Showing papers on "Fuzzy associative matrix published in 2016"

Control Synthesis of Discrete-Time T–S Fuzzy Systems via a Multi-Instant Homogenous Polynomial Approach

Abstract: This paper deals with the problem of control synthesis of discrete-time Takagi–Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.

Feature subset selection based on fuzzy neighborhood rough sets

Abstract: Rough set theory has been extensively discussed in machine learning and pattern recognition. It provides us another important theoretical tool for feature selection. In this paper, we construct a novel rough set model for feature subset selection. First, we define the fuzzy decision of a sample by using the concept of fuzzy neighborhood. A parameterized fuzzy relation is introduced to characterize fuzzy information granules for analysis of real-valued data. Then, we use the relationship between fuzzy neighborhood and fuzzy decision to construct a new rough set model: fuzzy neighborhood rough set model. Based on this model, the definitions of upper and lower approximation, boundary region and positive region are given, and the effects of parameters on these concepts are discussed. To make the new model tolerate noises in data, we introduce a variable-precision fuzzy neighborhood rough set model. This model can decrease the possibility that a sample is classified into a wrong category. Finally, we define the dependency between fuzzy decision and condition attributes and employ the dependency to evaluate the significance of a candidate feature, using which a greedy feature subset selection algorithm is designed. The proposed algorithm is compared with some classical algorithms. The experiments show that the proposed algorithm gets higher classification performance and the numbers of selected features are relatively small.

Mathematical Principles Of Fuzzy Logic

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An improved sobel edge detection method based on generalized type-2 fuzzy logic

Abstract: Edge detectors have traditionally been an essential part of many computer vision systems. There are different methods that have been proposed for improving edge detection in real images. This paper proposes an edge detection method based on the Sobel technique and generalized type-2 fuzzy logic systems. To limit the complexity of handling generalized type-2 fuzzy logic, the theory of $$\alpha $$?-planes is used. Simulation results are obtained with the Sobel operator (without fuzzy logic), then with a type-1 fuzzy logic system (T1FLS), an interval type-2 fuzzy logic system (IT2FLS) and with a generalized type-2 fuzzy logic system (GT2FLS). The proposed generalized type-2 fuzzy edge detection method is tested with synthetic images with promising results. To illustrate the advantages of using generalized type-2 fuzzy logic in combination with the Sobel operator, the figure of merit of Pratt measure is applied to measure the accuracy of the edge detection process.

Adaptive Fuzzy Control of Spacecraft Proximity Operations Using Hierarchical Fuzzy Systems

Abstract: The six-degrees-of-freedom relative motion control of a chaser spacecraft approaching a free tumbling target in deep space is investigated in this paper. In view of unknown model uncertainties and complex dynamic couplings in the dynamical model, a direct adaptive fuzzy nonlinear controller is constructed by using fuzzy logic systems to approximate the uncertainties and couplings, where the parameter vectors of fuzzy systems are estimated online by using a projection-based adaptive control method. Due to the great dimension of the system variables, hierarchical fuzzy logic systems are employed in the fuzzy control to reduce the amount of fuzzy rules and alleviate the online computation burden in the proposed control algorithm. It is proved that tracking errors of the chaser spacecraft and adaptive parameters of the fuzzy systems are uniformly ultimately bounded. Numerical simulations are performed to demonstrate the performance of the proposed control strategy.

Faces and dual of m-polar fuzzy planar graphs

Abstract: Recently, Ghorai and Pal (12) introduced the notion of m-polar fuzzy planar graphs using the concept of m-polar fuzzy multisets. In this paper, m-polar fuzzy faces and strong m-polar fuzzy faces are defined. Then m-polar fuzzy dual graph of an m-polar fuzzy planar graph is introduced with example. Some isomorphism properties of m-polar fuzzy planar graphs are also studied.

A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters

Abstract: Several methods currently exist for solving fuzzy linear programming problems under nonnegative fuzzy variables and restricted fuzzy coefficients. However, due to the limitation of these methods, they cannot be applied for solving fully fuzzy linear programming (FFLP) with unrestricted fuzzy coefficients and fuzzy variables. In this paper a new efficient method for FFLP has been proposed, in order to obtain the fuzzy optimal solution with unrestricted variables and parameters. This proposed method is based on crisp nonlinear programming and has a simple structure. To show the efficiency of our proposed method some numerical examples have been illustrated.

