The Experts below are selected from a list of 9747 Experts worldwide ranked by ideXlab platform
Thomas A. Runkler - One of the best experts on this subject based on the ideXlab platform.
-
type reduction operators for interval type 2 Defuzzification
Information Sciences, 2018Co-Authors: Thomas A. Runkler, Chao Chen, Robert JohnAbstract:Abstract Fuzzy sets are an important approach to model uncertainty. Defuzzification maps fuzzy sets to non–fuzzy (crisp) values. Type–2 fuzzy sets model uncertainty in the degree of membership in a fuzzy set. Type–2 Defuzzification maps type–2 fuzzy sets to non–fuzzy values. Type reduction maps type–2 fuzzy sets to type–1 fuzzy sets, in order to make type–2 Defuzzification easier and to implement more efficient type–2 Defuzzification algorithms. This paper is a first step towards a theoretical foundation of the emerging field of type reduction. Five mathematical properties of type reduction are defined, and two existing type reduction methods (Nie–Tan and uncertainty weight) are examined with respect to our five properties. Furthermore, two new type reduction methods are proposed: consistent linear type reduction and consistent quadratic type reduction. All our five properties are satisfied by consistent quadratic type reduction.
-
Type reduction operators for interval type–2 Defuzzification
Information Sciences, 2018Co-Authors: Thomas A. Runkler, Chao Chen, Robert JohnAbstract:Abstract Fuzzy sets are an important approach to model uncertainty. Defuzzification maps fuzzy sets to non–fuzzy (crisp) values. Type–2 fuzzy sets model uncertainty in the degree of membership in a fuzzy set. Type–2 Defuzzification maps type–2 fuzzy sets to non–fuzzy values. Type reduction maps type–2 fuzzy sets to type–1 fuzzy sets, in order to make type–2 Defuzzification easier and to implement more efficient type–2 Defuzzification algorithms. This paper is a first step towards a theoretical foundation of the emerging field of type reduction. Five mathematical properties of type reduction are defined, and two existing type reduction methods (Nie–Tan and uncertainty weight) are examined with respect to our five properties. Furthermore, two new type reduction methods are proposed: consistent linear type reduction and consistent quadratic type reduction. All our five properties are satisfied by consistent quadratic type reduction.
-
properties of interval type 2 Defuzzification operators
IEEE International Conference on Fuzzy Systems, 2015Co-Authors: Thomas A. Runkler, Simon Coupland, Robert JohnAbstract:Interval type-2 Defuzzification maps an interval type-2 fuzzy set to a crisp number. We show that the semantic meaning of the interval type-2 fuzzy set (the associated opportunity or risk) has to be considered in the choice of an appropriate interval type-2 Defuzzification method. Motivated by a list of “axioms” for type-1 Defuzzification we introduce twelve mathematical properties for interval type-2 Defuzzification that serve as a theoretical framework to assess different interval type-2 Defuzzification methods. We show that the well-known Karnik-Mendel algorithm violates at least four of these twelve properties.
-
FUZZ-IEEE - Properties of interval type-2 Defuzzification operators
2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2015Co-Authors: Thomas A. Runkler, Simon Coupland, Robert JohnAbstract:Interval type-2 Defuzzification maps an interval type-2 fuzzy set to a crisp number. We show that the semantic meaning of the interval type-2 fuzzy set (the associated opportunity or risk) has to be considered in the choice of an appropriate interval type-2 Defuzzification method. Motivated by a list of “axioms” for type-1 Defuzzification we introduce twelve mathematical properties for interval type-2 Defuzzification that serve as a theoretical framework to assess different interval type-2 Defuzzification methods. We show that the well-known Karnik-Mendel algorithm violates at least four of these twelve properties.
-
Kernel Based Defuzzification
Computational Intelligence in Intelligent Data Analysis, 2013Co-Authors: Thomas A. RunklerAbstract:Defuzzification converts a fuzzy set to a crisp value or set. Standard Defuzzification methods are the center of gravity (COG) and the mean of maxima (MOM). A popular parametric Defuzzification method is based on the basic Defuzzification distribution (BADD). COG and MOM are special cases of BADD for unit and infinite exponents, respectively. Kernelization is a popular approach to improve data processing methods by implicit transformation to higher dimensions. This article introduces kernelized Defuzzification. We present a kernelized version of COG and illustrate it for polynomial kernels (pkCOG) and Gaussian kernels (GkCOG). We show that pkCOG is equivalent to BADD. Experiments with various representative synthetic examples show that GkCOG is superior to pkCOG/BADD in terms of smoothness.
