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Fuzzy Sets (fuzzy + set)
Terms modified by Fuzzy Sets Selected AbstractsFlexible constraints for regularization in learning from dataINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 6 2004Eyke Hüllermeier By its very nature, inductive inference performed by machine learning methods mainly is data driven. Still, the incorporation of background knowledge,if available,can help to make inductive inference more efficient and to improve the quality of induced models. Fuzzy set,based modeling techniques provide a convenient tool for making expert knowledge accessible to computational methods. In this article, we exploit such techniques within the context of the regularization (penalization) framework of inductive learning. The basic idea is to express knowledge about an underlying data-generating process in terms of flexible constraints and to penalize those models violating these constraints. An optimal model is one that achieves an optimal trade-off between fitting the data and satisfying the constraints. © 2004 Wiley Periodicals, Inc. [source] Flexible querying of semistructured data: A fuzzy-set-based approachINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 7 2007Martine De Calmès This article provides a general discussion about how flexible querying can be applied to semistructured data (SSD). We adapt flexible querying ideas, already used for classically structured databases, to XQuery-like querying of SSD for managing users' priority and preferences, but also for tackling with the variability of SSD underlying structures. Indeed flexible querying seems to be still more useful for SSD than for classical databases, because of the potential structural heterogeneity of the former. Fuzzy sets are useful for expressing flexible requirements on attribute values and for estimating the degree of similarity of tags, or attribute labels, with elements present in the request. Priorities are introduced in the request for specifying the relative importance of elementary requirements in terms of their semantic contents, but also preferences about the location of information in the structure. The evaluation of the queries uses a qualitative scale with a finite number of levels, and retrieved pieces of SSD are rank-ordered using a lexicographic vector procedure. Illustrative examples are provided. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 723,737, 2007. [source] Rule reduction in fuzzy logic for better interpretability in reservoir operationHYDROLOGICAL PROCESSES, Issue 21 2007C. Sivapragasam Abstract Decision-making in reservoir operation has become easy and understandable with the use of fuzzy logic models, which represent the knowledge in terms of interpretable linguistic rules. However, the improvement in interpretability with increase in number of fuzzy sets (,low', ,high', etc) comes with the disadvantage of increase in number of rules that are difficult to comprehend by decision makers. In this study, a clustering-based novel approach is suggested to provide the operators with a limited number of most meaningful operating rules. A single triangular fuzzy set is adopted for different variables in each cluster, which are fine-tuned with genetic algorithm (GA) to meet the desired objective. The results are compared with the multi fuzzy set fuzzy logic model through a case study in the Pilavakkal reservoir system in Tamilnadu State, India. The results obtained are highly encouraging with a smaller set of rules representing the actual fuzzy logic system. Copyright © 2007 John Wiley & Sons, Ltd. [source] Relationships between entropy and similarity measure of interval-valued intuitionistic fuzzy setsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2010Qiansheng Zhang The concept of entropy of interval-valued intuitionistic fuzzy set (IvIFS) is first introduced. The close relationships between entropy and the similarity measure of interval-valued intuitionistic fuzzy sets are discussed in detail. We also obtain some important theorems by which entropy and similarity measure of IvIFSs can be transformed into each other based on their axiomatic definitions. Simultaneously, some formulae to calculate entropy and similarity measure of IvIFSs are put forward. © 2010 Wiley Periodicals, Inc. [source] Generalization of belief and plausibility functions to fuzzy sets based on the sugeno integralINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2007Chao-Ming Hwang Uncertainty has been treated in science for several decades. It always exists in real systems. Probability has been traditionally used in modeling uncertainty. Belief and plausibility functions based on the Dempster,Shafer theory (DST) become another method of measuring uncertainty, as they have been widely studied and applied in diverse areas. Conversely, a fuzzy set has been successfully used as the idea of partial memberships of multiple classes for the presentation of unsharp boundaries. It is well used as the representation of human knowledge in complex systems. Nowadays, there exist several generalizations of belief and plausibility functions to fuzzy sets in the literature. In this article, we propose a new generalization of belief and plausibility functions to fuzzy sets based on the Sugeno integral. We then make comparisons of the proposed generalization with some existing methods. The results show the effectiveness of the proposed generalization, especially for being able to catch more information about the change of fuzzy focal elements. