Showing papers on "Fuzzy associative matrix published in 2012"
TL;DR: A variable separation approach is developed to overcome the difficulty from the nonstrict-feedback structure and a state feedback adaptive fuzzy tracking controller is proposed, which guarantees that all of the signals in the closed-loop system are bounded, while the tracking error converges to a small neighborhood of the origin.
Abstract: Controlling nonstrict-feedback nonlinear systems is a challenging problem in control theory. In this paper, we consider adaptive fuzzy control for a class of nonlinear systems with nonstrict-feedback structure by using fuzzy logic systems. A variable separation approach is developed to overcome the difficulty from the nonstrict-feedback structure. Furthermore, based on fuzzy approximation and backstepping techniques, a state feedback adaptive fuzzy tracking controller is proposed, which guarantees that all of the signals in the closed-loop system are bounded, while the tracking error converges to a small neighborhood of the origin. Simulation studies are included to demonstrate the effectiveness of our results.
363 citations
TL;DR: This article investigates the group decision making problems in which all the information provided by the decision makers is expressed as IT2 fuzzy decision matrices, and the information about attribute weights is partially known, which may be constructed by various forms.
Abstract: Interval type-2 fuzzy sets (IT2 FSs) 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 (DMs) is expressed as IT2 fuzzy decision matrices, and the information about attribute weights is partially known, which may be constructed by various forms. We first use the IT2 fuzzy weighted arithmetic averaging operator to aggregate all individual IT2 fuzzy decision matrices provided by the DMs into the collective IT2 fuzzy decision matrix, then we utilize the ranking-value measure to calculate the ranking value of each attribute value and construct the ranking-value matrix of the collective IT2 fuzzy decision matrix. Based on the ranking-value 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 IT2 fuzzy weighted arithmetic average operator to fuse the IT2 fuzzy information in the collective IT2 fuzzy decision matrix to get the overall IT2 fuzzy values of alternatives by which the ranking of all the given alternatives can be found. Finally, we give an illustrative example.
158 citations
TL;DR: A new framework for the graph model for conflict resolution is developed so that decision makers (DMs) with fuzzy preferences can be included in conflict models and the four basic stability definitions for two or more DMs are extended.
Abstract: A new framework for the graph model for conflict resolution is developed so that decision makers (DMs) with fuzzy preferences can be included in conflict models. A graph model is both a formal representation for multiple participant-multiple objective decision problems and a set of analysis procedures that add insights into them. Within the new framework, graph models can include-and integrate into the analysis-both certain and uncertain information about DMs' preferences. One key contribution of this study is to extend the four basic stability definitions for two or more DMs to models with fuzzy preferences. Together, fuzzy Nash stability, fuzzy general metarationality, fuzzy symmetric metarationality, and fuzzy sequential stability provide anuanced description of human behavior. A state is fuzzy stable for a DM if a move to any other state is not sufficiently likely to yield an outcome which the DM prefers, where sufficiency is measured according to a fuzzy satisficing threshold that is the characteristic of the DM. A fuzzy equilibrium, which is an outcome that is fuzzy stable for all DMs, therefore represents a possible resolution of the strategic conflict. The practical application and interpretation of these new stability definitions are illustrated with an example.
124 citations
TL;DR: It is proved that a uniform fuzzy relation between fuzzy automata A and B is a forward bisimulation if and only if its kernel and co-kernel are forward bisIMulation fuzzy equivalence relations on A and A and there is a special isomorphism between factor fuzzy automATA with respect to these fuzzy equivalences relations.
94 citations
Journal Article•
[...]
TL;DR: It is shown that a fuzzy soft topological space gives a parametrized family of fuzzy topological spaces and that the constant mapping is not continuous in general.
Abstract: In the present paper we introduce the topological structure of fuzzy soft sets and fuzzy soft continuity of fuzzy soft mappings. We show that a fuzzy soft topological space gives a parametrized family of fuzzy topological spaces. Furthermore, with the help of an example it is shown that the constant mapping is not continuous in general. Then the notions of fuzzy soft closure and interior are introduced and their basic properties are investigated. Finally, the initial fuzzy soft topology and some properties of projection mappings are studied.
82 citations
TL;DR: The sampling defuzzifier is compared on aggregated type-2 fuzzy sets resulting from the inferencing stage of a FIS, in terms of accuracy and speed, with other methods including the exhaustive and techniques based on the @a-planes representation.
78 citations
TL;DR: The aim of this paper is to develop an effective method for solving matrix games with payoffs of triangular fuzzy numbers (TFNs) which always assures that players’ gain-floor and loss-ceiling have a common TFN-type fuzzy value and hereby any matrix game with payoff of TFNs has aTFN- type fuzzy value.
