Showing papers on "Fuzzy associative matrix published in 2007"
TL;DR: This paper aims to present an overview on fuzzy implication functions that usually are constructed from t-norms and t-conorms but also from other kinds of aggregation operators.
Abstract: One of the key operations in fuzzy logic and approximate reasoning is the fuzzy implication, which is usually performed by a binary operator, called an implication function or, simply, an implication. Many fuzzy rule based systems do their inference processes through these operators that also take charge of the propagation of uncertainty in fuzzy reasonings. Moreover, they have proved to be useful also in other fields like composition of fuzzy relations, fuzzy relational equations, fuzzy mathematical morphology, and image processing. This paper aims to present an overview on fuzzy implication functions that usually are constructed from t-norms and t-conorms but also from other kinds of aggregation operators. The four most usual ways to define these implications are recalled and their characteristic properties stated, not only in the case of [0,1] but also in the discrete case.
353 citations
TL;DR: This paper provides new algorithms for various operations on type-1 and type-2 fuzzy sets and for defuzzification and indicates that this approach reduces the execution speed of these operations.
Abstract: This paper presents a novel approach to the representation of type-1 and type-2 fuzzy sets utilising computational geometry. To achieve this our approach borrows ideas from the field of computational geometry and applies these techniques in the novel setting of fuzzy logic. We provide new algorithms for various operations on type-1 and type-2 fuzzy sets and for defuzzification. Results of experiments indicate that this approach reduces the execution speed of these operations
314 citations
TL;DR: The independence of fuzzy variables is defined based on the concept of marginal possibility distribution function, and the properties of the independent fuzzy variables are applied to a class of fuzzy random programming problems to study their convexity.
Abstract: This paper presents the independence of fuzzy variables as well as its applications in fuzzy random optimization. First, the independence of fuzzy variables is defined based on the concept of marginal possibility distribution function, and a discussion about the relationship between the independent fuzzy variables and the noninteractive (unrelated) fuzzy variables is included. Second, we discuss some properties of the independent fuzzy variables, and establish the necessary and sufficient conditions for the independent fuzzy variables. Third, we propose the independence of fuzzy events, and deal with its fundamental properties. Finally, we apply the properties of the independent fuzzy variables to a class of fuzzy random programming problems to study their convexity.
162 citations
TL;DR: This article investigates the group decision making problems in which all the information provided by the decision makers is expressed as intuitionistic fuzzy decision matrices where each of the elements is characterized by intuitionists fuzzy number, and the information about attribute weights is partially known.
Abstract: Intuitionistic fuzzy numbers, each of which is characterized by the degree of membership and the degree of non-membership of an element, are a very useful means to depict the decision information in the process of decision making. In this article, we investigate the group decision making problems in which all the information provided by the decision makers is expressed as intuitionistic fuzzy decision matrices where each of the elements is characterized by intuitionistic fuzzy number, and the information about attribute weights is partially known, which may be constructed by various forms. We first use the intuitionistic fuzzy hybrid geometric (IFHG) operator to aggregate all individual intuitionistic fuzzy decision matrices provided by the decision makers into the collective intuitionistic fuzzy decision matrix, then we utilize the score function to calculate the score of each attribute value and construct the score matrix of the collective intuitionistic fuzzy decision matrix. Based on the score matrix and the given attribute weight information, we establish some optimization models to determine the weights of attributes. Furthermore, we utilize the obtained attribute weights and the intuitionistic fuzzy weighted geometric (IFWG) operator to fuse the intuitionistic fuzzy information in the collective intuitionistic fuzzy decision matrix to get the overall intuitionistic fuzzy values of alternatives by which the ranking of all the given alternatives can be found. Finally, we give an illustrative example.
156 citations
TL;DR: The centroid of an interval type-2 fuzzy set (IT2 FS) provides a measure of the uncertainty of such a FS, and its calculation is very widely used in interval type 2 fuzzy logic systems as mentioned in this paper.
153 citations
01 Jan 2007
TL;DR: The results demonstrated the potential of the inference system for subsiding the failure modes and effects analysis (FMEA) in aging studies and the concept of a pure fuzzy logic system where the fuzzy rule base consists of a collection of fuzzy IF-THEN rules.
