Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018070
H. Frigui, F. Nasraoui
Feature selections techniques have been used extensively in supervised learning to choose a set of features for a data set that win facilitate and improve classification. In particular, a few techniques exist to select a different subset of feature for each known class, which we refer to as discriminative feature selection. The main objective guiding discriminative feature selection has been the ultimate performance of the classifier system. Unsupervised learning, however, is plagued by the problem of absence of the class labels. In this paper, we propose a fast algorithm for fuzzy unsupervised learning in Web mining, for the case when the attributes/features do not have the same relevance in all clusters. Being a relative of the fuzzy c-means and k-means clustering algorithms, our approach is computationally and implementationally simple, and if desired, can easily be implemented in a scalable mode in an identical manner to previous well known scalable implementations of the k-means. Most importantly, our approach learns a different set of attribute weights for each cluster. The performance of the proposed algorithm is illustrated on real collections of Web documents and Web sessions extracted from a Web server log file.
{"title":"A fast algorithm for discovering categories and attribute relevance in web data","authors":"H. Frigui, F. Nasraoui","doi":"10.1109/NAFIPS.2002.1018070","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018070","url":null,"abstract":"Feature selections techniques have been used extensively in supervised learning to choose a set of features for a data set that win facilitate and improve classification. In particular, a few techniques exist to select a different subset of feature for each known class, which we refer to as discriminative feature selection. The main objective guiding discriminative feature selection has been the ultimate performance of the classifier system. Unsupervised learning, however, is plagued by the problem of absence of the class labels. In this paper, we propose a fast algorithm for fuzzy unsupervised learning in Web mining, for the case when the attributes/features do not have the same relevance in all clusters. Being a relative of the fuzzy c-means and k-means clustering algorithms, our approach is computationally and implementationally simple, and if desired, can easily be implemented in a scalable mode in an identical manner to previous well known scalable implementations of the k-means. Most importantly, our approach learns a different set of attribute weights for each cluster. The performance of the proposed algorithm is illustrated on real collections of Web documents and Web sessions extracted from a Web server log file.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115515366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018039
O. Castillo, P. Melin
We describe in this paper a new approach for plant monitoring and diagnostics using type-2 fuzzy logic and fractal theory. The concept of the fractal dimension is used to measure the complexity of the time series of relevant variables for the process. A set of type-2 fuzzy rules is used to represent the knowledge for monitoring the process. In the type-2 fuzzy rules, the fractal dimension is used as a linguistic variable to help in recognizing specific patterns in the measured data. The fuzzy-fractal approach has been applied before in problems of financial time series prediction and for other types of problems, but now it is proposed to the monitoring of plants using type-2 fuzzy logic. We also compare the results of the type-2 fuzzy logic approach with the results of using only a traditional type-1 approach. Experimental results show a significant improvement in the monitoring ability with the type-2 fuzzy logic approach.
{"title":"A new hybrid approach for plant monitoring and diagnostics combining type-2 fuzzy logic and fractal theory","authors":"O. Castillo, P. Melin","doi":"10.1109/NAFIPS.2002.1018039","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018039","url":null,"abstract":"We describe in this paper a new approach for plant monitoring and diagnostics using type-2 fuzzy logic and fractal theory. The concept of the fractal dimension is used to measure the complexity of the time series of relevant variables for the process. A set of type-2 fuzzy rules is used to represent the knowledge for monitoring the process. In the type-2 fuzzy rules, the fractal dimension is used as a linguistic variable to help in recognizing specific patterns in the measured data. The fuzzy-fractal approach has been applied before in problems of financial time series prediction and for other types of problems, but now it is proposed to the monitoring of plants using type-2 fuzzy logic. We also compare the results of the type-2 fuzzy logic approach with the results of using only a traditional type-1 approach. Experimental results show a significant improvement in the monitoring ability with the type-2 fuzzy logic approach.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123846545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1007/978-3-7908-1902-1_1
L. A. Zadeh
{"title":"It is a fundamental limitation to base probability theory on bivalent logic","authors":"L. A. Zadeh","doi":"10.1007/978-3-7908-1902-1_1","DOIUrl":"https://doi.org/10.1007/978-3-7908-1902-1_1","url":null,"abstract":"","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116758516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018093
M. Cococcioni, G. Frosini, B. Lazzerini, F. Marcelloni
This paper presents a novel method for multiple classifier fusion. The classifier combiner operates on the single classifier outputs, which consist of vectors of pairs (c, d), with c being a class name and d the confidence degree with which a pattern is recognized as belonging to class c. The main idea of the combiner is to exploit the knowledge of the statistical behavior of the single classifiers on the training set to re-calculate a global recognition confidence degree based on the a posteriori probability that the input pattern belongs to a given class conditioned by the specific responses of the classifiers. Applying the Bayes's theorem we can also easily adapt our classifier combiner to a specific application. We compare our model with some popular techniques for classifier fusion on the Satimage and Phoneme data sets from. the database ELENA.. We show that our method is in most cases superior (or substantially equivalent) to the other techniques on both data sets.
