Showing papers on "Fuzzy associative matrix published in 2013"
TL;DR: This paper presents a concise and representative review of the most successful applications of type-2 fuzzy logic in the fields of pattern recognition, classification and clustering.
Abstract: In this paper a review of type-2 fuzzy logic applications in pattern recognition, classification and clustering problems is presented. Recently, type-2 fuzzy logic has gained popularity in a wide range of applications due to its ability to handle higher degrees of uncertainty. In particular, there have been recent applications of type-2 fuzzy logic in the fields of pattern recognition, classification and clustering, where it has helped improving results over type-1 fuzzy logic. In this paper a concise and representative review of the most successful applications of type-2 fuzzy logic in these fields is presented.
134 citations
TL;DR: A weighted fuzzy backward reasoning algorithm, based on WFSN P systems, is developed, which can accomplish dynamic fuzzy reasoning of a rule-based system more flexibly and intelligently.
Abstract: Spiking neural P systems (SN P systems) are a new class of computing models inspired by the neurophysiological behavior of biological spiking neurons. In order to make SN P systems capable of representing and processing fuzzy and uncertain knowledge, we propose a new class of spiking neural P systems in this paper called weighted fuzzy spiking neural P systems (WFSN P systems). New elements, including fuzzy truth value, certain factor, weighted fuzzy logic, output weight, threshold, new firing rule, and two types of neurons, are added to the original definition of SN P systems. This allows WFSN P systems to adequately characterize the features of weighted fuzzy production rules in a fuzzy rule-based system. Furthermore, a weighted fuzzy backward reasoning algorithm, based on WFSN P systems, is developed, which can accomplish dynamic fuzzy reasoning of a rule-based system more flexibly and intelligently. In addition, we compare the proposed WFSN P systems with other knowledge representation methods, such as fuzzy production rule, conceptual graph, and Petri nets, to demonstrate the features and advantages of the proposed techniques.
131 citations
TL;DR: A knowledge-leverage-based Takagi-Sugeno-Kang-type Fuzzy System (KL-TSK-FS), which intends to not only make full use of the data from the current scene in the learning procedure, but also effectively leverage the existing knowledge from the reference scenes.
Abstract: Classical fuzzy system modeling methods consider only the current scene where the training data are assumed to be fully collectable. However, if the data available from the current scene are insufficient, the fuzzy systems trained by using the incomplete datasets will suffer from weak generalization capability for the prediction in the scene. In order to overcome this problem, a knowledge-leverage-based fuzzy system (KL-FS) is studied in this paper from the perspective of transfer learning. The KL-FS intends to not only make full use of the data from the current scene in the learning procedure, but also effectively leverage the existing knowledge from the reference scenes. Specifically, a knowledge-leverage-based Takagi-Sugeno-Kang-type Fuzzy System (KL-TSK-FS) is proposed by integrating the corresponding knowledge-leverage mechanism. The new fuzzy system modeling technique is evaluated through experiments on synthetic and real-world datasets. The results demonstrate that KL-TSK-FS has better performance and adaptability than the traditional fuzzy modeling methods in scenes with insufficient data.
109 citations
TL;DR: A novel evolving Type-2 Mamdani-typed neural fuzzy system that employs a data-driven incremental learning scheme and is ensured a compact and up-to-date fuzzy rule base that is able to model the current underlying dynamics of the environment.
108 citations
01 Jan 2013
TL;DR: In this paper, the fuzzy Laplace transform is expressed and then some of its well-known properties are investigated and an existence theorem is given for fuzzy-valued function which possess the fuzzyLaplace transform.
Abstract: A natural way to model dynamic systems under uncertainty is to use fuzzy initial value problems (FIVPs) and related uncertain systems. In this paper, we express the fuzzy Laplace transform and then some of its well-known properties are investigated. In addition, an existence theorem is given for fuzzy-valued function which possess the fuzzy Laplace transform. Consequently, we investigate the solutions of FIVPs and the solutions in state-space description of fuzzy linear continuous-time systems under generalized H-differentiability as two new applications of fuzzy Laplace transforms. Finally, some examples are given to show the efficiency of the proposed method.
95 citations
TL;DR: Fuzzy programming technique and global criterion method are applied to derive optimal compromise solutions of multi-objectives and corresponding results are compared.
