Showing papers on "Fuzzy associative matrix published in 2009"
TL;DR: In this paper, the concept of fuzzy soft group is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied, including fuzzy soft function and fuzzy soft homomorphism.
Abstract: In this paper, the concept of fuzzy soft group is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied. Furthermore, definitions of fuzzy soft function and fuzzy soft homomorphism are defined and the theorems of homomorphic image and homomorphic pre-image are given. After that, the definition of normal fuzzy soft group is given and some of its basic properties are studied.
261 citations
TL;DR: This paper investigates the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval- values of IVIFN, and the information about attribute weights is partially known.
245 citations
TL;DR: The concept of the symmetric triangular fuzzy number is used and an approach to defuzzify a general fuzzy quantity is introduced and the FFLP transform to multi objective linear programming (MOLP) where all variables and parameters are crisp.
224 citations
TL;DR: A new rule-refinement scheme is proposed that is based on the maximization of fuzzy entropy on the training set, which is expected to have the advantages of improving the generalization capability of initial fuzzy IF-THEN rules and simultaneously overcoming the overfitting of refinement.
Abstract: When fuzzy IF-THEN rules initially extracted from data have not a satisfying performance, we consider that the rules require refinement. Distinct from most existing rule-refinement approaches that are based on the further reduction of training error, this paper proposes a new rule-refinement scheme that is based on the maximization of fuzzy entropy on the training set. The new scheme, which is realized by solving a quadratic programming problem, is expected to have the advantages of improving the generalization capability of initial fuzzy IF-THEN rules and simultaneously overcoming the overfitting of refinement. Experimental results on a number of selected databases demonstrate the expected improvement of generalization capability and the prevention of overfitting by a comparison of both training and testing accuracy before and after the refinement.
222 citations
TL;DR: The relation between strong paths and strongest paths in a fuzzy graph is analyzed and characterizations for fuzzy bridges, fuzzy trees and fuzzy cycles are obtained using the concept of @a-strong, @b-strong and @d-arcs.
219 citations
TL;DR: This paper presents a method to construct interval-valued fuzzy sets from a matrix, in such a way that the length of the interval representing the membership of any element to the new set is obtained from the differences between the values assigned to that element and its neighbors in the starting matrix.
212 citations
TL;DR: A new proposed approach, which uses feed forward neural networks to define fuzzy relation in high order fuzzy time series, is introduced and it is found that the proposed method produces better forecasts than the other methods.
Abstract: A given observation in time series does not only depend on preceding one but also previous ones in general. Therefore, high order fuzzy time series approach might obtain better forecasts than does first order fuzzy time series approach. Defining fuzzy relation in high order fuzzy time series approach are more complicated than that in first order fuzzy time series approach. A new proposed approach, which uses feed forward neural networks to define fuzzy relation in high order fuzzy time series, is introduced in this paper. The new proposed approach is applied to well-known enrollment data for the University of Alabama and obtained results are compared with other methods proposed in the literature. It is found that the proposed method produces better forecasts than the other methods.
163 citations
TL;DR: Some of the sources of conservativeness of fuzzy control designs based on the linear vertex models instead of the original nonlinear equations are reviewed and ideas that may overcome some of the Conservativeness issues (but increasing computational requirements) are discussed.
153 citations
01 Jan 2009
TL;DR: This book presents an uncertainty modeling approach using a new type of fuzzy system model via "Fuzzy Functions", which may be a reference for some related methodologies to most researchers on fuzzy systems analyses.
146 citations
01 Oct 2009
TL;DR: A new fuzzy control scheme with local nonlinear feedbacks is proposed, and the corresponding control synthesis conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs).
Abstract: This paper is concerned with the problem of designing fuzzy controllers for a class of nonlinear dynamic systems. The considered nonlinear systems are described by T-S fuzzy models with nonlinear local models, and the fuzzy models have fewer fuzzy rules than conventional T-S fuzzy models with local linear models. A new fuzzy control scheme with local nonlinear feedbacks is proposed, and the corresponding control synthesis conditions are given in terms of solutions to a set of linear matrix inequalities (LMIs). In contrast to the existing methods for fuzzy control synthesis, the new proposed control design method is based on fewer fuzzy rules and less computational burden. Moreover, the local nonlinear feedback laws in the new fuzzy controllers are also helpful in achieving good control effects. Numerical examples are given to illustrate the effectiveness of the proposed method.