{"title":"A new approach to combining outputs of multiple classifiers","authors":"M. Cococcioni, G. Frosini, B. Lazzerini, F. Marcelloni","doi":"10.1109/NAFIPS.2002.1018093","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018093","url":null,"abstract":"This paper presents a novel method for multiple classifier fusion. The classifier combiner operates on the single classifier outputs, which consist of vectors of pairs (c, d), with c being a class name and d the confidence degree with which a pattern is recognized as belonging to class c. The main idea of the combiner is to exploit the knowledge of the statistical behavior of the single classifiers on the training set to re-calculate a global recognition confidence degree based on the a posteriori probability that the input pattern belongs to a given class conditioned by the specific responses of the classifiers. Applying the Bayes's theorem we can also easily adapt our classifier combiner to a specific application. We compare our model with some popular techniques for classifier fusion on the Satimage and Phoneme data sets from. the database ELENA.. We show that our method is in most cases superior (or substantially equivalent) to the other techniques on both data sets.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"58 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123095097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018024
P. Melin, O. Castillo
We describe adaptive model-based control of non-linear plants using type-2 fuzzy logic and neural networks. First, the general concept of adaptive model-based control is described. Second, the use of type-2 fuzzy logic for adaptive control is described. Third, a neuro-fuzzy approach is proposed to learn the parameters of the fuzzy system for control. A specific non-linear plant is used to test the hybrid approach for adaptive control. A specific plant was used as a test bed in the experiments. The non-linear plant that was considered is the "Pendubot", which is a non-linear plant similar to the two-link robot arm. The results of the type-2 fuzzy logic approach for control were good, both in accuracy and efficiency.
{"title":"Intelligent control of non-linear dynamic plants using type-2 fuzzy logic and neural networks","authors":"P. Melin, O. Castillo","doi":"10.1109/NAFIPS.2002.1018024","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018024","url":null,"abstract":"We describe adaptive model-based control of non-linear plants using type-2 fuzzy logic and neural networks. First, the general concept of adaptive model-based control is described. Second, the use of type-2 fuzzy logic for adaptive control is described. Third, a neuro-fuzzy approach is proposed to learn the parameters of the fuzzy system for control. A specific non-linear plant is used to test the hybrid approach for adaptive control. A specific plant was used as a test bed in the experiments. The non-linear plant that was considered is the \"Pendubot\", which is a non-linear plant similar to the two-link robot arm. The results of the type-2 fuzzy logic approach for control were good, both in accuracy and efficiency.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"246 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115718102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018079
A. Shinmura, K. Taniguchi, K. Kawahara, T. Takagi
Currently on the Internet, there exists a host of illegal Web sites which specialize in the distribution of commercial software and music. This paper proposes a method to distinguish illegal Web sites from legal ones not only by using TF-IDF (term frequency-inverse document frequency) values but also by recognizing the purpose/meaning of the Web sites. This is achieved by describing what are considered to be illegal sites and by judging whether the objective Web sites match the description of illegality. Conceptual fuzzy sets (CFSs) are used to describe the concept of illegal Web sites. First, we introduce the usefulness of CFSs in overcoming those problems, and propose the realization of CFSs using RBF (radial basis function)-like networks. In a CFS, the meaning of a concept is represented by the distribution of the activation values of the other nodes. Because the distribution changes depend on which labels are activated as a result of the conditions, the activations show a context-dependent meaning. Next, we propose the architecture of a filtering system. Finally, we compare the proposed method with the TF-IDF method with a support vector machine. The e-measures, as a total evaluation, indicate that the proposed system shows better results as compared to the TF-IDF method with the support vector machine.
