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47
Designing fuzzy inference systems from data: an interpretabilityoriented review
 IEEE TRANS. FUZZY SYSTEMS
, 2001
"... Fuzzy inference systems (FIS) are widely used for process simulation or control. They can be designed either from expert knowledge or from data. For complex systems, FIS based on expert knowledge only may suffer from a loss of accuracy. This is the main incentive for using fuzzy rules inferred from ..."
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Cited by 88 (16 self)
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Fuzzy inference systems (FIS) are widely used for process simulation or control. They can be designed either from expert knowledge or from data. For complex systems, FIS based on expert knowledge only may suffer from a loss of accuracy. This is the main incentive for using fuzzy rules inferred from data. Designing a FIS from data can be decomposed into two main phases: automatic rule generation and system optimization. Rule generation leads to a basic system with a given space partitioning and the corresponding set of rules. System optimization can be done at various levels. Variable selection can be an overall selection or it can be managed rule by rule. Rule base optimization aims to select the most useful rules and to optimize rule conclusions. Space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters. Structure optimization is of a major importance: selecting variables, reducing the rule base and optimizing the number of fuzzy sets. Over the years, many methods have become available for designing FIS from data. Their efficiency is usually characterized by a numerical performance index. However, for humancomputer cooperation another criterion is needed: the rule interpretability. An implicit assumption states that fuzzy rules are by nature easy to be interpreted. This could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts. This paper analyzes the main methods for automatic rule generation and structure optimization. They are grouped into several families and compared according to the rule interpretability criterion. For this purpose, three conditions for a set of rules to be interpretable are defined.
GAfuzzy modeling and classification: complexity and performance
, 1999
"... The use of Genet ic Algorit hms (GAs) and ot her evolut ionary opt imizat ion met hodst o design fuzzy rules forsyst4E modeling anddat classificat73 have received much at4L t ion in recent litn at ure.AutL rs have focused on various aspect oft hese randomizedtz hniques, and a whole scale of algoritW ..."
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Cited by 64 (5 self)
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The use of Genet ic Algorit hms (GAs) and ot her evolut ionary opt imizat ion met hodst o design fuzzy rules forsyst4E modeling anddat classificat73 have received much at4L t ion in recent litn at ure.AutL rs have focused on various aspect oft hese randomizedtz hniques, and a whole scale of algoritW0 have been proposed. We comment on some recent work and describe a new and e#cient t wost5 approacht hat leads t good result forfunct3 n approximat ion, dynamic systNE modeling and da t classificat ion problems. First fuzzyclust5 ing is appliedt o obt in a compact initL7 rulebased model. Then ten model is optB6B3W by a realcoded GA subject4 t const raint st hat maint aint he semant ic propert ies oft he rules. We consider four examples from to litE657W0N a syntW386 nonlinear dynamic systcW model,t he Iris dat classificatNE problem, to Wine dat a classificat ion problem andt he dynamic modeling of a Diesel engine tW bocharger. The obt3845 result are comparedt o otB5 recentc proposed met8 ...
An Approach to Online Identification of TakagiSugeno Fuzzy Models
 IEEE Transactions on Systems, Man and Cybernetics—Part B
, 2004
"... Abstract—An approach to the online learning of Takagi–Sugeno (TS) type models is proposed in the paper. It is based on a novel learning algorithm that recursively updates TS model structure and parameters by combining supervised and unsupervised learning. The rulebase and parameters of the TS model ..."
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Cited by 59 (8 self)
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Abstract—An approach to the online learning of Takagi–Sugeno (TS) type models is proposed in the paper. It is based on a novel learning algorithm that recursively updates TS model structure and parameters by combining supervised and unsupervised learning. The rulebase and parameters of the TS model continually evolve by adding new rules with more summarization power and by modifying existing rules and parameters. In this way, the rulebase structure is inherited and updated when new data become available. By applying this learning concept to the TS model we arrive at a new type adaptive model called the Evolving Takagi–Sugeno model (ETS). The adaptive nature of these evolving TS models in combination with the highly transparent and compact form of fuzzy rules makes them a promising candidate for online modeling and control of complex processes, competitive to neural networks. The approach has been tested on data from an airconditioning installation serving a real building. The results illustrate the viability and efficiency of the approach. The proposed concept, however, has significantly wider implications in a number of fields, including adaptive nonlinear control, fault detection and diagnostics, performance analysis, forecasting, knowledge extraction, robotics, behavior modeling. Index Terms—Online recursive identification, rulebase adaptation, Takagi–Sugeno models. I.