71 citations
TL;DR: A new multi-objective genetic algorithm is applied to solve the simple assembly line balancing problem of type 2 (SALBP-2) with fuzzy job processing times since uncertainty, variability, and imprecision are often occurred in real-world production systems.
Abstract: This paper presents a fuzzy extension of the simple assembly line balancing problem of type 2 (SALBP-2) with fuzzy job processing times since uncertainty, variability, and imprecision are often occurred in real-world production systems. The jobs processing times are formulated by triangular fuzzy membership functions. The total fuzzy cost function is formulated as the weighted-sum of two bi-criteria fuzzy objectives: (a) Minimizing the fuzzy cycle time and the fuzzy smoothness index of the workload of the line. (b) Minimizing the fuzzy cycle time of the line and the fuzzy balance delay time of the workstations. A new multi-objective genetic algorithm is applied to solve the problem whose performance is studied and discussed over known test problems taken from the open literature.
70 citations
TL;DR: This work defines fuzzy soft ($fs) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory and constructs a decision making method which can be successfully applied to the problems that contain uncertainties.
Abstract: In this work, we dene fuzzy soft ( fs) matrices and their opera- tions which are more functional to make theoretical studies in the fs-set theory. We then dene products of fs-matrices and study their properties. We nally construct a fs-max-min decision making method which can be successfully applied to the problems that contain uncertainties.
60 citations
TL;DR: The results of comparative studies and numerical examples indicate that the proposed fuzzy regression model has a better performance than the least-squares method, especially when the data set includes some outlier data point(s).
54 citations
TL;DR: The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions, which are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers.
Abstract: The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T-S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.
TL;DR: This paper investigates H" ~ control for general 2D nonlinear systems based on a 2D Takagi-Sugeno (T-S) fuzzy model and demonstrates that the proposed method is less computationally expensive than the approach in which the input variable, state variable and its forward-stepping state are all separately considered, although these two methods can achieve the same optimal H"~ performance.
Book•
17 Oct 2012
TL;DR: This paper presents the results of experiments on Fuzzy Logic Systems Based Indirect Adaptive Control of a Flexible Link Manipulator based on the IF-THEN Logic of Natural Languages and Naturally Correct Inferences, and some of the proposed proposals to improve the accuracy of FBuzzy Linguistic Modeling.
Abstract: Preface. 1. The IF-THEN Logic of Natural Languages and Naturally Correct Inferences E. Hisdal. 2. Fussy Predicate Calculus and Fuzzy Rules P. Hajek. 3. The Generalized Modus Ponens in a Fuzzy Set Theoretical Framework C. Cornelis, et al. 4. Compositional Rule of Inference Based on Triangular Norms A. Kolesarova, E.E. Kerre. 5. Approximate Reasoning Based on Lattice-Valued Propositional Logic Lvpl Y. Xu, et al. 6. Mining Interesting Possibilistic Set-Valued Rules A.A. Savinov. 7. Complexity Reduction of a Generalised Rational Form P. Baranyi, Y. Yam. 8. Reasoning with Cognitive Structures of Agents I: Acquisition of Rules for Computational Theory of Perceptions by Fuzzy Relational Methods L.J. Kohout, E. Kim. 9. Different Proposals to Improve the Accuracy of Fuzzy Linguistic Modeling O. Cordon, et al. 10. Linguistic IF-THEN Rules in Large Scale Application of Fuzzy Control V. Novak, J. Kovar. 11. Fuzzy Rules Extraction-Based Linguistic and Numerical Heterogeneous Data Fusion for Intelligent Robotic Control C. Zhou, D. Ruan. 12. Fuzzy IF-THEN Rules for Pattern Classification H. Ishibuchi, et al. 13. Experiments on Fuzzy Logic Systems Based Indirect Adaptive Control of a Flexible Link Manipulator J.X. Lee, G. Vukovich. Index.
TL;DR: A new approach to solving fuzzy real and complex systems of linear equations based on the fuzzy center and width is presented here, where the unknown variable and right-hand side vector are considered as fuzzy, whereas the coefficient matrix is considered as crisp.
Abstract: A new approach to solving fuzzy real and complex systems of linear equations based on the fuzzy center and width is presented here. The unknown variable and right-hand side vector are considered as fuzzy, whereas the coefficient matrix is considered as crisp. First the system is solved in terms of the fuzzy center, and then this solution is used with the width to get the final solution of the original system. The presented procedure is applied to analyze three example problems. The results obtained are also compared with the known solutions and are found to be in good agreement.
29 Apr 2012
TL;DR: A new method to create model of nonlinear dynamic systems which gives a real opportunity for the interpretation of accumulated knowledge by combining methods of control theory with fuzzy logic rules is presented.