95 citations
20 Jun 2013
TL;DR: A new Gravitational Search Algorithm (GSA) using fuzzy logic to change alpha parameter and give a different gravitation and acceleration to each agent in order to improve its performance is proposed.
Abstract: In this paper we propose a new Gravitational Search Algorithm (GSA) using fuzzy logic to change alpha parameter and give a different gravitation and acceleration to each agent in order to improve its performance, we use this new approach for mathematical functions and present a comparison with original approach.
94 citations
TL;DR: This paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems and develops an approach to stabilization controller design through their stoChastic generalized Takagi-Sugeno (T-S) fuzzy approximation models.
Abstract: This paper investigates the universal fuzzy model and universal fuzzy controller problems for stochastic nonaffine nonlinear systems. The underlying mechanism of stochastic fuzzy logic is first discussed, and a stochastic generalized fuzzy model with new stochastic fuzzy rule base is then given. Based on their function approximation capability, these kinds of stochastic generalized fuzzy models are shown to be universal fuzzy models for stochastic nonaffine nonlinear systems under some sufficient conditions. An approach to stabilization controller design for stochastic nonaffine nonlinear systems is then developed through their stochastic generalized Takagi-Sugeno (T-S) fuzzy approximation models. Then, the results of universal fuzzy controllers for two classes of stochastic nonlinear systems, along with constructive procedures to obtain the universal fuzzy controllers, are also provided, respectively. Finally, a numerical example is presented to illustrate the effectiveness of the proposed approach.
88 citations
TL;DR: This paper investigates the stability of fuzzy-model-based (FMB) control system, formed by a T-S fuzzy model and a fuzzy controller connected in a close loop, based on a fuzzy-Lyapunov function and proposes a membership-function-dependent stability analysis approach.
81 citations
TL;DR: Improvements of recent stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems are proposed to bring together the so-called local transformations of membership functions and new piecewise fuzzy Lyapunov functions.
Abstract: Improvements of recent stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems are proposed. The key idea is to bring together the so-called local transformations of membership functions and new piecewise fuzzy Lyapunov functions. By relying on these special local transformations, the associated linear matrix inequalities that are used to prove the system's stability can be relaxed without increasing the number of conditions. In addition, to enhance the usefulness of the proposed methodology, one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives. A standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases.
TL;DR: Experimental results and theoretical analysis indicate that the proposed VOM2FNN performs better than the other fuzzy neural networks.
Abstract: This paper proposes a vectorization-optimization-method (VOM)-based type-2 fuzzy neural network (VOM2FNN) for noisy data classification. In handling problems with uncertainties, such as noisy data, type-2 fuzzy systems usually outperform their type-1 counterparts. Hence, type-2 fuzzy sets are adopted in the antecedent parts to model the uncertainty. To consider the classification problems, the discriminative capability is crucial to determine the performance. Therefore, a VOM is proposed in the consequent parts to increase the discriminability and reduce the parameters. Compared with other existing fuzzy neural networks, the novelty of the proposed VOM2FNN is its consideration of both uncertainty and discriminability. The effectiveness of the proposed VOM2FNN is demonstrated by three classification problems. Experimental results and theoretical analysis indicate that the proposed VOM2FNN performs better than the other fuzzy neural networks.
TL;DR: The work reported in this paper addresses the challenge of the efficient and accurate defuzzification of discretised generalised type-2 fuzzy sets as created by the inference stage of a Mamdani Fuzzy Inferencing System and finds Vertical Slice Centroid Type-Reduction to be the fastest technique.
TL;DR: Using semi‐tensor product (STP) of matrix, the fuzzy relation of multiple fuzzy is investigated and a new technique is developed to design a coupled fuzzy controller for multi‐input multi‐output (MIMO) systems with coupled multiple fuzzy relations.