Abstract: This paper presents a nuclear case study, in which a fuzzy inference system (FIS) is used as alternative approach in risk analysis. The main objective of this study is to obtain an understanding of the aging process of an important nuclear power system and how it affects the overall plant safety. This approach uses the concept of a pure fuzzy logic system where the fuzzy rule base consists of a collection of fuzzy IF-THEN rules. The fuzzy inference engine uses these fuzzy IF-THEN rules to determine a mapping from fuzzy sets in the input universe of discourse to fuzzy sets in the output universe of discourse based on fuzzy logic principles. The risk priority number (RPN), a traditional analysis parameter, was calculated and compared to fuzzy risk priority number (FRPN) using scores from expert opinion to probabilities of occurrence, severity and not detection. A standard four-loop pressurized water reactor (PWR) containment cooling system (CCS) was used as example case. The results demonstrated the potential of the inference system for subsiding the failure modes and effects analysis (FMEA) in aging studies.
152 citations
01 Jun 2007
TL;DR: Two new relaxed stabilization criteria for discrete-time T-S fuzzy systems are proposed based on the piecewise Lyapunov function and the conditions in the criteria and the fuzzy control design can be solved and achieved by means of linear matrix inequality tools.
Abstract: In this paper, two new relaxed stabilization criteria for discrete-time T-S fuzzy systems are proposed. In the beginning, the operation state space is divided into several subregions, and then, the T-S fuzzy system is transformed to an equivalent switching fuzzy system corresponding to each subregion. Consequently, based on the piecewise Lyapunov function, the stabilization criteria of the switching fuzzy system are derived. The criteria have two features: 1) the behavior of the two successive states of the system is considered in the inequalities and 2) the interactions among the fuzzy subsystems in each subregion Sj are presented by one matrix Xj. Due to the above two features, the feasible solutions of the inequalities in the criteria are much easier to be found. In other words, the criteria are much more relaxed than the existing criteria proposed in other literature. The proposed conditions in the criteria and the fuzzy control design can be solved and achieved by means of linear matrix inequality tools. Two examples are given to present the superiority of the proposed criteria and the effectiveness of the fuzzy controller's design, respectively
143 citations
23 Jul 2007
TL;DR: The development and design of a graphical user interface and a command line programming toolbox for construction, edition and observation of interval type-2 fuzzy inference systems are presented.
Abstract: This paper presents the development and design of a graphical user interface and a command line programming toolbox for construction, edition and observation of interval type-2 fuzzy inference systems. The interval type-2 fuzzy logic system toolbox (IT2FLS), is an environment for interval type-2 fuzzy logic inference system development. Tools that cover the different phases of the fuzzy system design process, from the initial description phase, to the final implementation phase, build the toolbox. The toolbox's best qualities are the capacity to develop complex systems and the flexibility that permits the user to extend the availability of functions for working with the use of type-2 fuzzy operators, linguistic variables, interval type-2 membership functions, defuzzification methods and the evaluation of interval type-2 fuzzy inference systems.
132 citations
07 Jul 2007
TL;DR: This work defines a framework consisting of a fuzzy ontology based on Fuzzy Description Logic and FuzzY---Owl, and describes how to introduce fuzziness in an ontology.
Abstract: The conceptual formalism supported by an ontology is not sufficient for handling vague information that is commonly found in many application domains. We describe how to introduce fuzziness in an ontology. To this aim we define a framework consisting of a fuzzy ontology based on Fuzzy Description Logic and Fuzzy---Owl.
129 citations
Book•
08 Feb 2007
TL;DR: In this article, the authors present a stability analysis of T-S Fuzzy Control Systems using a delay independent method and a delay dependent method for output tracking and fuzzy filter design.
Abstract: Stability Analysis of T-S Fuzzy Systems.- Extension to Fuzzy Large-Scale Systems.- Stabilization Methods for T-S Fuzzy Systems.- Variable Structure Control for T-S Fuzzy Systems.- Observer-Based Fuzzy Control: Delay-Independent Method.- Observer-Based Fuzzy Control: Delay-Dependent Method.- Output Tracking Control for T-S Fuzzy Systems.- Fuzzy Filter Design for T-S Fuzzy Systems.- Descriptor Method for T-S Fuzzy Control Systems.
