Pub Date : 1996-12-11DOI: 10.1109/AFSS.1996.583540
Zdzislaw Pawlak
In this talk we are going to present basic concepts of a new approach to data analysis, called rough set theory. The theory has attracted attention of many researchers and practitioners all over the world, who contributed essentially to its development and applications. Rough set theory overlaps with many other theories, especially with fuzzy set theory, evidence theory and Boolean reasoning methods, discriminant analysis-nevertheless it can be viewed in its own rights, as an independent, complementary, and not competing discipline. Rough set theory is based on classification. Consider, for example, a group of patients suffering from a certain disease. With every patient a data file is associated containing information like, e.g. body temperature, blood pressure, name, age, address and others. All patients revealing the same symptoms are indiscernible (similar) in view of the available information and can be classified in blocks, which can be understood as elementary granules of knowledge about patients (or types of patients). These granules are called elementary sets or concepts, and can be considered as elementary building blocks of knowledge about patients. Elementary concepts can be combined into compound concepts, i.e. concepts that are uniquely defined in terms of elementary concepts. Any union of elementary sets is called a crisp set, and any other sets are referred to as rough (vague, imprecise). With every set X we can associate two crisp sets, called the lower and the upper approximation of X. The lower approximation of X is the union of all elementary set which are included in X, whereas the upper approximation of X is the union of all elementary set which have non-empty intersection with X. In other words the lower approximation of a set is the set of all elements that surely belongs to X, whereas the upper approximation of X is the set of all elements that possibly belong to X. The difference of the upper and the lower approximation of X is its boundary region. Obviously a set is rough if it has non empty boundary region; otherwise the set is crisp. Elements of the boundary region cannot be classified, employing the available knowledge, either to the set or its complement. Approximations of sets are basic operation in rough set theory.
{"title":"Rough sets and data analysis","authors":"Zdzislaw Pawlak","doi":"10.1109/AFSS.1996.583540","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583540","url":null,"abstract":"In this talk we are going to present basic concepts of a new approach to data analysis, called rough set theory. The theory has attracted attention of many researchers and practitioners all over the world, who contributed essentially to its development and applications. Rough set theory overlaps with many other theories, especially with fuzzy set theory, evidence theory and Boolean reasoning methods, discriminant analysis-nevertheless it can be viewed in its own rights, as an independent, complementary, and not competing discipline. Rough set theory is based on classification. Consider, for example, a group of patients suffering from a certain disease. With every patient a data file is associated containing information like, e.g. body temperature, blood pressure, name, age, address and others. All patients revealing the same symptoms are indiscernible (similar) in view of the available information and can be classified in blocks, which can be understood as elementary granules of knowledge about patients (or types of patients). These granules are called elementary sets or concepts, and can be considered as elementary building blocks of knowledge about patients. Elementary concepts can be combined into compound concepts, i.e. concepts that are uniquely defined in terms of elementary concepts. Any union of elementary sets is called a crisp set, and any other sets are referred to as rough (vague, imprecise). With every set X we can associate two crisp sets, called the lower and the upper approximation of X. The lower approximation of X is the union of all elementary set which are included in X, whereas the upper approximation of X is the union of all elementary set which have non-empty intersection with X. In other words the lower approximation of a set is the set of all elements that surely belongs to X, whereas the upper approximation of X is the set of all elements that possibly belong to X. The difference of the upper and the lower approximation of X is its boundary region. Obviously a set is rough if it has non empty boundary region; otherwise the set is crisp. Elements of the boundary region cannot be classified, employing the available knowledge, either to the set or its complement. Approximations of sets are basic operation in rough set theory.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124814104","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583617
J. Lee, J. Kuo, W.T. Huang
A criteria trade-off analysis approach, based on relationships analysis for fuzzy decision-making, is proposed. The degrees of conflict and cooperation between any two individual criteria are first formulated. Relationships between individual criteria are identified based upon their conflicting and cooperative degrees. The criteria are converted into a disjunctive normal form to obtain a uniform representation of the criteria, and then arranged into a four-level hierarchical aggregation structure. A set of parameterized aggregation (fuzzy AND/OR) operators is selected to aggregate the judgements for the alternatives. A compromise alternative, which is proven to satisfy Pareto optimality, can thus be obtained based on the aggregation hierarchical structure.