Abstract: Using semi-tensor product (STP) of matrix, this paper investigates the fuzzy relation of multiple fuzzy and uses this to design coupled fuzzy control is designed. First of all, under the assumption that the universe of discourse is finite, a fuzzy logical variable can be expressed as a vector, which unifies the expression of elements, subsets, and fuzzy subsets of a universe of discourse. Then, the matrix expression of set mappings is naturally extended to fuzzy sets. Second, based on STP, logic-based matrix addition and product are proposed. These are particulary useful for the calculation of compounded fuzzy relations. Third, a dual fuzzy structure is introduced, which assures the finiteness of the universe of discourse, and is used for fuzzification and defuzzification. Finally, using the results obtained, a new technique is developed to design a coupled fuzzy controller for multi-input multi-output (MIMO) systems with coupled multiple fuzzy relations.
TL;DR: A novel high order fuzzy time series forecasting approach in which multiplicative neuron model is used to define fuzzy relations is proposed in order to reach high forecasting level and it is observed that the proposed approach gives the best forecasts for Taiwan future exchange time series.
Abstract: Determination of fuzzy logic relationships between observations is quite effective on the forecasting performance of fuzzy time series approaches. In various studies available in the literature, it has been seen that utilizing artificial neural networks for establishing fuzzy relations increase the forecasting accuracy. In this study, a novel high order fuzzy time series forecasting approach in which multiplicative neuron model is used to define fuzzy relations is proposed in order to reach high forecasting level. Also, particle swarm optimization method is utilized to train multiplicative neuron model. In order to show forecasting performance of the proposed method, it is applied to a well-known data Taiwan future exchange and the results produced by the proposed approach is compared to those obtained from other fuzzy time series forecasting models. As a result of the implementation, it is observed that the proposed approach gives the best forecasts for Taiwan future exchange time series.
TL;DR: This paper casts the Takagi-Sugeno (T-S) fuzzy system identification into a hierarchical sparse representation problem, where the goal is to establish a T-S fuzzy system with a minimal number of fuzzy rules, which simultaneously have a minimum number of nonzero consequent parameters.
Abstract: “The curse of dimensionality” has become a significant bottleneck for fuzzy system identification and approximation. In this paper, we cast the Takagi-Sugeno (T-S) fuzzy system identification into a hierarchical sparse representation problem, where our goal is to establish a T-S fuzzy system with a minimal number of fuzzy rules, which simultaneously have a minimal number of nonzero consequent parameters. The proposed method, which is called hierarchical sparse fuzzy inference systems ( H-sparseFIS), explicitly takes into account the block-structured information that exists in the T-S fuzzy model and works in an intuitive way: First, initial fuzzy rule antecedent part is extracted automatically by an iterative vector quantization clustering method; then, with block-structured sparse representation, the main important fuzzy rules are selected, and the redundant ones are eliminated for better model accuracy and generalization performance; moreover, we simplify the selected fuzzy rules consequent with sparse regularization such that more consequent parameters can approximate to zero. This algorithm is very efficient and shows good performance in well-known benchmark datasets and real-world problems.
TL;DR: By using 1-knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study, and which might be also perceived as a generalization of the trapezoidal approximation.
TL;DR: The concept of Alpha-matrix games is introduced and it is proved that players' fuzzy values are always identical, and hereby, any matrix game with payoffs expressed by TrFNs has a fuzzy value, which is also a TrFN.
Abstract: Of the different types of games, the matrix games with fuzzy payoffs have been extensively discussed. Two major kinds of solution methods have been devised. One is the defuzzification approach based on ranking functions. Another is the two-level linear programming method which can obtain membership functions of players' fuzzy values (or gain floor and loss ceiling). These methods cannot always ensure that players' fuzzy/defuzzified values have a common value. The aim of this paper is to develop an effective methodology for solving matrix games with payoffs expressed by trapezoidal fuzzy numbers (TrFNs). In this methodology, we introduce the concept of Alpha-matrix games and prove that players' fuzzy values are always identical, and hereby, any matrix game with payoffs expressed by TrFNs has a fuzzy value, which is also a TrFN. The upper and lower bounds of any Alpha-cut of the fuzzy value and the players' optimal strategies are easily obtained through solving the derived four linear programming problems with the upper and lower bounds of Alpha-cuts of the fuzzy payoffs. In particular, the fuzzy value can be explicitly estimated through solving the auxiliary linear programming with data taken from the 1-cut and 0-cut of the fuzzy payoffs. The proposed method in this paper is illustrated with a real example and compared with other methods to show validity and applicability.