Fuzzy Optimal Solution of Fully Fuzzy Linear Programming Problems with Equality Constrains

Abstract: In this chapter, the limitations of the method, presented in Chap. 2, are pointed out and to overcome these limitations, Kaur and Kumar’s method [1] is presented for solving fully fuzzy linear programming problems with equality constraints. To show the application of Kaur and Kumar’s method [1] a real life problem, which cannot be solved by using the method, presented in Chap. 2, is solved by using the Kaur and Kumar’s method [1].

A New Hybrid Fault Diagnostic Method for Combining Dependency Matrix Diagnosis and Fuzzy Diagnosis Based on an Enhanced Inference Operator

Abstract: This paper is devoted to the fault diagnosis of electronic systems by combining logical signals, such as built-in test output, and analog signals, such as voltage, current and temperature. First, the basic inference principles of dependency matrix (D matrix) diagnosis and fuzzy diagnosis are introduced, and the characteristics of their inference operators are summarized. Then, the similarities and differences between the two diagnostic methods are analyzed. Based on the judgement of close degree, a new enhanced inference operator is defined to suit both the D matrix and the fuzzy relation matrix (R matrix). A DR matrix is defined to describe the mixed relationships between faults and the two types of signals. Based on the enhanced inference operator and the DR matrix, a new hybrid diagnostic method is established. Finally, a signal modulating circuit is used to verify the effectiveness of the enhanced inference operator on the D matrix, the R matrix and the DR matrix, which demonstrates the high efficiency of the enhanced inference operator and the feasibility of the new hybrid diagnostic method.

Extended Fuzzy Logic: Sets and Systems

Abstract: The concepts of sets and approximate reasoning within extended fuzzy logic (FLe) provide a systematic procedure for transforming unprecisiated knowledge into a nonlinear mapping over what we define here as f -sets. An f -set differs from a fuzzy set in that it is associated with the restriction of validity in addition to that of possibility. Therefore, by f -set, we can simultaneously deal with two different types of uncertainties: one that is related to ill-known objects represented by incomplete information—information with its one or more aspects being imprecise/vague/partial/nonspecific/undetermined—and another that is related to truth values considering gradualness. Here, we define new concepts of $\vartheta $ -cuts and $\alpha \vartheta $ -cuts, introduce the f -extension principle, and consider arithmetic computations within FLe. We then address other aspects of the proposed FLe system such as fuzzification and validification operations in input processing stage, set-conversion and defuzzification in output processing stage, and inferencing. In fact, in this paper, we intend to develop FLe theoretically and practically from the stands of sets and systems to extend the concept of approximate reasoning. As a consequence of this development, we assert that considering the validity degree of methods and information can lead to more reasonable and trustworthy results through capturing more uncertainty.

Cooperative Fuzzy Model-Predictive Control

Abstract: In this paper, a cooperative fuzzy model-predictive control (CFMPC) is presented. The overall nonlinear plant is assumed to consist of several parallel input-coupled Takagi–Sugeno (T–S) fuzzy models. Each such T–S fuzzy subsystem is represented in the form of a local linear model network (LLMN). The control of each local linear model in each LLMN is realized by model-predictive control (MPC). For each LLMN, the outputs of the associated MPCs are blended by the fuzzy membership functions, which leads to a fuzzy model-predictive controller (FMPC). The resulting structure is one FMPC for each LLMN subsystem. Overall, a parallel combination of FMPCs results, which mutually affects all LLMN subsystems by their respective manipulated variables. To compensate detrimental cross-couplings in this setup, a cooperation between the FMPCs is introduced. For this cooperation, convergence is proven, and for the closed-loop system, a stability proof is given. It is demonstrated in a simulation example that the proposed input-constraint CFMPC algorithm achieves convergence of the fuzzy LLMNs within few cooperative iteration steps. Simulations are given to demonstrate the effectiveness of the theoretical results.

Mining fuzzy temporal association rules by item lifespans

Abstract: We propose a fuzzy temporal association rule mining algorithm (FTARM).Information inside transactions can be found correctly by using lifespan of items.Three datasets are used to show the FTARM is effective.Experiments show that FTARM can derive more rules than FAR.The derived rules are better than FAR in terms of supports and confidences. Data mining is the process of extracting desirable knowledge or interesting patterns from existing databases for specific purposes. In real-world applications, transactions may contain quantitative values and each item may have a lifespan from a temporal database. In this paper, we thus propose a data mining algorithm for deriving fuzzy temporal association rules. It first transforms each quantitative value into a fuzzy set using the given membership functions. Meanwhile, item lifespans are collected and recorded in a temporal information table through a transformation process. The algorithm then calculates the scalar cardinality of each linguistic term of each item. A mining process based on fuzzy counts and item lifespans is then performed to find fuzzy temporal association rules. Experiments are finally performed on two simulation datasets and the foodmart dataset to show the effectiveness and the efficiency of the proposed approach.