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1215,1228, 2007. [source] On (,, , , q)-fuzzy filters of R0 -algebrasMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 5 2009Xueling Ma Abstract In this paper, we introduce the notions of (,, , , q)-fuzzy filters and (,, , , q)-fuzzy Boolean (implicative) filters in R0 -algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters are derived. In particular, we prove that a fuzzy set in R0 -algebras is an (,, , , q)-fuzzy Boolean filter if and only if it is an (,, , , q)-fuzzy implicative filter. Finally, we consider the concepts of implication-based fuzzy Boolean (implicative) filters of R0 -algebras (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Omitting types in fuzzy logic with evaluated syntaxMLQ- MATHEMATICAL LOGIC QUARTERLY, Issue 3 2006Petra Murinová Abstract This paper is a contribution to the development of model theory of fuzzy logic in narrow sense. We consider a formal system Ev, of fuzzy logic that has evaluated syntax, i. e. axioms need not be fully convincing and so, they form a fuzzy set only. Consequently, formulas are provable in some general degree. A generalization of Gödel's completeness theorem does hold in Ev,. The truth values form an MV-algebra that is either finite or ,ukasiewicz algebra on [0, 1]. The classical omitting types theorem states that given a formal theory T and a set ,(x1, , , xn ) of formulas with the same free variables, we can construct a model of T which omits ,, i. e. there is always a formula from , not true in it. In this paper, we generalize this theorem for Ev,, that is, we prove that if T is a fuzzy theory and ,(x1, , , xn ) forms a fuzzy set , then a model omitting , also exists. We will prove this theorem for two essential cases of Ev,: either Ev, has logical (truth) constants for all truth values, or it has these constants for truth values from [0, 1] , , only. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] An Automatic Building Approach To Special Takagi-Sugeno Fuzzy Network For Unknown Plant Modeling And Stable ControlASIAN JOURNAL OF CONTROL, Issue 2 2003Chia-Feng Juang ABSTRACT In previous studies, several stable controller design methods for plants represented by a special Takagi-Sugeno fuzzy network (STSFN) have been proposed. In these studies, the STSFN is, however, derived directly from the mathematical function of the controlled plant. For an unknown plant, there is a problem if STSFN cannot model the plant successfully. In order to address this problem, we have derived a learning algorithm for the construction of STSFN from input-output training data. Based upon the constructed STSFN, existing stable controller design methods can then be applied to an unknown plant. To verify this, stable fuzzy controller design by parallel distributed compensation (PDC) method is adopted. In PDC method, the precondition parts of the designed fuzzy controllers share the same fuzzy rule numbers and fuzzy sets as the STSFN. To reduce the controller rule number, the precondition part of the constructed STSFN is partitioned in a flexible way. Also, similarity measure together with merging operation between each neighboring fuzzy set are performed in each input dimension to eliminate the redundant fuzzy sets. The consequent parts in STSFN are designed by correlation measure to select only the significant input terms to participate in each rule's consequence and reduce the network parameters. Simulation results in the cart-pole balancing system have shown that with the proposed STSFN building approach, we are able to model the controlled plant with high accuracy and, in addition, can design a stable fuzzy controller with small parameter number. [source] Detection of electrocardiogram beats using a fuzzy similarity indexEXPERT SYSTEMS, Issue 2 2007Elif Derya Übeyli Abstract: A new approach based on the computation of a fuzzy similarity index (FSI) is presented for the detection of electrocardiogram (ECG) beats. Four types of ECG beats (normal beat, congestive heart failure beat, ventricular tachyarrhythmia beat, atrial fibrillation beat) obtained from the Physiobank database were analysed. The ECG signals were decomposed into time,frequency representations using the discrete wavelet transform and wavelet coefficients were calculated to represent the signals. The aim of the study is detection of ECG beats by the combination of wavelet coefficients and the FSI. Toward achieving this aim, fuzzy