzzy rules that can subsequently be used by scientists and dental practitioners. The fuzzy system obtained has the special characteristic whereby the rule antecedents correspond to prebleaching shades of the well-known Vita commercial shade guide. Additionally, the rule consequents directly correspond with the expected CIELAB postbleaching values for each Vita shade, thanks to a modification of the system's inference structure. Finally, the values of these postbleaching CIELAB coordinates have been associated with Vita shades by evaluating their respective membership functions, thereby approximating which posttreatment Vita shades are to be expected for each prebleaching shade.

Design of Hybrid Fuzzy Neural Network for Function Approximation

In this paper, a hybrid Fuzzy Neural Network (FNN) system for function approximation is presented. The proposed FNN can handle numeric and fuzzy inputs simultaneously. The numeric inputs are fuzzified by input nodes upon presentation to the network while the Fuzzy rule based knowledge is translated directly into network architecture. The connections between input to hidden nodes represent rule antecedents and hidden to output nodes represent rule consequents. All the connections are represented by Gaussian fuzzy sets. The method of activation spread in the network is based on a fuzzy mutual subsethood measure. Rule (hidden) node activations are computed as a fuzzy inner product. For a given numeric o fuzzy input, numeric outputs are computed using volume based defuzzification. A supervised learning procedure based on gradient descent is employed to train the network. The model has been tested on two different approximation problems: sine-cosine function approximation and Narazaki-Ralescu function and shows its natural capability of inference, function approximation, and classification.

Produzir saberes entre aderência e desaderência

This article discusses the concept of development. This is done assuming that life is a permanent negotiation between obligation of living according to demands and cohertions from the present local-spatial, and different kinds of antecedent rules instituted from a distance of these local adherences. In this sense, it is proposed an ethical and epistemological posture that creates a new regime of knowledge production taking into consideration the knowledge and values developed by the local social authors. Key words: developement, ergology, knowledge, work.

Multi-objective genetic fuzzy classifiers for imbalanced and cost-sensitive datasets

We exploit an evolutionary three-objective optimization algorithm to produce a Pareto front approximation composed of fuzzy rule-based classifiers (FRBCs) with different trade-offs between accuracy (expressed in terms of sensitivity and specificity) and complexity (computed as sum of the conditions in the antecedents of the classifier rules). Then, we use the ROC convex hull method to select the potentially optimal classifiers in the projection of the Pareto front approximation onto the ROC plane. Our method was tested on 13 highly imbalanced datasets and compared with 2 two-objective evolutionary approaches and one heuristic approach to FRBC generation, and with three well-known classifiers. We show by the Wilcoxon signed-rank test that our three-objective optimization approach outperforms all the other techniques, except for one classifier, in terms of the area under the ROC convex hull, an accuracy measure used to globally compare different classification approaches. Further, all the FRBCs in the ROC convex hull are characterized by a low value of complexity. Finally, we discuss how, the misclassification costs and the class distributions are fixed, we can select the most suitable classifier for the specific application. We show that the FRBC selected from the convex hull produced by our three-objective optimization approach achieves the lowest classification cost among the techniques used as comparison in two specific medical applications.

On evolutionary designing and learning of flexible neuro-fuzzy structures for nonlinear classification

In the paper, the evolutionary strategy is applied for learning flexible neuro-fuzzy systems. In the process of evolution we determine: fuzzy inference (Mamdani type or logical type—described by an S -implication), specific fuzzy implication, if the logical type system is found in the process of evolution or specific t -norm connecting antecedents and consequences, if the Mamdani type system is found in the process of evolution, specific t -norm for aggregation of antecedents in each rule, specific triangular norm describing aggregation operator, shapes and parameters of fuzzy membership functions, weights describing importance of antecedents of rules, and weights describing importance of rules, parameters of adjustable triangular norms, parameters of soft triangular norms. It should be noted that the crossover and mutation operators are chosen in a self-adaptive way. The method is tested using well known classification benchmarks.