{"title":"Exposure of illegal Web sites using conceptual fuzzy sets-based information filtering system","authors":"A. Shinmura, K. Taniguchi, K. Kawahara, T. Takagi","doi":"10.1109/NAFIPS.2002.1018079","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018079","url":null,"abstract":"Currently on the Internet, there exists a host of illegal Web sites which specialize in the distribution of commercial software and music. This paper proposes a method to distinguish illegal Web sites from legal ones not only by using TF-IDF (term frequency-inverse document frequency) values but also by recognizing the purpose/meaning of the Web sites. This is achieved by describing what are considered to be illegal sites and by judging whether the objective Web sites match the description of illegality. Conceptual fuzzy sets (CFSs) are used to describe the concept of illegal Web sites. First, we introduce the usefulness of CFSs in overcoming those problems, and propose the realization of CFSs using RBF (radial basis function)-like networks. In a CFS, the meaning of a concept is represented by the distribution of the activation values of the other nodes. Because the distribution changes depend on which labels are activated as a result of the conditions, the activations show a context-dependent meaning. Next, we propose the architecture of a filtering system. Finally, we compare the proposed method with the TF-IDF method with a support vector machine. The e-measures, as a total evaluation, indicate that the proposed system shows better results as compared to the TF-IDF method with the support vector machine.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124778202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018067
J. Bezdek, R. Hathaway
Summary form only given, as follows. Let x be a real-valued scalar field, partitioned into t subsets of non-overlapping variables X/sub i/ (i=1, ..., t). Alternating optimization (AO) is an iterative procedure for minimizing (or maximizing) the function f(x)= f(X/sub 1/, X/sub 2/, ..., X/sub t/) jointly over all variables by alternating restricted minimizations (or maximizations) over the individual subsets of variables X/sub 1/, ..., X/sub t/. AO is the basis for the c-means clustering algorithm (t=2), many forms of vector quantization (t = 2, 3 and 4) and the expectation maximization algorithm (t=4) for normal mixture decomposition. First we review where and how AO fits into the overall optimization landscape. Then we state (without proofs) two new theorems that give very general local and global convergence and rate-of-convergence results which hold for all partitionings of x. Finally, we discuss the important problem of choosing a "best" partitioning of the input variables for the AO approach. We show that the number of possible AO iteration schemes is larger than the number of standard partitions of the input variables. Two numerical examples are given to illustrate that the selection of the t subsets of x has an important effect on the rate of convergence of the corresponding AO algorithm to a solution.
{"title":"Partitioning the variables for alternating optimization of real-valued scalar fields","authors":"J. Bezdek, R. Hathaway","doi":"10.1109/NAFIPS.2002.1018067","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018067","url":null,"abstract":"Summary form only given, as follows. Let x be a real-valued scalar field, partitioned into t subsets of non-overlapping variables X/sub i/ (i=1, ..., t). Alternating optimization (AO) is an iterative procedure for minimizing (or maximizing) the function f(x)= f(X/sub 1/, X/sub 2/, ..., X/sub t/) jointly over all variables by alternating restricted minimizations (or maximizations) over the individual subsets of variables X/sub 1/, ..., X/sub t/. AO is the basis for the c-means clustering algorithm (t=2), many forms of vector quantization (t = 2, 3 and 4) and the expectation maximization algorithm (t=4) for normal mixture decomposition. First we review where and how AO fits into the overall optimization landscape. Then we state (without proofs) two new theorems that give very general local and global convergence and rate-of-convergence results which hold for all partitionings of x. Finally, we discuss the important problem of choosing a \"best\" partitioning of the input variables for the AO approach. We show that the number of possible AO iteration schemes is larger than the number of standard partitions of the input variables. Two numerical examples are given to illustrate that the selection of the t subsets of x has an important effect on the rate of convergence of the corresponding AO algorithm to a solution.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117195967","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018091
P. Rastgoufard, F. Petry, B. Thumm, M. Montgomery
The purpose of this investigation is to apply Hard C-Mean (HCM) and Fuzzy C-Mean (FCM) rules in clustering data sets that correspond to different Load Tap Changer (LTC) contact conditions. The stress exerted on the moving arm of a LTC is measured and is then converted to a voltage output signal. It is shown that as the LTC contact conditions deteriorate, the repetitive patterns of the output signal changes correspondingly. The HCM, FCM, and their validity measures prove to be suitable tools for online equipment maintenance monitoring.