sets were obtained from the feature sets (wavelet coefficients) of the signals under study. The results demonstrated that the similarity between the fuzzy sets of the studied signals indicated the variabilities in the ECG signals. Thus, the FSI could discriminate the normal beat and the other three types of beats (congestive heart failure beat, ventricular tachyarrhythmia beat, atrial fibrillation beat). [source] Mining fuzzy quantitative association rulesEXPERT SYSTEMS, Issue 4 2006R.B.V. Subramanyam Abstract: The concept of fuzzy sets is one of the most fundamental and influential tools in the development of computational intelligence. In this paper the fuzzy pincer search algorithm is proposed. It generates fuzzy association rules by adopting combined top-down and bottom-up approaches. A fuzzy grid representation is used to reduce the number of scans of the database and our algorithm trims down the number of candidate fuzzy grids at each level. It has been observed that fuzzy association rules provide more realistic visualization of the knowledge extracted from databases. [source] Rule reduction in fuzzy logic for better interpretability in reservoir operationHYDROLOGICAL PROCESSES, Issue 21 2007C. Sivapragasam Abstract Decision-making in reservoir operation has become easy and understandable with the use of fuzzy logic models, which represent the knowledge in terms of interpretable linguistic rules. However, the improvement in interpretability with increase in number of fuzzy sets (,low', ,high', etc) comes with the disadvantage of increase in number of rules that are difficult to comprehend by decision makers. In this study, a clustering-based novel approach is suggested to provide the operators with a limited number of most meaningful operating rules. A single triangular fuzzy set is adopted for different variables in each cluster, which are fine-tuned with genetic algorithm (GA) to meet the desired objective. The results are compared with the multi fuzzy set fuzzy logic model through a case study in the Pilavakkal reservoir system in Tamilnadu State, India. The results obtained are highly encouraging with a smaller set of rules representing the actual fuzzy logic system. Copyright © 2007 John Wiley & Sons, Ltd. [source] Incorporating linguistic, probabilistic, and possibilistic information in a risk-based approach for ranking contaminated sitesINTEGRATED ENVIRONMENTAL ASSESSMENT AND MANAGEMENT, Issue 4 2010Kejiang Zhang Abstract Different types of uncertain information,linguistic, probabilistic, and possibilistic,exist in site characterization. Their representation and propagation significantly influence the management of contaminated sites. In the absence of a framework with which to properly represent and integrate these quantitative and qualitative inputs together, decision makers cannot fully take advantage of the available and necessary information to identify all the plausible alternatives. A systematic methodology was developed in the present work to incorporate linguistic, probabilistic, and possibilistic information into the Preference Ranking Organization METHod for Enrichment Evaluation (PROMETHEE), a subgroup of Multi-Criteria Decision Analysis (MCDA) methods for ranking contaminated sites. The identification of criteria based on the paradigm of comparative risk assessment provides a rationale for risk-based prioritization. Uncertain linguistic, probabilistic, and possibilistic information identified in characterizing contaminated sites can be properly represented as numerical values, intervals, probability distributions, and fuzzy sets or possibility distributions, and linguistic variables according to their nature. These different kinds of representation are first transformed into a 2-tuple linguistic representation domain. The propagation of hybrid uncertainties is then carried out in the same domain. This methodology can use the original site information directly as much as possible. The case study shows that this systematic methodology provides more reasonable results. Integr Environ Assess Manag 2010;6:711,724. © 2010 SETAC [source] Assessing early warning signals of currency crises: a fuzzy clustering approachINTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE & MANAGEMENT, Issue 4 2006Shuhua Liu In the period of 1990s alone, four waves of financial crises occurred around the world. The repeated occurrence of financial crises stimulated a large number of theoretical and empirical studies on the phenomena, in particular studies on the determinants of or early warning signals of financial crises. Nonetheless, the different studies of early warning systems have achieved mixed results and there remains much room for further investigation. Since, so far, the empirical studies have focused on conventional economic modelling methods such as simplified probabilistic models and regression models, in this study we examine whether new insights can be gained from the application of the fuzzy clustering method. The