122 citations
TL;DR: An intelligent system for automated quality control in sound speaker manufacturing is developed that has a type-2 fuzzy rule base containing the knowledge of human experts in quality control.
TL;DR: An effective approach is developed to establish affine Takagi-Sugeno (T-S) fuzzy model for a given nonlinear system from its input-output data, and an affine T-S fuzzy model with compact IF-THEN rules could thus be generated systematically.
Abstract: An effective approach is developed to establish affine Takagi-Sugeno (T-S) fuzzy model for a given nonlinear system from its input-output data. Firstly, the fuzzy c-regression model (FCRM) clustering technique is applied to partition the product space of the given input-output data into hyper-plan-shaped clusters. Each cluster is essentially a basis of the fuzzy rule that describes the system behaviour, and the number of clusters is just the number of fuzzy rules. Particularly, a novel cluster validity criterion for FCRM is set up to choose the appropriate number of clusters (rules). Once the number of clusters is determined, the consequent parameters of each IF-THEN rule are directly obtained from the functional cluster representatives (affine linear functions). The antecedent fuzzy sets of each IF-THEN fuzzy rule are acquired by projecting the fuzzy partitions matrix U onto the axes of individual antecedent variable to obtain point-wise defined fuzzy sets and to approximate these point-wise defined fuzzy sets by normal bell-shaped membership functions. Additionally, a check and repartition algorithm is suggested to prevent the inappropriate premise structure where separate regions of data shared the same regression model. Finally, the gradient descent algorithm is included to adjust the fuzzy model precisely. An affine T-S fuzzy model with compact IF-THEN rules could thus be generated systematically. Several simulation examples are provided to demonstrate the accuracy and effectiveness of the affine T-S fuzzy modelling algorithm.
TL;DR: A new method for design of a fuzzy-rule-based classifier using genetic algorithms (GAs) is discussed, and results indicate that highly accurate classifiers could be designed with relatively few fuzzy rules.
01 Nov 2007
TL;DR: The FS-FCSVM is a fuzzy system constructed by fuzzy if-then rules with fuzzy singletons in the consequence that is applied to skin color segmentation and comparisons with a fuzzy neural network, the Gaussian kernel SVM, and mixture of Gaussian classifiers are performed.
Abstract: This paper proposes a Fuzzy System learned through Fuzzy Clustering and Support Vector Machine (FS-FCSVM). The FS-FCSVM is a fuzzy system constructed by fuzzy if-then rules with fuzzy singletons in the consequence. The structure of FS-FCSVM is constructed by fuzzy clustering on the input data, which helps to reduce the number of rules. Parameters in FS-FCSVM are learned through a support vector machine (SVM) for the purpose of achieving higher generalization ability. In contrast to nonlinear kernel-based SVM or some other fuzzy systems with a support vector learning mechanism, both the number of parameters/rules in FS-FCSVM and the computation time are much smaller. FS-FCSVM is applied to skin color segmentation. For color information representation, different types of features based on scaled hue and saturation color space are used. Comparisons with a fuzzy neural network, the Gaussian kernel SVM, and mixture of Gaussian classifiers are performed to show the advantage of FS-FCSVM.
TL;DR: In this article, a method based on iterative rule learning using a fuzzy rule-based genetic classifier was proposed to provide an intelligent intrusion detection system (IIDS) that uses two of the most popular data mining tasks, namely classification and association rules mining together for predicting different behaviors in networked computers.
01 Jan 2007
TL;DR: The Hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities (LMIs) instead of a second-order Hamilton-Jacobi inequality.
