Rule Base Simplification Research Articles

Refining the rule base of fuzzy classifier to support the evaluation of fetal condition

The paper proposes a method to simplify a rule base of zero order Takagi–Sugeno–Kang fuzzy classifier, involving the determination of the ɛ-similar rules based on fuzzy clustering with ɛ-hyperballs. The rule simplification process is based on the concept of ɛ-insensitivity areas underlying the partitioning process of rule centers (centers of membership functions in the rule premises), which directly corresponds to the idea of rule ɛ-similarity. Clustering parameters leading to the best performance of the modified rule base, including the degree of rule ɛ-similarity, are determined by means of the evolution strategy. Since our main objective was to maintain the high performance of the resulting classifier, two rule-based simplification procedures, both called rule base refinement, are proposed. The work focuses mainly on the practical application to support the diagnosis of fetal condition based on the analysis of CardioTocoGraphic (CTG) signals. The publicly available collection of CTG recordings (CTU-UHB) was used in order to verify the quality of the introduced solutions. The classification performance was assessed with respect to the reference evaluation of fetal state determined on the basis of a retrospective analysis using the newborn outcome defined with different thresholds of the blood pH from the umbilical artery. The experiments confirmed the high generalization ability of the refined fuzzy classifier, in particular its high efficiency in supporting the qualitative assessment of fetal condition based on the analysis of parameters quantitatively describing fetal signals.

Creating a list of word alignments from parallel Russian simplification data.

This work describes the development of a list of monolingual word alignments taken from parallel Russian simplification data. This word lists can be used in such lexical simplification tasks as rule-based simplification applications and lexically constrained decoding for neural machine translation models. Moreover, they constitute a valuable source of information for developing educational materials for teaching Russian as a second/foreign language. In this work, a word list was compiled automatically and post-edited by human experts. The resulting list contains 1409 word pairs in which each “complex” word has an equivalent “simpler” (shorter, more frequent, modern, international) synonym. We studied the contents of the word list by comparing the frequencies of the words in the pairs and their levels in the special CEFR-graded vocabulary lists for learners of Russian as a foreign language. The evaluation demonstrated that lexical simplification by means of single-word synonym replacement does not occur often in the adapted texts. The resulting list also illustrates the peculiarities of the lexical simplification task for L2 learners, such as the choice of a less frequent but international word.

On [formula omitted]-insensitive simplification of fuzzy rules for fetal distress assessment

Objective: The work introduces ε-insensitive distance based approach to simplification (by reducing the rules number) of the fuzzy classifier rule base. To obtain premises of the initial rules, a modified clustering with pairs of ε-hyperballs procedure is used. The goal of the presented solutions is to achieve high quality support for fetal distress assessment, based on cardiotocographic (CTG) signals classification with a reduced number of fuzzy rules.Methods: In the presented rule base simplification solution, two rules are considered similar (or contradictory) when the distances between their premises do not exceed the assumed value of ε. The proposed simplification process consists of two phases: the first with combining similar rules into representative rules, and the second (optional) with the removal of contradictory rules. In addition, two methods of determining conclusions for representative rules are considered: a representative rule retains the original (unchanged) conclusion, or from the conclusions of similar rules the one with the highest absolute value is chosen. In the introduced clustering with pairs of ε-hyperballs the sizes of object classes are taken into account, to reduce the potential adverse impact of the unbalanced classes in the considered research material. In experiments, two reference assessments for CTG signals based on the retrospective fetal state evaluation were considered.Results and conclusions: In the two-stage classification, the modified clustering outperformed the original procedure in terms of classification sensitivity and the QI index being the geometric mean of sensitivity and specificity. Among the examined rule base simplification methods, we consider the best to be the one based only on combining similar rules, with the unchanged value of conclusion for a representative rule. With the smallest number of rules (after simplification), an increased sensitivity, and in the case of pH-based reference assessment also increased QI value is obtained. Moreover, the achieved sensitivity and QI are higher in comparison to the reference methods and values reported in literature.Significance and main impact: The results confirmed the effectiveness of the ε-insensitive distance rule base simplification. The proposed methods can be applied to any fuzzy rules with premise membership functions with a defined center. Therefore, we believe that this work may have a positive impact on other studies concerning fuzzy rule-based systems.