141 citations
TL;DR: The concept of a mapping on classes of fuzzySoft sets is defined and the properties of fuzzy soft images and fuzzy soft inverse images of fuzzysoft sets are studied.
Abstract: We define the concept of a mapping on classes of fuzzy soft sets and study the properties of fuzzy soft images and fuzzy soft inverse images of fuzzy soft sets, and support them with examples and counterexamples.
TL;DR: The fuzzy concept is used to design a two-step color image filter cascading a fuzzy rule-based switching impulse noise filter by a fuzzy average filtering over the same fuzzypeer , which leads to computational savings.
Abstract: The peer group of an image pixel is a pixel similarity-based concept which has been successfully used to devise image denoising methods. However, since it is difficult to define the pixel similarity in a crisp way, we propose to represent this similarity in fuzzy terms. In this paper, we introduce the fuzzy peer group concept, which extends the peer group concept in the fuzzy setting. A fuzzy peer group will be defined as a fuzzy set that takes a peer group as support set and where the membership degree of each peer group member will be given by its fuzzy similarity with respect to the pixel under processing. The fuzzy peer group of each image pixel will be determined by means of a novel fuzzy logic-based procedure. We use the fuzzy peer group concept to design a two-step color image filter cascading a fuzzy rule-based switching impulse noise filter by a fuzzy average filtering over the fuzzy peer group. Both steps use the same fuzzy peer group, which leads to computational savings. The proposed filter is able to efficiently suppress both Gaussian noise and impulse noise, as well as mixed Gaussian-impulse noise. Experimental results are provided to show that the proposed filter achieves a promising performance.
27 Feb 2009-World Academy of Science, Engineering and Technology, International Journal of Computer, Electrical, Automation, Control and Information Engineering
TL;DR: To analyze the fuzzy system reliability, the reliability of each component of the system as a triangular intuitionistic fuzzy number is considered and their arithmetic operations are introduced.
Abstract: In general fuzzy sets are used to analyze the fuzzy system reliability. Here intuitionistic fuzzy set theory for analyzing the fuzzy system reliability has been used. To analyze the fuzzy system reliability, the reliability of each component of the system as a triangular intuitionistic fuzzy number is considered. Triangular intuitionistic fuzzy number and their arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system and a parallel system following triangular intuitionistic fuzzy numbers have been described. Here an imprecise reliability model of an electric network model of dark room is taken. To compute the imprecise reliability of the above said system, reliability of each component of the systems is represented by triangular intuitionistic fuzzy numbers. Respective numerical example is presented. Keywords—Fuzzy set, Intuitionistic fuzzy number, System reliability, Triangular intuitionistic fuzzy number.
TL;DR: The significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets, and a decision paradigm called the method of least commitment is introduced.
Abstract: We first discuss the significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets We then consider the extension to intuitionistic fuzzy subsets of a number of ideas from standard fuzzy subsets In particular we look at the measure of specificity We also look at the problem of alternative selection when decision criteria satisfaction is expressed using intuitionistic fuzzy subsets We introduce a decision paradigm called the method of least commitment We briefly look at the problem of defuzzification of intuitionistic fuzzy subsets
TL;DR: This paper investigates some logical properties and shows the decidability of a fuzzy extension of the logic SROIQ, theoretical basis of the language OWL 1.1, by providing a reasoning preserving procedure to obtain a crisp representation for it.
TL;DR: The switching relation between type-2 fuzzy sets and intuitionistic fuzzy sets is defined axiomatically, and the switching results are applied to show the usefulness of the proposed method in pattern recognition and medical diagnosis reasoning.
Abstract: When dealing with vagueness, there are situations when there is insufficient information available, making it impossible to satisfactorily evaluate membership. The intuitionistic fuzzy set theory is more suitable than fuzzy sets to deal with such problem. In 1996, Atanassov proposed the mapping from intuitionistic fuzzy sets to fuzzy sets. Furthermore, intuitionistic fuzzy sets are isomorphic to interval valued fuzzy sets, and interval valued fuzzy sets are regarded as the special cases of type-2 fuzzy sets in recently studies. However, their discussions are not only hardly comprehending but also lacking the reliable applications. In this study, the advantage of type-2 fuzzy sets is employed, and the switching relation between type-2 fuzzy sets and intuitionistic fuzzy sets is defined axiomatically. The switching results are applied to show the usefulness of the proposed method in pattern recognition and medical diagnosis reasoning.