Genetic Tuning of Fuzzy Rule Deep Structures for Linguistic Modeling
 IEEE TRANS. ON FUZZY SYSTEMS
, 2001
"... Tuning fuzzy rulebased systems for Linguistic Modeling is an interesting and widely developed task. It involves adjusting some of the components composing the knowledge base without completely redefining it. To do that, as the fuzzy rule symbolic representations (known as fuzzy rule surface structu ..."
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Cited by 50 (13 self)
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Tuning fuzzy rulebased systems for Linguistic Modeling is an interesting and widely developed task. It involves adjusting some of the components composing the knowledge base without completely redefining it. To do that, as the fuzzy rule symbolic representations (known as fuzzy rule surface structures) as the meaning of the involved membership functions (which together with the surface structures are known as fuzzy rule deep structures) may be modified. This contribution introduces a genetic tuning process for jointly fitting these two components, i.e., whole deep structures. To adjust the symbolic representations, we propose to use linguistic hedges to perform slight modifications keeping a good interpretability. To change the membership function meanings, two different ways considering basic or extended expressions are proposed. As the accomplished experimental study shows, the good performance of our proposal mainly lies in the consideration of this tuning approach performed at two different levels of significance.
Compact and transparent fuzzy models and classifiers through iterative complexity reduction. Fuzzy Systems
 IEEE Transactions on
"... Abstract—In our previous work 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 reduct ..."
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Cited by 40 (1 self)
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Abstract—In our previous work 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 databased 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 lowhuman intervention. The proposed modeling approach is then demonstrated for a system identification and a classification problem. Results are compared to other approaches in the literature. Attractive models with respect to compactness, transparency and accuracy, are the result of this symbiosis. Index Terms—Fuzzy classifier, genetic algorithm (GA), Iris data, rule base reduction, Takagi–Sugeno (T–S) fuzzy model, transparency and accuracy. I.
Linguistic modeling by hierarchical systems of linguistic rules
 IEEE Trans. Fuzzy Systems
"... Linguistic modeling by hierarchical systems of linguistic rules ..."
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Cited by 28 (12 self)
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Linguistic modeling by hierarchical systems of linguistic rules
Supervised fuzzy clustering for rule extraction
 in Proc. FUZZIEEE’99, Seoul, Korea
, 1999
"... Abstract—This paper is concerned with the application of orthogonal transforms and fuzzy clustering to extract fuzzy rules from data. It is proposed to use the orthogonal least squares method to supervise the progress of the fuzzy clustering algorithm and remove clusters of less importance with resp ..."
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Cited by 24 (1 self)
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Abstract—This paper is concerned with the application of orthogonal transforms and fuzzy clustering to extract fuzzy rules from data. It is proposed to use the orthogonal least squares method to supervise the progress of the fuzzy clustering algorithm and remove clusters of less importance with respect to describing the data. Clustering takes place in the product space of systems inputs and outputs and each cluster corresponds to a fuzzy IFTHEN rule. By initializing the clustering with an overestimated number of clusters and subsequently remove less important ones as the clustering progresses, it is sought to obtain a suitable partition of the data in an automated manner. The approach is generally applicable to the fuzzymeans and related algorithms. It is studied in this paper for adaptive distance norm fuzzy clustering and applied to the identification of Takagi–Sugeno type rules. Both a synthetic example as well as a realworld modeling problem are considered to illustrate the working and the applicability of the algorithm. Index Terms—Clustering methods, fuzzy systems, identification, modeling, transforms. I.
On the interpretation and identification of dynamic TakagiSugeno fuzzy models
 IEEE Transactions on Fuzzy Systems
, 2000
"... Abstract—Dynamic TakagiSugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. Ideally, it is desirable that a dynamic TakagiSugeno fuzzy model should give accurate global nonlinear prediction and at the same time that its local models a ..."