Rule Base Simplification and Constrained Learning for Interpretability in TSK Neuro-Fuzzy Modelling

Neuro-fuzzy systems based on a fuzzy model proposed by Takagi, Sugeno and Kang known as the TSK fuzzy model provide a powerful method for modelling uncertain and highly complex non-linear systems. The initial fuzzy rule base in TSK neuro-fuzzy systems is usually obtained using data driven approaches. This process induces redundancy into the system by adding redundant fuzzy rules and fuzzy sets. This increases complexity which adversely affects generalization capability and transparency of the fuzzy model being designed. In this article, the authors explore the potential of TSK fuzzy modelling in developing comparatively interpretable neuro-fuzzy systems with better generalization capability in terms of higher approximation accuracy. The approach is based on three phases, the first phase deals with automatic data driven rule base induction followed by rule base simplification phase. Rule base simplification uses similarity analysis to remove similar fuzzy sets and resulting redundant fuzzy rules from the rule base, thereby simplifying the neuro-fuzzy model. During the third phase, the parameters of membership functions are fine-tuned using a constrained hybrid learning technique. The learning process is constrained which prevents unchecked updates to the parameters so that a highly complex rule base does not emerge at the end of model optimization phase. An empirical investigation of this methodology is done by application of this approach to two well-known non-linear benchmark forecasting problems and a real-world stock price forecasting problem. The results indicate that rule base simplification using a similarity analysis effectively removes redundancy from the system which improves interpretability. The removal of redundancy also increased the generalization capability of the system measured in terms of increased forecasting accuracy. For all the three forecasting problems the proposed neuro-fuzzy system demonstrated better accuracy-interpretability tradeoff as compared to two well-known TSK neuro-fuzzy models for function approximation.

Handling interpretability issues in ANFIS using rule base simplification and constrained learning

Adaptive neuro-fuzzy inference system (ANFIS) is a well-known neuro-fuzzy model for approximating highly complex non-linear systems. ANFIS uses precise fuzzy modelling concept that aims at accuracy of a fuzzy model being designed than on interpretability. But interpretability of a fuzzy system is an equally important aspect of fuzzy modelling as accuracy. So far the research based on ANFIS has been mostly application based due to which the various issues related to the interpretability of ANFIS have not been dealt with. The rule base of ANFIS is typically obtained using data driven clustering algorithms. But this process introduces redundancy in the system in terms of similar fuzzy sets and redundant fuzzy rules which unnecessarily increases system complexity. This in turn reduces both the interpretability as well as generalization capability of ANFIS. Additionally in case of ANFIS, unconstrained gradient descent based learning algorithms are used to fine-tune the membership function parameters which usually result in a rule base with inconsistent, excessively overlapping and indistinguishable membership functions for input variables and thus the interpretability of the final optimized system is not guaranteed. This paper is based on addressing the issue of rule base redundancy in ANFIS to reduce complexity and enforcing constraints during learning phase to ensure interpretability of the final optimized system. Rule base redundancy is removed using similarity analysis based rule base simplification in which similar fuzzy sets are merged and subsequently resulting fuzzy rules with equal premises are combined. Hybrid learning technique which is an efficient parameter tuning method for ANFIS is constrained to prevent inconsistency, excessive overlapping and inclusion of membership functions so that the final fuzzy partitions of inputs stay interpretable. The empirical analysis of the impact of rule base simplification and constrained learning on ANFIS is done by application to two well-known benchmark problems and a real world stock price prediction problem. The introduction of rule base simplification and constrained learning in ANFIS modeling has shown better results in terms of obtaining a desired accuracy-interpretability tradeoff than conventional ANFIS.