TL;DR: It is shown that the proposed variable input partitioning leads to a flexible decision making framework and fairly accurate results with a small number of rules and a simple, fast and robust training process.
01 Sep 2009
TL;DR: The implementation and tests of the method for response integration in multi-net neural systems using interval type-2 fuzzy logic and fuzzy integrals are shown to be a tool that can improve the results of a neural system by facilitating the representation of human perceptions.
Abstract: In this paper we present a method for response integration in multi-net neural systems using interval type-2 fuzzy logic and fuzzy integrals, with the purpose of improving the performance in the solution of problems with a great volume of information. The method can be generalized for pattern recognition and prediction problems, but in this work we show the implementation and tests of the method applied to the face recognition problem using modular neural networks. In the application we use two interval type-2 fuzzy inference systems (IT2-FIS); the first IT2-FIS was used for feature extraction in the training data, and the second one to estimate the relevance of the modules in the multi-net system. Fuzzy logic is shown to be a tool that can help improve the results of a neural system by facilitating the representation of human perceptions.
TL;DR: The main purpose of the present paper is to determine the @a-, @b- and @c-duals of the classical sets of sequences of fuzzy numbers and is to give the necessary and sufficient conditions on an infinite matrix of fuzzyNumbers transforming one of the Classical sets to the another one.
Abstract: The convergence of a series of fuzzy sets was examined via Zadeh's Extension Principle by M. Stojakovic and Z. Stojakovic [M. Stojakovic, Z. Stojakovic, Addition and series of fuzzy sets, Fuzzy Sets and Systems 83 (1996), 341-346]. Since the utilization of this approach is quite difficult in practice, we prefer the idea of using the sum of the series of @l-level sets. The main purpose of the present paper is to determine the @a-, @b- and @c-duals of the classical sets of sequences of fuzzy numbers and is to give the necessary and sufficient conditions on an infinite matrix of fuzzy numbers transforming one of the classical sets to the another one.
01 Jan 2009
TL;DR: This work considers two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems, and develops fuzzy primal simplex algorithms for solving these problems.
Abstract: Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. We consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.
TL;DR: The results show that the proposed schemas and models perform very well in selecting feature set and can improve accuracy in diagnosing both the rolling element bearing and electrical motor faults.
TL;DR: The proposed weighted fuzzy interpolative reasoning method performs better than the ones obtained by the traditional fuzzy inference system, Huang and Shen's method, and Chen and Ko's method.
Abstract: In this paper, we present a new weighted fuzzy interpolative reasoning method for sparse fuzzy rule-based systems. The proposed method uses weighted increment transformation and weighted ratio transformation techniques to handle weighted fuzzy interpolative reasoning in sparse fuzzy rule-based systems. It allows each variable that appears in the antecedent parts of fuzzy rules to associate with a weight between zero and one. Moreover, we also propose an algorithm that automatically tunes the optimal weights of the antecedent variables appearing in the antecedent parts of fuzzy rules. We also apply the proposed weighted fuzzy interpolative reasoning method to handle the truck backer-upper control problem. The proposed weighted fuzzy interpolative reasoning method performs better than the ones obtained by the traditional fuzzy inference system (2000), Huang and Shen's method (2008), and Chen and Ko's method (2008). The proposed method provides us with a useful way to deal with weighted fuzzy interpolative reasoning in sparse fuzzy rule-based systems.
TL;DR: Four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, and experiments are presented which demonstrate that by using the proposed methodology, the most influential type- 2 fuzzy rules can be effectively retained in order to construct parsimonious type-1 fuzzy models.