Abstract: The paper presents a new method to create model of nonlinear dynamic systems which gives a real opportunity for the interpretation of accumulated knowledge. By combining methods of control theory with fuzzy logic rules a good accuracy of the model can be achieved with use of a small number of fuzzy rules.
TL;DR: This study attempts to construct fuzzy circles in a fuzzy geometrical plane using the conventional basic definitions of crisp circles and shows that the center of a fuzzy circle may not be a fuzzy point.
TL;DR: Duality theory is developed for this class of linear programming problems having fuzzy goals/constraints that can be described by (Atanassov’s) I-fuzzy sets which is subsequently applied to define a new solution concept for two persons zero-sum matrix games with I- fuzzy goals.
Abstract: In this paper we study a class of linear programming problems having fuzzy goals/constraints that can be described by (Atanassov's) I-fuzzy sets. Duality theory is developed for this class of problems in the I-fuzzy sense which is subsequently applied to define a new solution concept for two persons zero-sum matrix games with I-fuzzy goals.
TL;DR: This paper presents a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches, and provides a practical application to illustrate the usefulness of the intervaltype-2rough fuzzy sets model.
Abstract: In this paper, we present a general framework for the study of interval type-2 rough fuzzy sets by using both constructive and axiomatic approaches. First, several concepts and properties of interval type-2 fuzzy sets are introduced. Then, a pair of lower and upper interval type-2 rough fuzzy approximation operators with respect to a crisp binary relation is proposed. Classical representations of the interval type-2 rough fuzzy approximation operators are then constructed, and the connections between the special binary relations and the interval type-2 rough fuzzy approximation operators are investigated. Furthermore, an operator-oriented characterization of interval type-2 rough fuzzy sets is proposed; that is, interval type-2 rough fuzzy approximation operators are characterized by axioms. Different axiom sets of interval type-2 fuzzy set-theoretic operators guarantee the existence of different types of crisp binary relations, which produce the same operators. Furthermore, the relationship between interval type-2 rough fuzzy sets and interval type-2 fuzzy topological spaces is obtained. The sufficient and necessary condition for the conjecture that an interval type-2 fuzzy interior (closure) operator derived from an interval type-2 fuzzy topological space can be associated with a reflexive and transitive binary relation such that the corresponding lower (upper) interval type-2 rough fuzzy approximation operator is the interval type-2 fuzzy interior (closure) operator is examined. Finally, we provide a practical application to illustrate the usefulness of the interval type-2 rough fuzzy sets model.
01 Oct 2012
TL;DR: Simulation results are presented showing that the developed evolving T-S fuzzy model can identify the nonlinear systems satisfactorily with appropriate input variables and delay selection and a reasonable number of rules.
Abstract: This paper proposes a new method for soft sensors (SS) design for industrial applications based on a Takagi-Sugeno (T-S) fuzzy model. The learning of the T-S model is performed from input/output data to approximate unknown nonlinear processes by a coevolationary genetic algorithm (GA). The proposed method is an automatic tool for SS design since it does not require any prior knowledge concerning the structure (e.g. the number of rules) and the database (e.g. antecedent fuzzy sets) of the T-S fuzzy model, and concerning the selection of the adequate input variables and their respective time delays for the prediction setting. The GA approach is composed by five hierarchical levels and has the global goal of maximizing the prediction accuracy. The first level consists in the selection of the set of input variables and respective delays for the T-S fuzzy model. The second level considers the encoding of the membership functions. The individual rules are defined at the third level, the population of the set of rules is treated in fourth level, and a population of fuzzy systems is handled at the fifth level. To validate and demonstrate the performance and effectiveness of the proposed algorithm, it is applied on two prediction problems. The first is the Box-Jenkins benchmark problem, and the second is the estimation of the flour concentration in the effluent of a real-world wastewater treatment system. Simulation results are presented showing that the developed evolving T-S fuzzy model can identify the nonlinear systems satisfactorily with appropriate input variables and delay selection and a reasonable number of rules. The proposed methodology is able to design all the parts of the T-S fuzzy prediction model. Moreover, presented comparison results indicate that the proposed method outperforms other previously proposed methods for the design of prediction models, including methods previously proposed for the design of T-S models.
01 Sep 2012
TL;DR: A novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented and a learning algorithm from the cost function for adjusting of fuzzy weights is proposed.
Abstract: In this paper, a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large field called neural computing or soft computing. The model finds the approximated solution of fuzzy differential equation inside of its domain for the close enough neighborhood of the fuzzy initial point. We propose a learning algorithm from the cost function for adjusting of fuzzy weights. Finally, we illustrate our approach by numerical examples and an application example in engineering.
TL;DR: A novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and fuzzy inputs, is presented.