Abstract: This paper describes the robust fuzzy filtering design for a class of nonlinear stochastic systems. The system dynamic is modelled by Ito-type stochastic differential equations. For general nonlinear stochastic systems, the filter can be obtained by solving a second-order nonlinear Hamilton-Jacobi inequality. In general, it is difficult to solve the second-order nonlinear Hamilton-Jacobi inequality. In this paper, using fuzzy approach (Takagi-Sugeno (T-S) fuzzy model), the fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities (LMIs) instead of a second-order Hamilton-Jacobi inequality. When the worst-case fuzzy disturbance is considered, a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error. The near minimum variance fuzzy filtering problem under the worst-case fuzzy disturbance is also characterized in terms of linear matrix inequality problem (LMIP), which can be efficiently solved by the convex optimization techniques. Simulation examples are provided to illustrate the design procedure and expected performance.
TL;DR: The global asymptotic stability problem of TS fuzzy bi-directional associative memories (BAM) neural networks with time-varying delays and parameter uncertainties is considered and a modified TS fuzzy model is established in which the consequent parts are composed of a set of BAM neural networks that can be easily solved by some standard numerical packages.
TL;DR: This paper examines the problem of static output feedback control of a Takagi-Sugeno (TS) fuzzy system and proposes an iterative algorithm based on the linear matrix inequality to compute the Static output feedback gain.
TL;DR: The procedures here will allow to set up linear matrix inequality conditions which are less conservative than the cited ones, by exploiting the TP structure of the membership functions.
TL;DR: Experimental results on high-dimensional benchmark problems have shown that by using the proposed scheme the most influential fuzzy rules can be effectively induced and selected, and at the same time feature ranking results can also be obtained to construct parsimonious fuzzy classifiers with better generalization performance than the well-known algorithms in literature.
Abstract: In this paper, a new scheme for constructing parsimonious fuzzy classifiers is proposed based on the L2-support vector machine (L2-SVM) technique with model selection and feature ranking performed simultaneously in an integrated manner, in which fuzzy rules are optimally generated from data by L2-SVM learning. In order to identify the most influential fuzzy rules induced from the SVM learning, two novel indexes for fuzzy rule ranking are proposed and named as alpha-values and omega-values of fuzzy rules in this paper. The alpha-values are defined as the Lagrangian multipliers of the L2-SVM and adopted to evaluate the output contribution of fuzzy rules, while the omega-values are developed by considering both the rule base structure and the output contribution of fuzzy rules. As a prototype-based classifier, the L2-SVM-based fuzzy classifier evades the curse of dimensionality in high-dimensional space in the sense that the number of support vectors, which equals the number of induced fuzzy rules, is not related to the dimensionality. Experimental results on high-dimensional benchmark problems have shown that by using the proposed scheme the most influential fuzzy rules can be effectively induced and selected, and at the same time feature ranking results can also be obtained to construct parsimonious fuzzy classifiers with better generalization performance than the well-known algorithms in literature.
TL;DR: This paper proposes several new necessary and sufficient criteria for the so-called Mamdani relation to be a solution to the system and proves that in the general case, these same criteria are sufficient (but not always necessary) for the solvability of the system.
23 Jul 2007
TL;DR: This work proposes a novel semantics combining the common product t-norm with the standard negation, and shows some interesting properties of the logic and proposes a reasoning algorithm based on a mixture of tableaux rules and the reduction to mixed integer quadratically constrained programming.
Abstract: Fuzzy description logics (fuzzy DLs) have been proposed as a language to describe structured knowledge with vague concepts. It is well known that the choice of the fuzzy operators may determine some logical properties. However, up to date the study of fuzzy DLs has been restricted to the Lukasiewicz logic and the "Zadeh semantics". In this work, we propose a novel semantics combining the common product t-norm with the standard negation. We show some interesting properties of the logic and propose a reasoning algorithm based on a mixture of tableaux rules and the reduction to mixed integer quadratically constrained programming.
TL;DR: An adaptive fuzzy control method is developed to control unified chaotic systems and an adaptive technique is employed to construct controllers, which drive state variables into a small neighborhood of the origin.
Abstract: An adaptive fuzzy control method is developed to control unified chaotic systems. Fuzzy logic systems are used to approximate nonlinear functions in the chaotic system and an adaptive technique is employed to construct controllers, which drive state variables into a small neighborhood of the origin. The simulation results are provided to demonstrate the effectiveness and feasibility of the proposed method.