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Cited by 23 (1 self)
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Abstract—Dynamic TakagiSugeno fuzzy models are not always easy to interpret, in particular when they are identified from experimental data. Ideally, it is desirable that a dynamic TakagiSugeno fuzzy model should give accurate global nonlinear prediction and at the same time that its local models are close approximations to the local linearizations of the nonlinear dynamic system. The latter is important in many applications where the constituent local models are used individually and aids validation and interpretation of the model considerably. This defines a multiobjective identification problem, namely, the construction of a dynamic model that is a good approximation of both local and global dynamics of the underlying system. While these objectives are often conflicting, it is shown that there exists a close relationship between dynamic TakagiSugeno fuzzy models and dynamic linearization when using affine local model structures, which suggests that a solution to the multiobjective identification problem exists. However, it is also shown that the affine local model structure is a highly sensitive parameterization when applied in transient operating regimes, i.e., far away from equilibrium. The reason is essentially that the constant term in the affine local model tends to dominate over the linear term during transients. In addition, it is inherently more difficult to design informative experiments in transient regions compared to nearequilibrium regions. Due to the multiobjective nature of the identification problem studied here, special considerations must be made during model structure selection, experiment design, and identification in order to meet both objectives. Some guidelines for experiment design are suggested and some robust nonlinear identification algorithms are studied. These include constrained and regularized identification and locally weighted identification. Their usefulness in the present context is illustrated by examples. Index Terms—Dynamic analysis, fuzzy models, linearization, system identification, transient dynamics.
On MultiObjective Identification Of TakagiSugeno Fuzzy Model Parameters
 IN: IFAC WORLD CONGRESS
, 2002
"... The problem of identifying the parameters of the constituent local linear models of TakagiSugeno fuzzy models is considered. In order to address the tradeoff between global model accuracy and interpretability of the local models as linearizations of a nonlinear system, two multiobjective identi ..."
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Cited by 20 (0 self)
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The problem of identifying the parameters of the constituent local linear models of TakagiSugeno fuzzy models is considered. In order to address the tradeoff between global model accuracy and interpretability of the local models as linearizations of a nonlinear system, two multiobjective identification algorithms are studied. Particular attention is paid to the analysis of conflicts between objectives, and we show that such information can be easily computed from the solution of the multiobjective optimization. This information is useful to diagnose the model and tune the weighting/priorities of the multiobjective optimization. Moreover, the result of the conflict analysis can be used as a constructive tool to modify the fuzzy model structure (including membership functions) in order to meet the multiple objectives. The methods are illustrated on an experimental lungs respiration application.
Transparent Fuzzy Systems: Modeling and Control
, 2002
"... During the last twenty years, fuzzy logic has been successfully applied to many modeling and control problems. One of the reasons of success is that fuzzy logic provides humanfriendly and understandable knowledge representation that can be utilized in expert knowledge extraction and implementation. ..."
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Cited by 11 (4 self)
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During the last twenty years, fuzzy logic has been successfully applied to many modeling and control problems. One of the reasons of success is that fuzzy logic provides humanfriendly and understandable knowledge representation that can be utilized in expert knowledge extraction and implementation. It is observed, however, that transparency, which is vital for undistorted information transfer, is not a default property of fuzzy systems, moreover, application of algorithms that identify fuzzy systems from data will most likely destroy any semantics a fuzzy system ever had after initialization. This thesis thoroughly investigates the issues related to transparency. Fuzzy systems are generally divided into two classes. It is shown here that for these classes different definitions of transparency apply. For standard fuzzy systems that use fuzzy propositions in IFTHEN rules, explicit transparency constraints have been derived. Based on these constraints, exploitation/modification schemes of existing identification algorithms are suggested, moreover, a new algorithm for training standard fuzzy systems has been proposed, with a considerable potential to reduce the gap between accuracy and transparency in fuzzy modeling. For 1st order TakagiSugeno systems that are interpreted in terms of local linear models, such conditions cannot be derived due to system architecture and its undesirable interpolation properties of 1st order TS systems. It is, however, possible to solve the transparency preservation problem in the context of modeling with another proposed method that benefits from rule activation degree exponents. 1st order TS systems that admit valid interpretation of local models as linearizations of the modeled system are useful, for example, in gainscheduled control. Transparent standard fuzzy systems, on the other hand, are vital to this branch of intelligent control that seeks solutions by emulating the mechanisms of reasoning and decision processes of human beings not limited to knowledgebased fuzzy control. Performing the local inversion of the modeled system it is possible to extract relevant control information, which is demonstrated with the application of fedbatch fermentation. The more a fuzzy controller resembles the experts role in a control task, the higher will be the implementation benefit of the fuzzy engine. For example, a hierarchy of fuzzy (and nonfuzzy) controllers simulates an existing hierarchy in the human decision process and leads to improved control performance. Another benefit from hierarchy is that it assumes problem decomposition. This is especially important with fuzzy logic where large number of system variables leads to exponential explosion of rules (curse of dimensionality) that makes controller design extremely difficult or even impossible. The advantages of hierarchical control are illustrated with truck backerupper applications.