Showing papers on "Fuzzy associative matrix published in 2010"
TL;DR: Some relations and operations of interval-valued intuitionistic fuzzy numbers are introduced, some types of matrices are defined and a method based on distance measure for group decision making with interval-value intuitionistic fuzziness matrices is developed.
256 citations
TL;DR: This paper proposes a new method based on Fuzzy K-Means clustering for reducing the size of the concept lattices and demonstrates the implementation of proposed method on two application areas: information retrieval and information visualization.
Abstract: During the design of concept lattices, complexity plays a major role in computing all the concepts from the huge incidence matrix. Hence for reducing the size of the lattice, methods based on matrix decompositions like SVD are available in the literature. However, SVD computation is known to have large time and memory requirements. In this paper, we propose a new method based on Fuzzy K-Means clustering for reducing the size of the concept lattices. We demonstrate the implementation of proposed method on two application areas: information retrieval and information visualization.
214 citations
TL;DR: A new method for multi-variable fuzzy forecasting based on fuzzy clustering and fuzzy rule interpolation techniques and the experimental results show that the proposed method produces better forecasting results than several existing methods.
141 citations
TL;DR: New inconsistency index of reciprocal matrix with fuzzy elements is introduced and newly designed method of logarithmic least squares for eliciting associated weights is applied.
136 citations
TL;DR: An I-FIFOWG and FIFWG (fuzzy number intuitionistic fuzzy weighted geometric) operators-based approach is developed to solve the MAGDM under the fuzzy number intuitionism fuzzy environment.
Abstract: With respect to multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of fuzzy number intuitionistic fuzzy numbers, a new group decision making analysis method is developed. Firstly, some operational laws of fuzzy number intuitionistic fuzzy numbers, score function and accuracy function of fuzzy number intuitionistic fuzzy numbers are introduced. Then a new aggregation operator called induced fuzzy number intuitionistic fuzzy ordered weighted geometric (I-FIFOWG) operator is proposed, and some desirable properties of the I-FIFOWG operators are studied, such as commutativity, idempotency and monotonicity. An I-FIFOWG and FIFWG (fuzzy number intuitionistic fuzzy weighted geometric) operators-based approach is developed to solve the MAGDM under the fuzzy number intuitionistic fuzzy environment. Furthermore, we propose the induced fuzzy number intuitionistic fuzzy ordered weighted avera...
122 citations
TL;DR: Comparing the proposed approach with some other fuzzy systems and neural networks, it is shown that the developed TSK fuzzy system exhibits better results with higher accuracy and smaller size of architecture.
116 citations
TL;DR: A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models.
Abstract: The intuitionistic fuzzy set (IF-set) has not been applied to matrix game problems yet since it was introduced by K.T.Atanassov. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers (TIFNs). Firstly the concept of TIFNs and their arithmetic operations and cut sets are introduced as well as the ranking order relations. Secondly the concept of solutions for matrix games with payoffs of TIFNs is defined. A lexicographic methodology is developed to determine the solutions of matrix games with payoffs of TIFNs for both Players through solving a pair of bi-objective linear programming models derived from two new auxiliary intuitionistic fuzzy programming models. The proposed method is illustrated with a numerical example.
108 citations
TL;DR: It is shown that @k=@k^' for a fuzzy tree and it is the minimum of the strengths of its strong arcs as well as the value of all these parameters are equal in a compete fuzzy graph.
106 citations
TL;DR: The proposed recurrent self-evolving fuzzy neural network with local feedbacks (RSEFNN-LF) is applied to dynamic system identification, chaotic sequence prediction, and speech recognition problems and is compared with other recurrent fuzzy neural networks.
96 citations
TL;DR: This paper examines the continuity of fuzzy directed complete posets (dcpos for short) based on complete residuated lattices and shows that a fuzzy partial order in the sense of Fan and Zhang and an L-order in thesense of Belohlavek are equivalent to each other.
95 citations
TL;DR: It is shown that whenever the exact discrete-time fuzzy model is asymptotically stabilizable via the sampled-data fuzzy controller uniformly bounded in the state, then so is the original nonlinear system.
Abstract: This paper addresses stabilization problems for a nonlinear system via a sampled-data fuzzy controller. The nonlinear system is assumed to be exactly modeled in Takagi-Sugeno's form, at least locally. Unlike the conventional direct discrete-time design approach based on an approximate discrete-time model, the sampled-data fuzzy controllers are designed based on an exact discrete-time model. Sufficient design conditions are formulated in terms of linear matrix inequalities. It is shown that whenever the exact discrete-time fuzzy model is asymptotically stabilizable via the sampled-data fuzzy controller uniformly bounded in the state, then so is the original nonlinear system. A numerical example is given to illustrate the effectiveness of the proposed methodology.