Less is more: A rule-based syntactic simplification module for improved text-to-pictograph translation

In order to enable or facilitate online communication for people with an intellectual disability, the Text-to-Pictograph translation system automatically translates Dutch written text into a series of Sclera or Beta pictographs. The baseline system presents the reader with a more or less verbatim pictograph-per-word translation. As a result, long and complex input sentences lead to long and complex pictograph translations, leaving the end users confused and distracted. To overcome these problems, we developed a rule-based simplification system for Dutch Text-to-Pictograph translation. By using recursion and applying the simplification operations in a logical way, only one syntactic parse is needed per message. Promising results are obtained.

Aggregation of inconsistent rules for fuzzy rule base simplification

Aggregation of inconsistent rules for fuzzy rule base simplification

Fuzzy rule base simplification using multidimensional scaling and constrained optimization

This paper proposes a novel approach for the development of highly accurate and interpretable fuzzy models with Gaussian fuzzy sets, under the framework of multidimensional scaling and non-linear constrained optimization. Upon the assumption that an accurate initial fuzzy model has already been designed, we introduce an effective methodology to approximate the similarity measure between fuzzy sets. The resulting similarity degrees guide the quantification of the dissimilarity degrees between rule antecedents. We, then, put the multidimensional scaling in place in order to transform the rule antecedents into points in a low dimensional Euclidean space. The elaboration on the distribution of these points is carried out by means of an objective-function based fuzzy clustering using a cluster validity index. Rules that correspond to points belonging to the same cluster are similar and therefore, are unified through a specialized merging process. With respect to each dimension, the aforementioned merging process acts to create a topology of fuzzy sets that enables us to elicit interpretability constraints, which are used to minimize the model's performance index in terms of non-linear constrained optimization. The established fuzzy model appears to possess a simple and transparent (i.e. interpretable) structure while maintaining a highly accurate behavior. The overall method is rigorously tested and evaluated through a number of simulation experiments that involve low and high dimensional data sets.

PClass: An Effective Classifier for Streaming Examples

In this paper, a novel evolving fuzzy-rule-based classifier, termed parsimonious classifier (pClass), is proposed. pClass can drive its learning engine from scratch with an empty rule base or initially trained fuzzy models. It adopts an open structure and plug and play concept where automatic knowledge building, rule-based simplification, knowledge recall mechanism, and soft feature reduction can be carried out on the fly with limited expert knowledge and without prior assumptions to underlying data distribution. In this paper, three state-of-the-art classifier architectures engaging multi-input-multi-output, multimodel, and round robin architectures are also critically analyzed. The efficacy of the pClass has been numerically validated by means of real-world and synthetic streaming data, possessing various concept drifts, noisy learning environments, and dynamic class attributes. In addition, comparative studies with prominent algorithms using comprehensive statistical tests have confirmed that the pClass delivers more superior performance in terms of classification rate, number of fuzzy rules, and number of rule-base parameters.

Rule base simplification in fuzzy systems by aggregation of inconsistent rules

This paper proposes a rule base simplification method for fuzzy systems. The method is based on aggregation of rules with different linguistic values of the output for identical permutations of linguistic values of the inputs which are known as inconsistent rules. The simplification removes the redundancy in the fuzzy rule base by replacing each group of inconsistent rules with a single equivalent rule. The simulation results from a transportation demand management case study show that the aggregated fuzzy system with the consistent rule base approximates better the given data than the original fuzzy system with the inconsistent rule base. The main advantage of the proposed method over other methods is that it does not require any refinement of the rule base using additional data sets or expert knowledge. In this context, the method is quite suitable for applications where rule base refinement is unacceptable due to time constraints or impossible due to lack of additional data or knowledge.