Abstract: In this paper, a novel hybrid method based on fuzzy neural network for approximate fuzzy coefficients (parameters) of fuzzy linear and nonlinear regression models with fuzzy output and fuzzy inputs, is presented. Here, a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed. Finally, we illustrate our approach by some numerical examples.
TL;DR: A new method to find the exact fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy coefficients and unrestricted fuzzy variables is proposed and a real life problem is solved by using the proposed method.
Abstract: Kumar et al (Appl Math Model 35:817---823, 2011) pointed out that there is no method in literature to find the exact fuzzy optimal solution of fully fuzzy linear programming (FFLP) problems and proposed a new method to find the fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients There may exist several FFLP problems with equality constraints in which no restriction can be applied on all or some of the fuzzy variables but due to the limitation of the existing method these types of problems can not be solved by using the existing method In this paper a new method is proposed to find the exact fuzzy optimal solution of FFLP problems with equality constraints having non-negative fuzzy coefficients and unrestricted fuzzy variables The proposed method can also be used to solve the FFLP problems with equality constraints having non-negative fuzzy variables and unrestricted fuzzy coefficients To show the advantage of the proposed method over existing method the results of some FFLP problems with equality constraints, obtained by using the existing and proposed method, are compared Also, to show the application of proposed method a real life problem is solved by using the proposed method
TL;DR: This paper employs linear programming (abbreviated to LP) with equality constraints to find a non-negative fuzzy number matrix X ∼ which satisfies A ∼ X ∼ = B ∼ , where A ∼ and B ∼ are two fuzzy number matrices.
TL;DR: A novel methodology based on T2 fuzzy sets is proposed i.e. T2SDSA-FNN (Type-2 Self-Developing and Self-Adaptive Fuzzy Neural Networks), which has superior accuracy performance on electric forecasting problem than other techniques shown in existing literatures.
Book•
27 Jan 2012
TL;DR: This book is to present a methodology for designing and tuning fuzzy expert systems in order to identify nonlinear objects to build input-output models using expert and experimental information, and includes applications of the proposed methodology in dynamic and inventory control systems.
Abstract: The purpose of this book is to presenta methodology for designing and tuning fuzzyexpert systems in order to identify nonlinear objects; that is, to build input-output models using expert and experimental information. The results of these identifications are used for direct and inverse fuzzy evidence in forecasting and diagnosis problem solving. The book is organised as follows: Chapter 1 presents the basic knowledge about fuzzy sets, genetic algorithms and neural nets necessary for a clear understanding of the rest of this book. Chapter 2analyzesdirect fuzzy inference based on fuzzy if-then rules. Chapter 3is devoted to the tuning of fuzzy rulesfor direct inference using genetic algorithms and neural nets. Chapter4presents models and algorithms for extracting fuzzy rules from experimental data. Chapter 5 describesa method for solving fuzzy logic equationsnecessary for the inverse fuzzy inference indiagnostic systems. Chapters6 and 7 aredevoted to inverse fuzzy inferencebased on fuzzy relations andfuzzy rules. Chapter 8presents a method for extracting fuzzy relations from data. Allthe algorithms presented in Chapters 2-8 arevalidated by computer experiments and illustrated bysolving medical and technicalforecasting anddiagnosis problems. Finally, Chapter 9includes applications of the proposed methodology in dynamicand inventory control systems, prediction of results of football games,decisionmaking in road accident investigations, project management and reliability analysis.
26 Jun 2012
TL;DR: This work provides a class of t-norms and an expressive fuzzy DL for which ontology consistency is linearly reducible to crisp reasoning, and thus has its same complexity.
Abstract: Fuzzy Description Logics (DLs) with t-norm semantics have been studied as a means for representing and reasoning with vague knowledge. Recent work has shown that even fairly inexpressive fuzzy DLs become undecidable for a wide variety of t-norms. We complement those results by providing a class of t-norms and an expressive fuzzy DL for which ontology consistency is linearly reducible to crisp reasoning, and thus has its same complexity. Surprisingly, in these same logics crisp models are insufficient for deciding fuzzy subsumption.
TL;DR: Experimental results demonstrated the efficiency of the diagnosis system proposed that had superior results as compared with other conventional and intelligent methods.
TL;DR: This work provides a simple solution to join these two formalisms and define a fuzzy rough DL, which is more general than other related approaches, including tight and loose fuzzy rough approximations and being independent of the fuzzy logic operators considered.
TL;DR: The design scheme of the indirect adaptive fuzzy observer and controller based on the interval type-2 (IT2) T–S fuzzy model is presented and the simulation results show that the proposed method can handle unpredicted disturbance and data uncertainties very well in advantage of the effectiveness of observation and control.