TL;DR: One of the primary objectives of this study is to show that how a multi-objective aggregate production planning problem which is stated as a fuzzy mathematical programming model can also be solved directly by employing fuzzy ranking methods and a metaheuristic algorithm.
TL;DR: The proposed approach for modeling and analysis of time critical, dynamic and complex systems using stochastic Petri nets together with fuzzy sets can take into consideration both dimensions of uncertainty in system modeling, stochastically variability and imprecision.
Abstract: In this paper, an approach for modeling and analysis of time critical, dynamic and complex systems using stochastic Petri nets together with fuzzy sets is presented The presented method consists of two stages The first stage is same as the conventional stochastic Petri nets with the difference that the steady-state probabilities are obtained parametrically in terms of transition firing rates In the second stage, the transition firing rates are described by triangular fuzzy numbers and then by applying fuzzy mathematics, the fuzzy steady-state probabilities are calculated A numerical example for modeling and analysis of a flexible manufacturing cell is given to show the applicability of proposed method The importance of the proposed approach is that it can take into consideration both dimensions of uncertainty in system modeling, stochastic variability and imprecision
TL;DR: A novel fuzzy-modeling approach is proposed, which is based on a new fuzzy c-regression model (NFCRM) clustering algorithm and is able to determine the right number of rules automatically and is applied in fuzzy modeling of a typical boiler-turbine system successfully.
Abstract: In order to build accurate model for complicated nonlinear system in engineering, like boiler-turbine system, a novel fuzzy-modeling approach is proposed, which is based on a new fuzzy c-regression model (NFCRM) clustering algorithm and is able to determine the right number of rules automatically. In this method, NFCRM is applied to build the fuzzy structure and then identify the premise parameters; a new criterion is proposed to auto determine the number of rules in fuzzy modeling; after the fuzzy rules have been decided, orthogonal least square is exploited to identify the consequent parameters. Simulation examples are given to demonstrate the validity of the proposed modeling approach, and the results show the new approach is very efficient with high accuracy. Finally, the new approach is applied in fuzzy modeling of a typical boiler-turbine system successfully.
TL;DR: The frequent fuzzy pattern tree (fuzzy FP-tree) is proposed for extracting frequent fuzzy itemsets from the transactions with quantitative values and the mining process based on the tree is presented.
Abstract: Due to the increasing occurrence of very large databases, mining useful information and knowledge from transactions is evolving into an important research area. In the past, many algorithms were proposed for mining association rules, most of which were based on items with binary values. Transactions with quantitative values are, however, commonly seen in real-world applications. In this paper, the frequent fuzzy pattern tree (fuzzy FP-tree) is proposed for extracting frequent fuzzy itemsets from the transactions with quantitative values. When extending the FP-tree to handle fuzzy data, the processing becomes much more complex than the original since fuzzy intersection in each transaction has to be handled. The fuzzy FP-tree construction algorithm is thus designed, and the mining process based on the tree is presented. Experimental results on three different numbers of fuzzy regions also show the performance of the proposed approach.
TL;DR: It is shown that the state reduction problem for fuzzy automata is related to the problem of finding a solution to a particular system of fuzzy relation equations in the set of all fuzzy equivalences on its set of states, and an effective procedure is given for computing the greatest right (resp. left) invariant fuzzy equivalence.
TL;DR: A new modified fuzzy linear model form is introduced where the identified model output can envelop all the observed data and ensure a total inclusion property of the model fuzziness independently from the collected data distribution.
TL;DR: In this article, the authors proposed a fuzzy statistical control chart that can explain existing fuzziness in data while considering the essential variability between observations, which avoids defuzzification methods such as fuzzy mean, fuzzy mode, fuzzy midrange, and fuzzy median.
TL;DR: It is proved that the weighted trapezoidal approximation-preserving core is always a fuzzy number and properties of the approximation strategy including translation invariance, scale invariance identity and continuity are discussed.
Abstract: Recently, various researchers have proved that approximations of fuzzy numbers may fail to be fuzzy numbers. In this contribution, we suggest a new weighted trapezoidal approximation of an arbitrary fuzzy number, which preserves its cores. We prove that the weighted trapezoidal approximation-preserving core is always a fuzzy number. We then discuss properties of the approximation strategy including translation invariance, scale invariance identity and continuity. The advantage is that the method presented here is simpler than other methods computationally.
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 crisp inputs, is presented.
Book•
18 Feb 2010
TL;DR: This chapter discusses Regression and Self-regression Models with Fuzzy Coefficients and FuzzY Variables, as well as fuzzy Input-Output Model, and its applications in Linear Programming and Geometric Programming.