TL;DR: Comparison with non-hybrid interval A1-C0 type-1 Takagi-Sugeno-Kang fuzzy logic systems shows that the proposed hybrid mechanism is a well-performing non-linear adaptive method that enables the interval type-2 fuzzy model to match an unknown non- linear mapping and to converge very fast.
TL;DR: This paper proposes the creation of a new paradigm for fuzzy system comprehensibility analysis based on fuzzy systems' inference maps, so-called fuzzy inference-grams (fingrams), by analogy with scientograms used for visualizing the structure of science.
Abstract: Since Zadeh's proposal and Mamdani's seminal ideas, interpretability is acknowledged as one of the most appreciated and valuable characteristics of fuzzy system identification methodologies. It represents the ability of fuzzy systems to formalize the behavior of a real system in a human understandable way, by means of a set of linguistic variables and rules with a high semantic expressivity close to natural language. Interpretability analysis involves two main points of view: readability of the knowledge base description (regarding complexity of fuzzy partitions and rules) and comprehensibility of the fuzzy system (regarding implicit and explicit semantics embedded in fuzzy partitions and rules, as well as the fuzzy reasoning method). Readability has been thoroughly treated by many authors who have proposed several criteria and metrics. Unfortunately, comprehensibility has usually been neglected because it involves some cognitive aspects related to human reasoning, which are very hard to formalize and to deal with. This paper proposes the creation of a new paradigm for fuzzy system comprehensibility analysis based on fuzzy systems' inference maps, so-called fuzzy inference-grams (fingrams), by analogy with scientograms used for visualizing the structure of science. Fingrams show graphically the interaction between rules at the inference level in terms of co-fired rules, i.e., rules fired at the same time by a given input. The analysis of fingrams offers many possibilities: measuring the comprehensibility of fuzzy systems, detecting redundancies and/or inconsistencies among fuzzy rules, identifying the most significant rules, etc. Some of these capabilities are explored in this study for the case of fuzzy models and classifiers.
TL;DR: This paper shows that for implicative fuzzy models, the non-monotonicity problem can be circumvented by making explicit the semantics of the fuzzy rules by subjecting the antecedent and consequent fuzzy sets to the at-least and/or at-most modifiers.
01 Sep 2013
TL;DR: This work provides a reasoning algorithm for the family of operators that are representable using a Mixed Integer Linear Programming optimization problem and shows how to encode some examples of aggregation operators using the language Fuzzy OWL 2.
Abstract: Fuzzy ontologies extend classical ontologies to allow the representation of imprecise and vague knowledge. Although a relatively important amount of work has been carried out in the field during the last years and they have been successfully used in several applications, several notions from fuzzy logic have not been considered yet in fuzzy ontologies. Among them are aggregation operators, mathematical functions used to fuse different pieces of information, which is a very common need. Some examples of aggregation operators are weighted sums, Ordered Weighting Averaging operators and fuzzy integrals. In this work, we integrate fuzzy ontologies and aggregation operators. As a theoretical formalism, we provide the syntax and semantics of a fuzzy Description Logic with fuzzy aggregation operators. We provide a reasoning algorithm for the family of operators that are representable using a Mixed Integer Linear Programming optimization problem. We also show how to encode some examples of aggregation operators using the language Fuzzy OWL 2.
TL;DR: The solution of fuzzy linear controlled sys- tem with fuzzy initial conditions is found by using -cuts and presentation of numbers in a more compact form by moving to the eld of complex numbers.
Abstract: In this article we found the solution of fuzzy linear controlled sys- tem with fuzzy initial conditions by using -cuts and presentation of numbers in a more compact form by moving to the eld of complex numbers Next, a fuzzy optimal control problem for a fuzzy system is considered to optimize the expected value of a fuzzy objective function Based on Pontryagin Maximum Principle, a constructive equation for the problem is presented In the last section, three examples are used to show that the method in eective to solve fuzzy and fuzzy optimal linear controlled systems
TL;DR: Simulation results indicate that this neuro-fuzzy computing system can be a good candidate to be used for creating artificial brain and all synaptic weights in this method are always non-negative, and there is no need to adjust them precisely.