Abstract: Type-2 fuzzy systems are increasing in popularity, and there are many examples of successful applications. While many techniques have been proposed for creating parsimonious type-1 fuzzy systems, there is a lack of such techniques for type-2 systems. The essential problem is to reduce the number of rules, while maintaining the system's approximation performance. In this paper, four novel indexes for ranking the relative contribution of type-2 fuzzy rules are proposed, which are termed R-values, c-values, omega1-values, and omega2-values. The R-values of type-2 fuzzy rules are obtained by applying a QR decomposition pivoting algorithm to the firing strength matrices of the trained fuzzy model. The c-values rank rules based on the effects of rule consequents, while the omega1-values and omega2-values consider both the rule-base structure (via firing strength matrices) and the output contribution of fuzzy rule consequents. Two procedures for utilizing these indexes in fuzzy rule selection (termed ldquoforward selectionrdquo and ldquobackward eliminationrdquo) are described. Experiments are presented which demonstrate that by using the proposed methodology, the most influential type-2 fuzzy rules can be effectively retained in order to construct parsimonious type-2 fuzzy models.
TL;DR: The proposed method can solve a variety of PDEs encountered in engineering and is shown to be able to solve the convergence of error equations in mesh points from the energy perspective.
Abstract: A new technique using an adaptive fuzzy algorithm to obtain the solutions to a class of partial differential equations (PDEs) is presented. The design objective is to find a fuzzy solution to satisfy precisely the PDEs with boundary conditions. According to the adaptive scheme of fuzzy logic systems, a fuzzy solution with adjustable parameters for the PDE is first described. Then, a set of adaptive laws for tuning the free parameters in the consequent part is derived from minimizing an appropriate error function. In addition, an elegant approximated error bound between the exact solution and the proposed fuzzy solution with respect to the number of fuzzy rules and solution errors has also been derived. Furthermore, the convergence of error equations in mesh points is also discussed from the energy perspective. In this paper, we show that the proposed method can solve a variety of PDEs encountered in engineering. Comparisons are also made with solutions obtained by the finite-element method.
TL;DR: The developed computational method provides a better approach to overcome the drawback of existing high-order fuzzy time series models and its simplicity lies with the use of differences in consecutive values of various orders as forecasting parameter and a w-step fuzzy predictor in place of complicated computations of fuzzy logical relations.
Abstract: This paper presents a computational method of forecasting based on high-order fuzzy time series. The developed computational method provides a better approach to overcome the drawback of existing high-order fuzzy time series models. Its simplicity lies with the use of differences in consecutive values of various orders as forecasting parameter and a w-step fuzzy predictor in place of complicated computations of fuzzy logical relations. The objective of the present study is to examine the suitability of various high-order fuzzy time series models in forecasting. The general suitability of the developed method has been tested by implementing it in the forecasting of student enrollments of the University of Alabama and in the forecasting of crop (Lahi) production, a case of high uncertainty in time series data. The results obtained have been compared in terms of average error of forecast to show superiority of the proposed model.
TL;DR: A fuzzy logic approach for decision-making of maintenance is presented, based on the domain experts' experiences in production line and maintenance department, to satisfy the quick response requirement of production controller.
Abstract: In many manufacturing processes, real-time information can be obtained from process control computers and other monitoring devices. However, production control problems are frequently accompanied by certain and uncertain conditions. Problems with uncertainty conditions generally include difficulty in identifying an optimal solution in real-time using conventional mathematical approaches. This study presents a fuzzy logic approach for decision-making of maintenance. Some linguistic variables and rules-of-thumb are used to form the fuzzy logic models, based on the domain experts' experiences in production line and maintenance department. The historical production data are used to train and tune the fuzzy models. The tuned fuzzy models are then embedded into an internet-based and event-oriented information system as fuzzy agent. The production controller can easily make suitable production control decisions based on the inference results of fuzzy agents to satisfy the quick response requirement.
TL;DR: Experation shows that the fuzzy and-operator and product-operator are suitable to reach efficient solutions for the problem on hand and the fuzzy mathematical programming approach is used and fuzzy achievement function of the model is defined by six different fuzzy operators.
TL;DR: The objective is to investigate and evaluate the proposed rule-based model against commonly used time series models including ''standard'' architectures such as autoregressive (AR) models and selected topologies of neural networks.
TL;DR: It is shown that the main properties of the classical connective Xor are preserved by the connective fuzzy Xor, and, therefore, this new definition of the connectives extends the related classical approach.
TL;DR: A random fuzzy programming model and a methodology for solving a multi-stage supply chain design problem of a realistic scale in the random fuzzy environment is proposed and may be applied to any optimization problems with random fuzzy factors.