Abstract: Prepare Knowledge.- Regression and Self-regression Models with Fuzzy Coefficients.- Regression and Self-regression Models with Fuzzy Variables.- Fuzzy Input-Output Model.- Fuzzy Cluster Analysis and Fuzzy Recognition.- Fuzzy Linear Programming.- Fuzzy Geometric Programming.- Fuzzy Relative Equation and Its Optimizing.- Interval and Fuzzy Differential Equations.- Interval and Fuzzy Functional and their Variation.
TL;DR: A Gentzen-style calculus for the resulting logic is introduced and used to compare the CADIAG-2 system's behaviour with t-norm based fuzzy logics.
01 Jan 2010
TL;DR: The aim of this paper is to present an analytical method for measuring the criticality in a fuzzy project network, where the duration time of each activity is represented by a trapezoidal fuzzy number and applies to the float time (slack time) for each activity in the fuzzy projectnetwork to find the critical path.
Abstract: Critical path method (CPM) techniques have become widely recognized as valuable tools for the planning and scheduling of large projects. The aim of this paper is to present an analytical method for measuring the criticality in a fuzzy project network , where the duration time of each activity is represented by a trapezoidal fuzzy number. In this paper, we use a new defuzzification formula for trapezoidal fuzzy number and apply to the float time (slack time) for each activity in the fuzzy project network to find the critical path. The defuzzification formula used for critical path can not be applied to the trapezoidal fuzzy number having equal elements because that trapezoidal fuzzy number is a crisp number. The proposed method can overcome the drawback of the existing fuzzy CPM method. We use examples to compare our proposed method with the existing method. The comparison reveal that the method proposed in this paper is more effective in determining the activity criticalities and finding the critical path.
TL;DR: The exponential stability of TS fuzzy neural networks with impulsive effect and time-varying delays is investigated and a modified TS fuzzy model is established in which the consequent parts are composed of a set of impulsive neural networks in order to demonstrate the applicability of the result using LMI control toolbox in MATLAB.
TL;DR: An AdaBoost ensemble of relational neuro-fuzzy classifiers is built, resulting in normalization of individual rule bases during learning and is tested on several known benchmarks and compared with other machine learning solutions from the literature.
Abstract: A method frequently used in classification systems for improving classification accuracy is to combine outputs of several classifiers. Among various types of classifiers, fuzzy ones are tempting because of using intelligible fuzzy if-then rules. In the paper we build an AdaBoost ensemble of relational neuro-fuzzy classifiers. Relational fuzzy systems bond input and output fuzzy linguistic values by a binary relation; thus, fuzzy rules have additional, comparing to traditional fuzzy systems, weights — elements of a fuzzy relation matrix. Thanks to this the system is better adjustable to data during learning. In the paper an ensemble of relational fuzzy systems is proposed. The problem is that such an ensemble contains separate rule bases which cannot be directly merged. As systems are separate, we cannot treat fuzzy rules coming from different systems as rules from the same (single) system. In the paper, the problem is addressed by a novel design of fuzzy systems constituting the ensemble, resulting in normalization of individual rule bases during learning. The method described in the paper is tested on several known benchmarks and compared with other machine learning solutions from the literature.
01 Mar 2010
TL;DR: In this paper, the authors proposed two new fuzzy basis function models to increase the capability of FF-LSE by widening the regression matrix with lagged input-output values and using Gaussian membership functions.
Abstract: In this study, auto regressive with exogenous input (ARX) modeling is improved with fuzzy functions concept (FF-ARX). Fuzzy function with least squares estimation (FF-LSE) method has been recently developed and widely used with a small improvement with respect to least squares estimation method (LSE). FF-LSE is structured with only inputs and their membership values. This proposed model aims to increase the capability of the FF-LSE by widening the regression matrix with lagged input-output values. In addition, by using same idea, we proposed also two new fuzzy basis function models. In the first, basis of the fuzzy system and lagged input-output values are structured together in the regression matrix and named as ''L-FBF''. Secondly, instead of using basis function, the membership values of the lagged input-output values are used in the regression matrix by using Gaussian membership functions, called ''M-FBF''. Therefore, the power of the fuzzy basis function is also enhanced. For the corresponding models, antecedent part parameters for the input vectors are determined with fuzzy c-means (FCM) clustering algorithm. The consequent parameters of the all models are estimated with the LSE. The proposed models are utilized and compared for the identification of nonlinear benchmark problems.