Journal Article•
TL;DR: To investigate the problems of clustering intuitionistic fuzzy sets, the concept of intuitionists' fuzzy similarity degree is defined, and intuitionist fuzzy similarity matrix and intuitionism fuzzy equivalence matrix are constructed.
Abstract: To investigate the problems of clustering intuitionistic fuzzy sets,the concept of intuitionistic fuzzy similarity degree is defined,and intuitionistic fuzzy similarity matrix and intuitionistic fuzzy equivalence matrix are constructed.A compound operational law of intuitionistic fuzzy similarity matrix is defined and an approach to transforming the intuitionistic fuzzy similarity matrices into the intuitionistic fuzzy equivalence matrices is given.Moreover,λ-cutting matrices of the intuitionistic fuzzy similarity matrix and intuitionistic fuzzy equivalence matrix are given,and then an approach to clustering intuitionistic fuzzy sets is proposed.Finally,a numerical example is given to illustrate and analyze the proposed approach.
TL;DR: A new family of normalized distance measures between binary fuzzy operators, along with its dual family of similarity measures, are introduced, based on matrix norms and arise from the study of the aggregate plausibility of set-operations.
Book•
08 Jan 2007
TL;DR: This book presents a systematic study on the inherent complexity in fuzzy systems, resulting from the large number and the poor transparency of the fuzzy rules, aimed at compressing the fuzzy rule base by removing the redundancy while preserving the solution.
Abstract: This book presents a systematic study on the inherent complexity in fuzzy systems, resulting from the large number and the poor transparency of the fuzzy rules. The study uses a novel approach for complexity management, aimed at compressing the fuzzy rule base by removing the redundancy while preserving the solution. The compression is based on formal methods for presentation, manipulation, transformation and simplification of fuzzy rule bases.
TL;DR: This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics‐based Takagi–Sugeno–Kang (TSK) rules, using a two‐stage evolutionary algorithm based on MOGUL to consider the interaction between input and output variables.
Abstract: This work presents the use of local fuzzy prototypes as a new idea to obtain accurate local semantics-based Takagi–Sugeno–Kang ~TSK! rules. This allow us to start from prototypes considering the interaction between input and output variables and taking into account the fuzzy nature of the TSK rules. To do so, a two-stage evolutionary algorithm based on MOGUL ~a methodology to obtain Genetic Fuzzy Rule-Based Systems under the Iterative Rule Learning approach! has been developed to consider the interaction between input and output variables. The first stage performs a local identification of prototypes to obtain a set of initial local semantics-based TSK rules, following the Iterative Rule Learning approach and based on an evolutionary generation process within MOGUL ~taking as a base some initial linguistic fuzzy partitions!. Because this generation method induces competition among the fuzzy rules, a postprocessing stage to improve the global system performance is needed. Two different processes are considered at this stage, agenetic niching-based selection process to remove redundant rules and a genetic tuning process to refine the fuzzy model parameters. The proposal has been tested with two real-world problems, achieving good results. © 2007 Wiley Periodicals, Inc.
TL;DR: Some elementary operations on triangular fuzzy numbers (TFNs) are defined and some important properties of TFMs are presented and the concept of adjoints on TFM is discussed and some of their properties are presented.
Abstract: In this paper, some elementary operations on triangular fuzzy numbers (TFNs) are defined. We also define some operations on triangu- lar fuzzy matrices (TFMs) such as trace and triangular fuzzy determinant (TFD). Using elementary operations, some important properties of TFMs are presented. The concept of adjoints on TFM is discussed and some of their properties are. Some special types of TFMs (e.g. pure and fuzzy triangular, symmetric, pure and fuzzy skew-symmetric, singular, semi-singular, constant) are defined and a number of properties of these TFMs are presented.
TL;DR: Fuzzy Techniques in Manufacturing Systems and Technology Management, and Neural Fuzzy Approaches to Modeling of Musculoskeletal Responses in Manual Lifting Tasks.
TL;DR: A complex number representation of the @a-level sets of the fuzzy system is used and theorems that provide the solutions under such representation are proved, which is applicable to practical computations and also has some implications for theory.