Simplifications of the Rule base for the stabilization of Inverted Pendulum System

Control of an inverted pendulum on a carriage which moves in a horizontal path, is one of the classic problems in the area of control. The basic aim of our work was to design appropriate controller to control the angle of the pendulum and the position of the cart in order to stabilize the inverted pendulum system. The main objective of this paper to keep the stabilization of the inverted pendulum based on the simplification of rule base. The proposed fuzzy control scheme successfully fulfills the control objectives and also has an excellent stabilizing ability to overcome the external impact acting on the pendulum system. The effectiveness of this controller is verified by experiments on a simple inverted pendulum with fixed cart length.

Simplified Fuzzy Logic Speed Controller for Vector Controlled Permanent Magnet Synchronous Motor Drives

This paper presents simplified fuzzy logic speed control (FLSC) for vector controlled permanent magnet synchronous motor (PMSM) drives. The fuzzy logic controller is a multi-parameter controller where the performance depends upon the chosen shape of membership function (MF), rule base and scaling factor. In this paper, rule base is viewed as a control strategy to design the simplified FLSC. The FLSC simplification is designed by rule base simplification through two diferrent approaches. The first approach implements the rule simplification by reducing the number of MF used and adjusting the arrangement of chosen MFs for each fuzzy variable. The second approach obtains the rule simplification by eliminating the rules that are infrequently fired by the PMSM drives while maintaining the dominant rules. In doing so, the standard 49 rules is simplified become 9 rules by first approach while the other approach produces 7 rules. The efficacies of the FLSC simplifications are investigated based on comparative studies of speed performances with the standard FLSC which consisting of 49 rules. The standard FLSC is designed based on common criteria from numerous literatures. The mathematical model of the PMSM drive system is simulated in MATLAB environment with Simulink and Fuzzy Logic Toolbox. The simulation results are validated with the experimental results for various operating conditions, load disturbances and inertia variations. The simulation and experimental results showed that the simplified FLSCs obtain nearly equivalent performance with the standard FLSC, thus indicating the effectiveness of the rule simplification

Rule base simplification by using a similarity measure of fuzzy sets

In fuzzy models, redundancy may be present in the form of similar fuzzy sets, especially in the construction of a fuzzy system from a set of given training examples. In this paper, a simple formula for calculating the degree of similarity of Trapezoidal membership functions is derived in order to merge similar membership functions and hence to obtain a more transparent rule-base with a minimum number of membership functions. A simplification algorithm by using the proposed similarity measure has been applied to fuzzy models of nonlinear functions approximation.

Learning interpretable fuzzy inference systems with FisPro

Fuzzy inference systems (FIS) are likely to play a significant part in system modeling, provided that they remain interpretable following learning from data. The aim of this paper is to set up some guidelines for interpretable FIS learning, based on practical experience with fuzzy modeling in various fields. An open source software system called FisPro has been specifically designed to provide generic tools for interpretable FIS design and learning. It can then be extended with the addition of new contributions. This work presents a global approach to design data-driven FIS that satisfy certain interpretability and accuracy criteria. It includes fuzzy partition generation, rule learning, input space reduction and rule base simplification. The FisPro implementation is discussed and illustrated through several detailed case studies.

A New Fuzzy Set Merging Technique Using Inclusion-Based Fuzzy Clustering

This paper proposes a new method of merging parameterized fuzzy sets based on clustering in the parameters space, taking into account the degree of inclusion of each fuzzy set in the cluster prototypes. The merger method is applied to fuzzy rule base simplification by automatically replacing the fuzzy sets corresponding to a given cluster with that pertaining to cluster prototype. The feasibility and the performance of the proposed method are studied using an application in mobile robot navigation. The results indicate that the proposed merging and rule base simplification approach leads to good navigation performance in the application considered and to fuzzy models that are interpretable by experts. In this paper, we concentrate mainly on fuzzy systems with Gaussian membership functions, but the general approach can also be applied to other parameterized fuzzy sets.

A genetic method for designing TSK models based on objective weighting: application to classification problems.