{"title":"Application of fuzzy logic pattern recognition in load tap changer transformer maintenance","authors":"P. Rastgoufard, F. Petry, B. Thumm, M. Montgomery","doi":"10.1109/NAFIPS.2002.1018091","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018091","url":null,"abstract":"The purpose of this investigation is to apply Hard C-Mean (HCM) and Fuzzy C-Mean (FCM) rules in clustering data sets that correspond to different Load Tap Changer (LTC) contact conditions. The stress exerted on the moving arm of a LTC is measured and is then converted to a voltage output signal. It is shown that as the LTC contact conditions deteriorate, the repetitive patterns of the output signal changes correspondingly. The HCM, FCM, and their validity measures prove to be suitable tools for online equipment maintenance monitoring.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116506800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018021
I. Kalaykov, G. Tolt
The paper presents the development of fast fuzzy logic based hardware for various applications such as controllers for very fast processes, real-time image processing and pattern recognition. It is based on the fired-rules-hyper-cube (FRHC) concept, characterized by extremely simple way of the fuzzy inference in a layered parallel architecture. The processing time slightly depends on the number of inputs of the fuzzy system and does not depend on the number of rules and fuzzy partitioning of all variables. Most important is the inherent high speed of processing because of the parallelism and pipelining, implemented in all layers.
{"title":"Fast fuzzy signal and image processing hardware","authors":"I. Kalaykov, G. Tolt","doi":"10.1109/NAFIPS.2002.1018021","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018021","url":null,"abstract":"The paper presents the development of fast fuzzy logic based hardware for various applications such as controllers for very fast processes, real-time image processing and pattern recognition. It is based on the fired-rules-hyper-cube (FRHC) concept, characterized by extremely simple way of the fuzzy inference in a layered parallel architecture. The processing time slightly depends on the number of inputs of the fuzzy system and does not depend on the number of rules and fuzzy partitioning of all variables. Most important is the inherent high speed of processing because of the parallelism and pipelining, implemented in all layers.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129383230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2002-08-07DOI: 10.1109/NAFIPS.2002.1018055
H. Ying
Fuzzy controllers are best used as nonlinear controllers although they can be linear, piecewise linear or nonlinear. Currently, there exist no theoretical methods to determine whether a fuzzy controller is nonlinear. Because a fuzzy controller has many degrees of freedom in terms of its components selection (e.g., input fuzzy sets, output fuzzy sets, and fuzzy rules), linear controllers can be unconsciously and undesirably generated. In the present paper, we establish conditions under which nonlinearity of a general class of Mamdani fuzzy controllers can be determined. These fuzzy controllers can use input fuzzy sets of any types, arbitrary fuzzy rules, arbitrary singleton output fuzzy sets, arbitrary inference methods, Zadeh fuzzy logic AND operator, and the centroid defuzzifier. We prove that the fuzzy controllers using Zadeh AND operator are always nonlinear, regardless of choice of the other components. The general fuzzy controllers using the product AND operator are also always nonlinear except when all input fuzzy sets are triangular or trapezoidal and a couple of other conditions are satisfied. The exceptions lead to piecewise linear or linear controllers.
{"title":"Conditions for general Mamdani fuzzy controllers to be nonlinear","authors":"H. Ying","doi":"10.1109/NAFIPS.2002.1018055","DOIUrl":"https://doi.org/10.1109/NAFIPS.2002.1018055","url":null,"abstract":"Fuzzy controllers are best used as nonlinear controllers although they can be linear, piecewise linear or nonlinear. Currently, there exist no theoretical methods to determine whether a fuzzy controller is nonlinear. Because a fuzzy controller has many degrees of freedom in terms of its components selection (e.g., input fuzzy sets, output fuzzy sets, and fuzzy rules), linear controllers can be unconsciously and undesirably generated. In the present paper, we establish conditions under which nonlinearity of a general class of Mamdani fuzzy controllers can be determined. These fuzzy controllers can use input fuzzy sets of any types, arbitrary fuzzy rules, arbitrary singleton output fuzzy sets, arbitrary inference methods, Zadeh fuzzy logic AND operator, and the centroid defuzzifier. We prove that the fuzzy controllers using Zadeh AND operator are always nonlinear, regardless of choice of the other components. The general fuzzy controllers using the product AND operator are also always nonlinear except when all input fuzzy sets are triangular or trapezoidal and a couple of other conditions are satisfied. The exceptions lead to piecewise linear or linear controllers.","PeriodicalId":348314,"journal":{"name":"2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622)","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131367258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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