Abstract: In this paper, a novel neuro-fuzzy computing system is proposed where its learning is based on the creation of fuzzy relations by using a new implication method without utilizing any exact mathematical techniques. Then, a simple memristor crossbar-based analog circuit is designed to implement this neuro-fuzzy system which offers very interesting properties. In addition to high connectivity between neurons and being fault tolerant, all synaptic weights in our proposed method are always non-negative, and there is no need to adjust them precisely. Finally, this structure is hierarchically expandable, and it can do fuzzy operations in real time since it is implemented through analog circuits. Simulation results confirm the efficiency and applicability of our neuro-fuzzy computing system. They also indicate that this system can be a good candidate to be used for creating artificial brain.
TL;DR: A genetic algorithm (GA)-based solution is described that uses the flexible nature of the 2-tuple linguistic representation to discover rules that occur at the intersection of fuzzy set boundaries that were lost with the traditional approach.
Abstract: In Web usage mining, fuzzy association rules that have a temporal property can provide useful knowledge about when associations occur. However, there is a problem with traditional temporal fuzzy association rule mining algorithms. Some rules occur at the intersection of fuzzy sets' boundaries where there is less support (lower membership), so the rules are lost. A genetic algorithm (GA)-based solution is described that uses the flexible nature of the 2-tuple linguistic representation to discover rules that occur at the intersection of fuzzy set boundaries. The GA-based approach is enhanced from previous work by including a graph representation and an improved fitness function. A comparison of the GA-based approach with a traditional approach on real-world Web log data discovered rules that were lost with the traditional approach. The GA-based approach is recommended as complementary to existing algorithms, because it discovers extra rules.
TL;DR: By aggregating conjugate fuzzy implications it is shown that an I"A fuzzy implication can be preserved by action of an order automorphism and a family I of fuzzy implications is introduced.
TL;DR: Motivations for introducing the extended class of convex fuzzyNumbers, for convex as well for ordered fuzzy numbers, are presented, together with operations on them.
Abstract: Defuzzification functionals, which play the main role when dealing with fuzzy controllers and fuzzy inference systems, for convex as well for ordered fuzzy numbers, are discussed. Three characteristic conditions for them are formulated. It is shown that most of the known defuzzification functionals satisfy them. Motivations for introducing the extended class of convex fuzzy numbers are presented, together with operations on them.
TL;DR: It is shown that subsystems, reverse subsystems and double subsystems of a fuzzy transition system T form both closure and opening systems in the lattice of fuzzy subsets of A, where A is the set of states of T, and efficient procedures for computing related closures and openings of an arbitrary fuzzy subset of A are provided.
Abstract: In this paper we study subsystems, reverse subsystems and double subsystems of a fuzzy transition system. We characterize them in terms of fuzzy relation inequalities and equations, as eigen fuzzy sets of the fuzzy quasi-order Q"@d and the fuzzy equivalence E"@d generated by fuzzy transition relations, and as linear combinations of aftersets and foresets of Q"@d and equivalence classes of E"@d. We also show that subsystems, reverse subsystems and double subsystems of a fuzzy transition system T form both closure and opening systems in the lattice of fuzzy subsets of A, where A is the set of states of T, and we provide efficient procedures for computing related closures and openings of an arbitrary fuzzy subset of A. These procedures boil down to computing the fuzzy quasi-order Q"@d or the fuzzy equivalence E"@d, which can be efficiently computed using the well-known algorithms for computing the transitive closure of a fuzzy relation.
TL;DR: The existence of solution of FLS is proved in details and some numerical examples are solved to illustrate the accuracy and capability of the method.
01 Apr 2013
TL;DR: Some new numerical methods to solve a fully fuzzy linear system (FFLS) with triangular fuzzy numbers of the form m, alpha, beta so as to widen the scope of fuzzy linear systems in scientific applications.
Abstract: In this paper, we discuss some new numerical methods to solve a fully fuzzy linear system (FFLS) with triangular fuzzy numbers of the form $$ ( {m,\alpha ,\beta }) $$ . Almost every existing method that intends to solve a FFLS confines the coefficient matrix and the solutions to be non-negative fuzzy numbers. The main intent of the proposed methods is to remove these restrictions and widen the scope of fuzzy linear systems in scientific applications. The methods are illustrated with the help of numerical examples and are conceptually easy to understand and apply in real life situations.