TL;DR: A linear programming model based on goal programming is proposed to calculate theregression coefficients that can deal with both symmetric and non-symmetric triangular fuzzy data as well as trapezoidal fuzzy data which have rarely been considered in the previous works.
Abstract: The fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. A linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. In contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstructing the regression model. Furthermore, the model can dealwith both symmetric and non-symmetric triangular fuzzy data as wellas trapezoidal fuzzy data which have rarely been considered in theprevious works. To show the efficiency of the proposed model, somenumerical examples are solved and a simulation study is performed.The computational results are compared with some earlier methods.
TL;DR: It is shown that other types of fuzzy relations, which are closely related to Takagi-Sugeno (T-S) models, are of major interest as well, and these fuzzy relations are based on addition and multiplication only, from which they get the name arithmetic fuzzy models.
Abstract: It is well known that a fuzzy rule base can be interpreted in different ways. From a logical point of view, the conjunctive interpretation is preferred, while from a practical point of view, the disjunctive interpretation has been dominantly present. Each of these interpretations results in a specific fuzzy relation that models the fuzzy rule base. Basic interpolation requirements naturally suggest a corresponding inference mechanism: the direct image for the conjunctive interpretation and the subdirect image for the disjunctive interpretation. Interpolation then corresponds to solvability of some system of fuzzy relational equations. In this paper, we show that other types of fuzzy relations, which are closely related to Takagi-Sugeno (T-S) models, are of major interest as well. These fuzzy relations are based on addition and multiplication only, from which we get the name arithmetic fuzzy models. Under some mild requirements, these fuzzy relations turn out to be solutions of the same systems of fuzzy relational equations. The impact of these results is both theoretical and practical: There exist simple solutions to systems of fuzzy relational equations, other than the extremal solutions that have received all the attention so far, which are, moreover, easy to implement.
08 Nov 2010
TL;DR: Fuzzy Cognitive Maps are fuzzy weighted directed graphs with feedback that create models that emulate the behavior of complex decision processes using fuzzy causal relations and might contribute to the progress of more intelligent and independent control systems.
Abstract: This paper presents Fuzzy Cognitive Maps as an approach in modeling the behavior and operation of complex systems. This technique is the fusion of the advances of the fuzzy logic and cognitive maps theories, they are fuzzy weighted directed graphs with feedback that create models that emulate the behavior of complex decision processes using fuzzy causal relations. There are some applications in diverse domains (manage, multiagent systems, etc.) and novel works (dynamical characteristics, learning procedures, etc.) to improve the performance of these systems. First the description and the methodology that this theory suggests is examined, also some ideas for using this approach in the control process area, and then the implementation of a tool based on Fuzzy Cognitive Maps is described. The application of this theory in the field of control and systems might contribute to the progress of more intelligent and independent control systems. Fuzzy Cognitive Maps have been fruitfully used in decision making and simulation of complex situation and analysis.
01 Jan 2010
TL;DR: This work deals with the problems of the Expremal Fuzzy Continuous Dynamic System (EFCDS) optimization problems and briefly discusses the results developed by G. Sirbiladze [31]–[38].
Abstract: This work deals with the problems of the Expremal Fuzzy Continuous Dynamic System (EFCDS) optimization problems and briefly discuss the results developed by G. Sirbiladze [31]–[38]. The basic properties of extended extremal fuzzy measure are considered and several variants of their representation are given. In considering extremal fuzzy measures, several transformation theorems are represented for extended lower and upper Sugeno integrals. Values of extended extremal conditional fuzzy measures are defined as a levels of an expert knowledge reflections of EFCDS states in the fuzzy time intervals. The notions of extremal fuzzy time moments and intervals are introduced and their monotone algebraic structures that form the most important part of the fuzzy instrument of modeling extremal fuzzy dynamic systems are discussed. New approaches in modeling of EFCDS are developed. Applying the results of [31] and [32], fuzzy processes with possibilistic uncertainty, the source of which is extremal fuzzy time intervals, are constructed. The dynamics of EFCDS’s is described. Questions of the ergodicity of EFCDS’s are considered. Fuzzy-integral representations of controllable extremal fuzzy processes are given. Sufficient and necessary conditions are presented for the existence of an extremal fuzzy optimal control processes, for which we use R. Bellman’s optimality principle and take into consideration the gain-loss fuzzy process. A separate consideration is given to the case where an extremal fuzzy control process acting on the EFCDS does not depend on an EFCDS state. Applying Bellman’s optimality principle and assuming that the gain-loss process exists for the EFCDS, a variant of the fuzzy integral representation of an optimal control is given for the EFCDS. This variant employs the instrument of extended extremal fuzzy composition measures constructed in [32]. An example of constructing of the EFCDS optimal control is presented.