theories of fuzzy sets and fuzzy logic offer us the means to deal with uncertainties inherent in a wide variety of tasks, especially when the uncertainty is not the result of randomness but the result of unknown factors and relationships that are difficult to explain. They also provide us with the instruments to treat vague and imprecise linguistic values and to model nonlinear relationships. This paper presents empirical results from analysing the Finnish currency crisis in 1992 using the fuzzy C-means clustering method. We first provide the relevant background knowledge and introduce the fuzzy clustering method. We then show how the use of fuzzy C-means method can help us to identify the critical levels of important economic indicators for predicting of financial crises. Copyright © 2007 John Wiley & Sons, Ltd. [source] Relationships between entropy and similarity measure of interval-valued intuitionistic fuzzy setsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2010Qiansheng Zhang The concept of entropy of interval-valued intuitionistic fuzzy set (IvIFS) is first introduced. The close relationships between entropy and the similarity measure of interval-valued intuitionistic fuzzy sets are discussed in detail. We also obtain some important theorems by which entropy and similarity measure of IvIFSs can be transformed into each other based on their axiomatic definitions. Simultaneously, some formulae to calculate entropy and similarity measure of IvIFSs are put forward. © 2010 Wiley Periodicals, Inc. [source] On aggregating uncertain information by type-2 OWA operators for soft decision makingINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 6 2010Shang-Ming Zhou Yager's ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts' individual opinions or preferences for achieving an overall decision. The traditional Yager's OWA operator focuses exclusively on the aggregation of crisp numbers. However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. Type-2 fuzzy sets provide an efficient way of knowledge representation for modeling linguistic terms. In order to aggregate linguistic opinions via OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator, to aggregate the linguistic opinions or preferences in human decision making modeled by type-2 fuzzy sets. A Direct Approach to aggregating interval type-2 fuzzy sets by type-2 OWA operator is suggested in this paper. Some examples are provided to delineate the proposed technique. © 2010 Wiley Periodicals, Inc. [source] Scalar and fuzzy cardinalities of crisp and fuzzy multisetsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 6 2009Jaume Casasnovas We define in an axiomatic way scalar and fuzzy cardinalities of finite multisets over ]0, 1], and we obtain explicit descriptions for them. We show that, for multisets over ]0, 1] associated to finite fuzzy sets, the cardinalities defined in this study are equivalent to the cardinalities of the corresponding fuzzy sets previously introduced in the literature. Finally, we also define in an axiomatic way scalar and fuzzy cardinalities of finite fuzzy multisets over any set X, and we use the descriptions of the cardinalities of finite multisets over ]0, 1] to obtain explicit characterizations of the former. © 2009 Wiley Periodicals, Inc. [source] From fuzzy sets to shadowed sets: Interpretation and computingINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 1 2009Witold Pedrycz In this study, we discuss a concept of shadowed sets and present their applications. To establish some sound compromise between the qualitative Boolean (two-valued) description of data and quantitative membership grades, we introduce an interpretation framework of shadowed sets. Shadowed sets are discussed as three-valued constructs induced by fuzzy sets assuming three values (that could be interpreted as full membership, full exclusion, and uncertain membership). The algorithm of converting membership functions into this quantification is a result of a certain optimization problem guided by the principle of uncertainty localization. We revisit fundamental ideas of relational calculus in the setting of shadowed sets. We demonstrate how shadowed sets help in problems in data interpretation in fuzzy clustering by leading to the three-valued quantification of data structure that consists of core, shadowed, and uncertain structure. © 2008 Wiley Periodicals, Inc. [source] Intelligent social network analysis using granular computingINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2008Ronald R. Yager An introduction to some basic ideas of graph (relational network) theory is first provided. We then discuss some concepts from granular computing in particular the fuzzy set paradigm of computing with words. The natural connection between graph theory and granular computing, particularly fuzzy set theory, is pointed out. This connection is grounded in the fact that these are both set-based technologies. Our objective here is to take a step toward the