{"title":"Fuzzy decision making through relationships analysis between criteria","authors":"J. Lee, J. Kuo, W.T. Huang","doi":"10.1109/AFSS.1996.583617","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583617","url":null,"abstract":"A criteria trade-off analysis approach, based on relationships analysis for fuzzy decision-making, is proposed. The degrees of conflict and cooperation between any two individual criteria are first formulated. Relationships between individual criteria are identified based upon their conflicting and cooperative degrees. The criteria are converted into a disjunctive normal form to obtain a uniform representation of the criteria, and then arranged into a four-level hierarchical aggregation structure. A set of parameterized aggregation (fuzzy AND/OR) operators is selected to aggregate the judgements for the alternatives. A compromise alternative, which is proven to satisfy Pareto optimality, can thus be obtained based on the aggregation hierarchical structure.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"104 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114291008","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583668
Chang-Shing Lee, Y. Kuo
A multi-dimensional weighted fuzzy mean (MWFM) filter used in color image restoration is proposed and analyzed. MWFM is an extension of the weighted fuzzy mean (WFM) filter obtained by embedding a fuzzy detector and a dynamic selection procedure into WFM to overcome the drawback of WFM in detail signal preservation. The fuzzy detector uses two fuzzy intervals and refers the WFM-filtered outputs to detect the amplitude of impulse noise which will be used in the dynamic selection procedure. Using the dynamic selection approach, MWFM not only preserves the high stability and performance of WFM when removing heavy additive impulse noise, but also improves the performance of WFM on light additive impulse noise.
{"title":"Multi-dimensional WFM filter: an application to color image restoration","authors":"Chang-Shing Lee, Y. Kuo","doi":"10.1109/AFSS.1996.583668","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583668","url":null,"abstract":"A multi-dimensional weighted fuzzy mean (MWFM) filter used in color image restoration is proposed and analyzed. MWFM is an extension of the weighted fuzzy mean (WFM) filter obtained by embedding a fuzzy detector and a dynamic selection procedure into WFM to overcome the drawback of WFM in detail signal preservation. The fuzzy detector uses two fuzzy intervals and refers the WFM-filtered outputs to detect the amplitude of impulse noise which will be used in the dynamic selection procedure. Using the dynamic selection approach, MWFM not only preserves the high stability and performance of WFM when removing heavy additive impulse noise, but also improves the performance of WFM on light additive impulse noise.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116978432","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583675
M. Ying, B. Bouchon-Meunier
The authors propose a formalization of fuzzy logic and obtain some interesting results on fuzzy quantifiers, modifiers, and qualifiers in this setting.
{"title":"Quantifiers, modifiers and qualifiers in fuzzy logic","authors":"M. Ying, B. Bouchon-Meunier","doi":"10.1109/AFSS.1996.583675","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583675","url":null,"abstract":"The authors propose a formalization of fuzzy logic and obtain some interesting results on fuzzy quantifiers, modifiers, and qualifiers in this setting.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128437036","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583711
Chung-Jie Lin, Yung-Yaw Chen, Fan-Ren Hang
A new application of fuzzy set theory to the problem of GPS positioning accuracy improvement is presented. We employed fuzzy processing on the C/A code stand-alone receiver and the DGPS receiver. The membership functions for the processing are determined by position dilution of precision (PDOP), signal-to-noise ratio (SNR) and the reliable factor of fixed position. We can select more accurate position fixes according to the values of the reliable factors. The accuracy of positioning has been improved by selecting position fixes from the original ones.
{"title":"Fuzzy processing on GPS data to improve the position accuracy","authors":"Chung-Jie Lin, Yung-Yaw Chen, Fan-Ren Hang","doi":"10.1109/AFSS.1996.583711","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583711","url":null,"abstract":"A new application of fuzzy set theory to the problem of GPS positioning accuracy improvement is presented. We employed fuzzy processing on the C/A code stand-alone receiver and the DGPS receiver. The membership functions for the processing are determined by position dilution of precision (PDOP), signal-to-noise ratio (SNR) and the reliable factor of fixed position. We can select more accurate position fixes according to the values of the reliable factors. The accuracy of positioning has been improved by selecting position fixes from the original ones.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"2009 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129488171","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583550
Te-Min Chang, Yuehwern Yih
This paper proposes a general methodology to generate fuzzy rule-based systems automatically from examples. The objective of this work is to generate fuzzy systems with good mapping ability and generalization ability as well. This methodology consists of five steps. Inductive learning is incorporated to enhance fuzzy system's generalization ability. Experiments are conducted to evaluate the system performance of generated fuzzy systems based on two sets of data in the literature.