Ronald R. Yager - One of the best experts on this subject based on the ideXlab platform.
-
Knowledge-based Defuzzification
Fuzzy Sets and Systems, 1996Co-Authors: Ronald R. YagerAbstract:Abstract We suggest a new approach to the problem of Defuzzification. This approach is a knowledge-based approach in that it uses knowledge in terms of combinability function to help to more intelligently guide the Defuzzification process. This approach makes use of a view of the Defuzzification process as a kind of clustering problem and uses the basic idea used in the mountain clustering method.
-
On the use of combinability functions for intelligent Defuzzification
Proceedings of 1995 IEEE International Conference on Fuzzy Systems. The International Joint Conference of the Fourth IEEE International Conference on , 1995Co-Authors: Ronald R. YagerAbstract:We suggest a new approach to the problem of Defuzzification. This approach is a knowledge based approach in that it uses knowledge in terms of a combinability function to help to more intelligently guide the Defuzzification process. This approach makes use of a view of the Defuzzification process as a kind of clustering problem and uses the basic idea used in the mountain clustering method. >
-
An adaptive approach to Defuzzification based on level sets
Fuzzy Sets and Systems, 1993Co-Authors: Dimitar Petrov Filev, Ronald R. YagerAbstract:Abstract We look at the process of Defuzzification used in fuzzy logic controllers. We provide a parametrized formulation for this procedure based upon the use of level sets which we call generalized level set Defuzzification. We show that the commonly used Defuzzification procedures, mean of maxima and center of area, are special cases of this general procedure and are simply distinguished by the choice of the parameter. We provide a simple algorithm for adaptive choice of the best Defuzzification procedure.
-
SLIDE: A simple adaptive Defuzzification method
IEEE Transactions on Fuzzy Systems, 1993Co-Authors: Ronald R. Yager, Dimitar Petrov FilevAbstract:We introduce a parameterized family of defuznfica- tion operators called the Semi LInear Defuzzification (SLIDE) method. This method is based upon a simple transformation of the fuzzy output set of the controller. We suggest an algorithm for the learning of the parameter from a data set. In an attempt to simplify the parameter learning we suggest a modified version of the SLIDE method which results in a simple learning algorithm. The development of the learning algorithm is based upon the use of the Kalman filter N fuzzy logic control systems (l), (2) the Defuzzification I step involves the selection of one value as the output of the controller. More specifically, starting with a fuzzy subset (possibility distribution) F over the output space X of the controller, the Defuzzification step uses this fuzzy subset to select a representative element x*. The two most often used methods of Defuzzification found in the literature are the center of area (COA) and mean of maxima (MOM) (3)-(6) methods. We recall that the MOM method takes as its defuzzified value the mean of the elements that attain the maximum membership grade in F. The COA method takes as its defuzzified value d = Ci(ui * xi), where ui = F(xi)/Cj F(xj). In (7) and (8) we formulated a general Defuzzification method via BAsic Defuzzification Distribution (BADD) transformations. The main idea of this BADD approach is to transform the possibility distribution F into a probability distribution P and then the defuzzified value is the expected value of the probability distribution. The process of transforming F into P was seen as a two-step process. The first step was to transform F into a new possibility distribution, E, and then to normalize E to obtain P. The step of obtaining E from F involved the use of a BADD transformation in which E(xi) = (F(z;))~, where 6 E (O,co). It was shown in (7) that the generalized BADD method implies the COA and MOM methods as special cases. In particular the COA method is obtained for a = 1 and the MOM is obtained for 6 = 00. When S = 0 we get a defuzzified value that is the unweighted mean of the output space, d = Xi xi. The BADD transformation has the advantage of being based on a single parameter, which allows us the potential of adaptively learning the best method of Defuzzification for a given controller. While the family of all defuzzified values that can be obtained by the generalized BADD Defuzzification method was parameterized, an undesirable property of the method was the nonlinear
-
A GENERALIZED Defuzzification METHOD VIA BAD DISTRIBUTIONS
International Journal of Intelligent Systems, 1991Co-Authors: Dimitar Petrov Filev, Ronald R. YagerAbstract:Defuzzification in fuzzy logic controllers concerns itself with the issue of selecting an appropriate crisp value from the fuzzy output of the controller. We provide a parametized family of Defuzzification operations. We call this family BAsic Defuzzification Distributions (BADD). We show that the commonly used methods. Mean of Maximum and Center of Area are special cases of this family. We suggest the use of these BADD transformations form the basis of a learning scheme to obtain the optimal Defuzzification method in a given application. We suggest that the parameter in the BADD family, the distinction between different Defuzzification methods, is related to the confidence we have in the rest of the controller.