development of intelligent social network analysis using granular computing. In particular one can start by expressing in a human-focused manner concepts associated with social networks then formalize these concepts using fuzzy sets and then evaluate these concepts with respect to social networks that have been represented using set-based relational network theory. We capture this approach in what we call the paradigm for intelligent social network analysis, PISNA. Using this paradigm, we provide definitions of a number of concepts related to social networks. © 2008 Wiley Periodicals, Inc. [source] Generation of interval-valued fuzzy and atanassov's intuitionistic fuzzy connectives from fuzzy connectives and from K, operators: Laws for conjunctions and disjunctions, amplitudeINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 6 2008H. Bustince In this paper, we study in-depth certain properties of interval-valued fuzzy sets and Atanassov's intuitionistic fuzzy sets (A-IFSs). In particular, we study the manner in which to construct different interval-valued fuzzy connectives (or Atanassov's intuitionistic fuzzy connectives) starting from an operator. We further study the law of contradiction and the law of excluded middle for these sets. Furthermore, we analyze the following properties: idempotency, absorption, and distributiveness. We conclude relating idempotency with the capacity that some of the connectives studied have for maintaining, in certain conditions, the amplitude (or Atanassov's intuitionistic index) of the intervals on which they act. © 2008 Wiley Periodicals, Inc. [source] On the difference of fuzzy setsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 3 2008Claudi Alsina We formulate and solve a collection of functional equations arising in the framework of fuzzy logic when modeling the concept of a difference operation between couples of fuzzy sets. © 2008 Wiley Periodicals, Inc. [source] Generalization of belief and plausibility functions to fuzzy sets based on the sugeno integralINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 11 2007Chao-Ming Hwang Uncertainty has been treated in science for several decades. It always exists in real systems. Probability has been traditionally used in modeling uncertainty. Belief and plausibility functions based on the Dempster,Shafer theory (DST) become another method of measuring uncertainty, as they have been widely studied and applied in diverse areas. Conversely, a fuzzy set has been successfully used as the idea of partial memberships of multiple classes for the presentation of unsharp boundaries. It is well used as the representation of human knowledge in complex systems. Nowadays, there exist several generalizations of belief and plausibility functions to fuzzy sets in the literature. In this article, we propose a new generalization of belief and plausibility functions to fuzzy sets based on the Sugeno integral. We then make comparisons of the proposed generalization with some existing methods. The results show the effectiveness of the proposed generalization, especially for being able to catch more information about the change of fuzzy focal elements. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1215,1228, 2007. [source] Fuzzy logic-based networks: A study in logic data interpretationINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 12 2006Xiaofeng Liang Fuzzy neurons may have outstanding learning abilities and are endowed with significant interpretation capabilities. In this study, we are concerned with the development of logic networks composed of fuzzy neurons. The main phase of the design includes the granulation of the output space (via triangular fuzzy sets) being realized with the use of fuzzy equalization. In the sequel these fuzzy sets are used to guide the construction of a family of fuzzy sets in the input space. Further processing of the resulting fuzzy sets deals with some additional aggregation of those that are not sufficiently distinct. This helps reduce the size of the logic network. We include comprehensive experimentation and offer a thorough interpretation of the networks. Experiments concerning real-world continuous data help evaluate the network's appealing properties: transparent interpretability and practical feasibility. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 1249,1267, 2006. [source] Fuzzy set methods for uncertainty management in intelligence analysisINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 5 2006Ronald R. Yager Considerable concern has arisen regarding the quality of intelligence analysis. This has been, in large part, motivated by the task of determining whether Iraq had weapons of mass destruction. One problem that made this analysis difficult was the uncertainty in much of the information available to the intelligence analysts. In this work, we introduce some tools that can be of use to intelligence analysts for representing and processing uncertain information. We make considerable use of technologies based on fuzzy sets and related disciplines such as approximate reasoning. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 523,544, 2006. [source] Fuzzy entropy on intuitionistic fuzzy setsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 4 2006Wen-Liang Hung In this article we exploit the concept of probability for defining the fuzzy entropy of intuitionistic fuzzy sets (IFSs). We then propose two families of entropy measures for IFSs and also construct the axiom definition and properties. Two definitions of entropy for IFSs proposed by Burillo and Bustince in 1996 and Szmidt and Kacprzyk in 2001 are used. The first one allows us to measure the degree of intuitionism of an IFS, whereas the second one is a nonprobabilistic-type entropy measure with a geometric interpretation of IFSs used in comparison with our proposed entropy of IFSs in the numerical comparisons. The results show that the proposed entropy measures seem to be more reliable for presenting the degree of fuzziness of an IFS. © 2006 Wiley Periodicals, Inc. Int J Int Syst 21: 443,451, 2006. [source] Hybrid learning architecture for fuzzy control of quadruped walking robotsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 2 2005Huosheng Hu This article presents a hybrid learning architecture for fuzzy control of quadruped walking robots in the RoboCup domain. It combines reactive behaviors with deliberative reasoning to achieve complex goals in uncertain and dynamic environments. To achieve real-time and robust control performance, fuzzy logic controllers (FLCs) are used to encode the behaviors and a two-stage learning scheme is adopted to make these FLCs be adaptive to complex situations. The first stage is called structure learning, in which the rule base of an FLC is generated by a Q-learning scheme. The second stage is called parameter learning, in which the parameters of membership functions in input fuzzy sets are learned by using a real value genetic algorithm. The experimental results are provided to show the suitability of the architecture and effectiveness of the proposed learning scheme. © 2005 Wiley Periodicals, Inc. Int J Int Syst 20: 131,152, 2005. [source] Parameterized fuzzy operators in fuzzy decision makingINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 9 2003Qian Song The basic operations of fuzzy sets, such as negation, intersection, and union, usually are computed by applying the one-complement, minimum, and maximum operators to the membership functions of fuzzy sets. However, different decision agents may have different perceptions for these fuzzy operations. In this article, the concept of parameterized fuzzy operators will be introduced. A parameter , will be used to represent the degree of softness. The variance of , captures the differences of decision agents' subjective attitudes and characteristics, which result in their differing perceptions. The defined parameterized fuzzy operators also should satisfy the axiomatic requirements for the traditional fuzzy operators. A learning algorithm will be proposed to obtain the parameter , given a set of training data for each agent. In this article, the proposed parameterized fuzzy operators will be used in individual decision-making problems. An example is given to show the concept and application of the parameterized fuzzy operators. © 2003 Wiley Periodicals, Inc. [source] Emergence of self-learning fuzzy systems by a new virus DNA,based evolutionary algorithmINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 3 2003Lihong Ren In this article, we propose a new approach to the virus DNA,based evolutionary algorithm (VDNA-EA) to implement self-learning of a class of Takagi-Sugeno (T-S) fuzzy controllers. The fuzzy controllers use T-S fuzzy rules with linear consequent, the generalized input fuzzy sets, Zadeh fuzzy logic and operators, and the generalized defuzzifier. The fuzzy controllers are proved to be nonlinear proportional-integral (PI) controllers with variable gains. The fuzzy rules are discovered automatically and the design parameters in the input fuzzy sets and the linear rule consequent are optimized simultaneously by the VDNA-EA. The VDNA-EA uses the VDNA encoding method that stemmed from the structure of the VDNA to encode the design parameters of the fuzzy controllers. We use the frameshift decoding method of the VDNA to decode the DNA chromosome into the design parameters of the fuzzy controllers. In addition, the gene transfer operation and bacterial mutation operation inspired by a microbial evolution phenomenon are introduced into the VDNA-EA. Moreover, frameshift mutation operations based on the DNA genetic operations are used in the VDNA-EA to add and delete adaptively fuzzy rules. Our encoding method can significantly shorten the code length of the DNA chromosomes and improve the encoding efficiency. The length of the chromosome is variable and it is easy to insert and delete parts of the chromosome. It is suitable for complex knowledge