This paper proposes a genetic-based algorithm for generating simple and well-defined Takagi-Sugeno-Kang (TSK) models. The method handles several attributes simultaneously, such as the input partition, feature selection and estimation of the consequent parameters. The model building process comprises three stages. In stage one, structure learning is formulated as an objective weighting optimization problem. Apart from the mean square error (MSE) and the number of rules, three additional criteria are introduced in the fitness function for measuring the quality of the partitions. Optimization of these measures leads to models with representative rules, small overlapping and efficient data cover. To obtain models with good local interpretation, the consequent parameters are determined using a local MSE function while the overall model is evaluated on the basis of a global MSE function. The initial model is simplified at stage two using a rule base simplification routine. Similar fuzzy sets are merged and the “don’t care” premises are recognized. Finally, the simplified models are fine-tuned at stage three to improve the model performance. The suggested method is used to generate TSK models with crisp and polynomial consequents for two benchmark classification problems, the iris and the wine data. Simulation results reveal the effectiveness of our method. The resulting models exhibit simple structure, interpretability and superior recognition rates compared to other methods of the literature.

ON-LINE CONSTRUCTION AND RULE BASE SIMPLIFICATION BY REPLACEMENT IN FUZZY SYSTEMS APPLIED TO A WASTEWATER TREATMENT PLANT

Evolving Takagi-Sugeno (eTS) fuzzy models are used to build a computational model for the WasteWater Treatment Plant (WWTP) in a paper mill. The fuzzy rule base is constructed on-line from data using a recursive fuzzy clustering algorithm that develops the model structure and parameters. In order to avoid some redundancy in the fuzzy rule base mechanisms for merging membership functions and simplifying fuzzy rules are introduced. The rule base simplification is done by replacement allowing the preservation of the rule (cluster) centres as data points belonging to the original data set. Results for the WWTP show that it is possible to build less complex models and preserve a good balance between accuracy and transparency.

Learning fuzzy classification rules from labeled data

The automatic design of fuzzy rule-based classification systems based on labeled data is considered. It is recognized that both classification performance and interpretability are of major importance and effort is made to keep the resulting rule bases small and comprehensible. For this purpose, an iterative approach for developing fuzzy classifiers is proposed. The initial model is derived from the data and subsequently, feature selection and rule-base simplification are applied to reduce the model, while a genetic algorithm is used for parameter optimization. An application to the Wine data classification problem is shown.

Compact and transparent fuzzy models and classifiers through iterative complexity reduction

In our previous work (2000) we showed that genetic algorithms (GAs) provide a powerful tool to increase the accuracy of fuzzy models for both systems modeling and classification. In addition to these results, we explore the GA to find redundancy in the fuzzy model for the purpose of model reduction. An aggregated similarity measure is applied to search for redundancy in the rule base description. As a result, we propose an iterative fuzzy identification technique starting with data-based fuzzy clustering with an overestimated number of local models. The GA is then applied to find redundancy among the local models with a criterion based on maximal accuracy and maximal set similarity. After the reduction steps, the GA is applied with another criterion searching for minimal set similarity and maximal accuracy. This results in an automatic identification scheme with fuzzy clustering, rule base simplification and constrained genetic optimization with low-human intervention. The proposed modeling approach is then demonstrated for a system identification and a classification problem.

A systematic neuro-fuzzy modeling framework with application to material property prediction

A systematic neural-fuzzy modeling framework that includes the initial fuzzy model self-generation, significant input selection, partition validation, parameter optimization, and rule-base simplification is proposed in this paper. In this framework, the structure identification and parameter optimization are carried out automatically and efficiently by the combined use of a sell-organization network, fuzzy clustering, adaptive back-propagation learning, and similarity analysis-based model simplification. The proposed neuro-fuzzy modeling approach has been used for nonlinear system identification and mechanical property prediction in hot-rolled steels from construct composition and microstructure data. Experimental studies demonstrate that the predicted mechanical properties have a good agreement with the measured data by using the elicited fuzzy model with a small number of rules.