Design of rule-based models through information granulation

Abstract: Exploration of Fuzzy Rule generation using hierarchical clusteringDevelopment of granular rule conclusions with real valued intervalsDefinition of performance metrics for granular models for the assessment of model performanceDemonstration of the effectiveness of granular rule conclusions for modeling of real world dataComparison of hierarchical methods to Fuzzy C-Means when generating rule based models In this study, we explore the combination of two well defined topics in fuzzy systems research: fuzzy rule based systems, and information granulation. Rule based systems are a powerful and well-studied form of knowledge representation, due to their approximation abilities and interpretability. In recent years, these types of systems have become increasingly powerful with regards to modeling accuracy; however, many of these improvements come at the cost of model interpretability. This recent direction of research has left an unexplored avenue towards the generation of increasingly interpretable fuzzy rule based models, which we intend to explore. Information granulation is a relatively new, yet very promising area of research in human centric systems. As a form of knowledge representation, information granulation is very well suited to fuzzy rule based systems, where rules represent linguistic quantities in a, intuitively understandable format. It is notable that the combination of these two concepts has been left largely unstudied. We aim to explore this union by defining a methodology for the construction of a partially granular fuzzy rule based model. The aim of this novel model format is to provide a first step in the improvement of fuzzy model interpretability, through the use of information granulation. We are additionally interested in studying new ways of generating fuzzy rules; hence, we will also look at the use of hierarchical clustering as a potential alternative to the tried and tested Fuzzy C Means clustering algorithm. The models created using hierarchical clustering are then compared with those generated using Fuzzy C Means to evaluate the effectiveness of this algorithm. As a result of these experiments, we demonstrate that partially granular fuzzy rules are capable of providing a significant improvement to fuzzy rule interpretability, and we believe that granular fuzzy models present an exciting avenue of future research in human centric systems.

Entropy of Fuzzy Partitions and Entropy of Fuzzy Dynamical Systems

Abstract: In the paper we define three kinds of entropy of a fuzzy dynamical system using different entropies of fuzzy partitions. It is shown that different definitions of the entropy of fuzzy partitions lead to different notions of entropies of fuzzy dynamical systems. The relationships between these entropies are studied and connections with the classical case are mentioned as well. Finally, an analogy of the Kolmogorov–Sinai Theorem on generators is proved for fuzzy dynamical systems.

A genetic algorithm‐optimized fuzzy logic controller to avoid rear‐end collisions

Abstract: Summary In this paper, a rear-end collision control model is proposed using the fuzzy logic control scheme. Through detailed analysis of car-following cases, our fuzzy control system is established with reasonable control rules. Furthermore, a genetic algorithm is introduced into the fuzzy rules refining process to reduce the computational complexity while maintaining accuracy. Numerical results indicate that our genetic algorithm-optimized fuzzy logic controller outperforms the traditional fuzzy logic controller in terms of better safety guarantee and higher traffic efficiency. Copyright © 2016 John Wiley & Sons, Ltd.

Relationships Between Two Types of Intuitionistic Fuzzy Definite Integrals

Abstract: Intuitionistic fuzzy numbers (IFNs) are the basic components of Atanassov's intuitionistic fuzzy sets, which are very convenient and comprehensive in depicting the fuzzy characters of things in real life. In the existing literature, there are mainly two different types of definite integrals with respect to IFNs, which were developed from completely different aspects. The main purpose of this paper is to demonstrate their relationships in detail by deriving the definite integrals of two novel intuitionistic fuzzy functions. It is worth pointing out that one of the two types of definite integrals is shown to be a special case of another one, and finally, we also derive some other useful results for intuitionistic fuzzy calculus based on the division derivative.

Type-2 Fuzzy Neural Networks

Abstract: The two most common artificial intelligence techniques, FLSs and ANNs, can be used in the same structure simultaneously, namely as “fuzzy neural networks.” The advantages of ANNs such as learning capability from input-output data, generalization capability, and robustness and the advantages of fuzzy logic theory such as using expert knowledge are harmonized in FNNs. In this chapter, type-1 and type-2 TSK fuzzy logic models are introduced. Instead of using fuzzy sets in the consequent part (as in Mamdani models), the TSK model uses a function of the input variables. The order of the function determines the order of the model, e.g., zeroth-order TSK model, first-order TSK model, etc.