representation and is easy for the genetic operations at gene level to be introduced into the VDNA-EA. We show how to implement the new method to self-learn a T-S fuzzy controller in the control of a nonlinear system. The fuzzy controller can be constructed automatically by the VDNA-EA. Computer simulation results indicate that the new method is effective and the designed fuzzy controller is satisfactory. © 2003 Wiley Periodicals, Inc. [source] Fuzzy reasoning based on the extension principle,INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 4 2001Yang Xu According to the operation of decomposition (also known as representation theorem) (Negoita CV, Ralescu, DA. Kybernetes 1975;4:169,174) in fuzzy set theory, the whole fuzziness of an object can be characterized by a sequence of local crisp properties of that object. Hence, any fuzzy reasoning could also be implemented by using a similar idea, i.e., a sequence of precise reasoning. More precisely, we could translate a fuzzy relation "If A then B" of the Generalized Modus Ponens Rule (the most common and widely used interpretation of a fuzzy rule, A,,B, are fuzzy sets in a universe of discourse X, and of discourse Y, respectively) into a corresponding precise relation between a subset of P(X) and a subset of P(Y), and then extend this corresponding precise relation to two kinds of transformations between all L -type fuzzy subsets of X and those of Y by using Zadeh's extension principle, where L denotes a complete lattice. In this way, we provide an alternative approach to the existing compositional rule of inference, which performs fuzzy reasoning based on the extension principle. The approach does not depend on the choice of fuzzy implication operator nor on the choice of a t-norm. The detailed reasoning methods, applied in particular to the Generalized Modus Ponens and the Generalized Modus Tollens, are established and their properties are further investigated in this paper. © 2001 John Wiley & Sons, Inc. [source] New Traversability Indices and Traversability Grid for Integrated Sensor/Map-Based NavigationJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 3 2003Homayoun Seraji This paper presents new measures of terrain traversability at short range and long range of a mobile robot; namely, local and global traversability indices. The sensor-based local traversability index is related by a set of linguistic rules to large obstacles and surface softness within a short range of the robot measured by on-board sensors. The map-based global traversability index is obtained from the terrain topographic map, and is based on major surface features such as hills and lakes within a long range of the robot. These traversability indices complement the mid-range sensor-based regional traversability index introduced earlier. Each traversability index is represented by four fuzzy sets with the linguistic labels {POOR, LOW, MODERATE, HIGH}, corresponding to surfaces that are unsafe, moderately-unsafe, moderately-safe, and safe for traversal, respectively. The global terrain analysis also leads to the new concepts of traversability map and traversability grid for representation of terrain quality based on the global map information. The traversability indices are used in two sensor-based traverse-local and traverse-regional behaviors and one map-based traverse-global behavior. These behaviors are integrated with a map-based seek-goal behavior to ensure that the mobile robot reaches its goal safely while avoiding both sensed and mapped terrain hazards. This provides a unified system in which the two independent sources of terrain quality information, i.e., prior maps and on-board sensors, are integrated together for reactive robot navigation. The paper is concluded by a graphical simulation study. © 2003 Wiley Periodicals, Inc. [source] Vision-based terrain characterization and traversability assessmentJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 10 2001Ayanna Howard This article presents novel techniques for real-time terrain characterization and assessment of terrain traversability for a field mobile robot using a vision system and artificial neural networks. The key terrain traversability characteristics are identified as roughness, slope, discontinuity, and hardness. These characteristics are extracted from imagery data obtained from cameras mounted on the robot and are represented in a fuzzy logic framework using perceptual, linguistic fuzzy sets. The approach adopted is highly robust and tolerant to imprecision and uncertainty inherent in sensing and perception of natural environments. The four traversability characteristics are combined to form a single Fuzzy Traversability Index, which quantifies the ease-of-traversal of the terrain by the mobile robot. Experimental results are presented to demonstrate the capability of the proposed approach for classification of different terrain segments based on their traversability. © 2001 John Wiley & Sons, Inc. [source] | |||||||||||||