{"title":"Generating fuzzy rule-based systems from examples","authors":"Te-Min Chang, Yuehwern Yih","doi":"10.1109/AFSS.1996.583550","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583550","url":null,"abstract":"This paper proposes a general methodology to generate fuzzy rule-based systems automatically from examples. The objective of this work is to generate fuzzy systems with good mapping ability and generalization ability as well. This methodology consists of five steps. Inductive learning is incorporated to enhance fuzzy system's generalization ability. Experiments are conducted to evaluate the system performance of generated fuzzy systems based on two sets of data in the literature.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130297059","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583657
H. Arikawa, M. Mizumoto
The unexpected non-linearity of fuzzy reasoning output exists in the case of MIN operation adoption in order to calculate the antecedent matching degree. The unexpected non-linearity becomes more critical as the number of inputs increase. This paper discusses and evaluates this using a symmetrical section method which graphically shows the symmetrical cutting-line of the phase plane as a result of the arbitrary n-input fuzzy reasoning output.
{"title":"Unexpected non-linearity of fuzzy reasoning output amplified by multi-input","authors":"H. Arikawa, M. Mizumoto","doi":"10.1109/AFSS.1996.583657","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583657","url":null,"abstract":"The unexpected non-linearity of fuzzy reasoning output exists in the case of MIN operation adoption in order to calculate the antecedent matching degree. The unexpected non-linearity becomes more critical as the number of inputs increase. This paper discusses and evaluates this using a symmetrical section method which graphically shows the symmetrical cutting-line of the phase plane as a result of the arbitrary n-input fuzzy reasoning output.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123644118","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583637
Wentai Yu, Shui-Shong Lu
Nonlinear friction substantially affects the positioning accuracy of a machine, especially in torque controlled antibacklash twin worm index mechanism. A fuzzy controller is designed to achieve better positioning accuracy and robustness by using system parameters obtained from identification. Experimental results show that repeatability is improved as compared to the PDF controller.
{"title":"A fuzzy adjustable controller for an antibacklash twin worm index mechanism","authors":"Wentai Yu, Shui-Shong Lu","doi":"10.1109/AFSS.1996.583637","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583637","url":null,"abstract":"Nonlinear friction substantially affects the positioning accuracy of a machine, especially in torque controlled antibacklash twin worm index mechanism. A fuzzy controller is designed to achieve better positioning accuracy and robustness by using system parameters obtained from identification. Experimental results show that repeatability is improved as compared to the PDF controller.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127826708","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583563
I. Takeuchi, T. Furuhashi, Y. Hamada, Y. Uchikawa
The paper presents a self organizing network for acquisition of vague concepts. This network can autonomously select and generate layers for vague patterns for the attributes. Concepts can be described by the association among vague patterns for each attribute. Simulations are done to show the effectiveness of the network.
{"title":"A proposal of self-organizing network for aquisition of vague concept","authors":"I. Takeuchi, T. Furuhashi, Y. Hamada, Y. Uchikawa","doi":"10.1109/AFSS.1996.583563","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583563","url":null,"abstract":"The paper presents a self organizing network for acquisition of vague concepts. This network can autonomously select and generate layers for vague patterns for the attributes. Concepts can be described by the association among vague patterns for each attribute. Simulations are done to show the effectiveness of the network.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124873457","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 : 1996-12-11DOI: 10.1109/AFSS.1996.583630
Chih-Hsiu Wei, C. Fahn
Fuzzy clustering (c-means) is a widely known unsupervised clustering algorithm, but it can not guarantee to find the global minimum, because it approximates the minimum of an objective function by the iterative method in solving the differentiation problem, starting from a given point. For overcoming this drawback, we incorporate the genetic search strategies in the fuzzy clustering algorithm to explore the data space from a multiple-point concept. The direct application of the genetic algorithms to the fuzzy clustering is not suitable, because sometimes the data set is enormous. Under this situation, the chromosome would be too long, so a distributed approach to fuzzy clustering by genetic algorithms is proposed to divide the huge search space into many small ones. The simulation results show our algorithm works fine.
{"title":"A distributed approach to fuzzy clustering by genetic algorithms","authors":"Chih-Hsiu Wei, C. Fahn","doi":"10.1109/AFSS.1996.583630","DOIUrl":"https://doi.org/10.1109/AFSS.1996.583630","url":null,"abstract":"Fuzzy clustering (c-means) is a widely known unsupervised clustering algorithm, but it can not guarantee to find the global minimum, because it approximates the minimum of an objective function by the iterative method in solving the differentiation problem, starting from a given point. For overcoming this drawback, we incorporate the genetic search strategies in the fuzzy clustering algorithm to explore the data space from a multiple-point concept. The direct application of the genetic algorithms to the fuzzy clustering is not suitable, because sometimes the data set is enormous. Under this situation, the chromosome would be too long, so a distributed approach to fuzzy clustering by genetic algorithms is proposed to divide the huge search space into many small ones. The simulation results show our algorithm works fine.","PeriodicalId":197019,"journal":{"name":"Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1996-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129726438","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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