Qiang Song - One of the best experts on this subject based on the ideXlab platform.
-
On Optimal Defuzzification and Learning Algorithms: Theory and Applications
Fuzzy Optimization and Decision Making, 2003Co-Authors: Augustine O. Esogbue, Qiang SongAbstract:In this paper, the issue of optimal Defuzzification which is advocated in the Optimality Principle of Defuzzification (Song and Leland (1996)) is addressed. It was shown that Defuzzification can be treated as a mapping from a high dimensional space to the real line. When system performance indices are considered, the Defuzzification mapping which optimizes the performance indices for the given fuzzy sets is known as the optimal Defuzzification mapping. Thus, finding this optimal Defuzzification mapping becomes the essence of Defuzzification. The problem with this idea, however, is that the space formed by all possible continuous Defuzzification mappings is so large to search that the only recourse is an approximation to the optimal Defuzzification mapping. With this, learning algorithms can be devised to find the optimal parameters of defuzzifiers with fixed structures. The proposed method is rigorously examined and compared with some well-known Defuzzification methods. To overcome the resultant enormous computational load problem with this algorithm, the concept of Defuzzification filter is additionally proposed. An application of the method to the power system stabilization problem is presented.
-
Defuzzification Filters and Applications to Power System Stabilization Problems
Journal of Mathematical Analysis and Applications, 2000Co-Authors: Augustine O. Esogbue, Qiang Song, W.e. HearnesAbstract:AbstractDefuzzification is a very important step in fuzzy systems applications. There are a number of different Defuzzification methods reported in the literature. In this paper, the concept of Defuzzification filters in a control system setting is first discussed and a methodology for designing such filters considered. As will be seen, the design of such filters requires the knowledge of the plant model and its inverse. A reference control signal is computed and then is used to generate the actual defuzzified control signal which will be applied to control the plant. The application of the Defuzzification filter is made by introducing the filter into a power system in which a neuro-fuzzy self-learning controller was applied to stabilize the system but success could not always be guaranteed. With the Defuzzification filter, however, the system is always stabilized. Simulation results are presented
-
Adaptive learning Defuzzification techniques and applications
Fuzzy Sets and Systems, 1996Co-Authors: Qiang Song, R.p. LelandAbstract:Abstract In this paper, adaptive learning Defuzzification techniques are studied under the consideration of system performance indices. By treating Defuzzification processes as continuous mappings from space [0,1] n to the real line, the concept of the optimal Defuzzification mapping can be developed. Since all the continuous Defuzzification mappings considered in this paper form a Banach space, approximation to the optimal mapping with some known functions can be expressed as the parametric optimization problem. To find the optimal parameters, adaptive learning of the optimal Defuzzification mapping is investigated. Learning laws for the parameters in the Defuzzification mapping are derived in one case. Numerical results indicate that the adaptive learning Defuzzification method can give superior Defuzzification results to some popular Defuzzification methods.
-
Some properties of Defuzzification neural networks
Fuzzy Sets and Systems, 1994Co-Authors: Qiang Song, Giovanni BortolanAbstract:Abstract Fuzzy systems have gained more and more attention from researchers and practitioners of various fields. In such systems, the output represented by a fuzzy set sometimes needs to be transformed into a scalar value, and this task is known as the Defuzzification process. Several analytic methods have been proposed for this problem, but lately the neural network approach has been used for this purpose. When employed as defuzzifiers, a neural network is called a Defuzzification neural network. In this paper some preliminary results on properties of such Defuzzification networks will be reported.
Witold Kosiński - One of the best experts on this subject based on the ideXlab platform.
-
on orientation sensitive Defuzzification functionals
International Conference on Artificial Intelligence and Soft Computing, 2014Co-Authors: Tomek Bednarek, Witold Kosiński, Katarzyna WegrzynwolskaAbstract:The aim of the article is to investigate Defuzzification functionals in the theory of Ordered Fuzzy Numbers (OFN). The model of OFN was introduced in 2002 to overcome drawbacks of classical (convex) fuzzy numbers. Each OFN is equipped with an additional feature – the orientation. New forms of Defuzzification functionals are proposed which are sensitive to the orientation change.
-
ICAISC (2) - On Orientation Sensitive Defuzzification Functionals
Artificial Intelligence and Soft Computing, 2014Co-Authors: Tomek Bednarek, Witold Kosiński, Katarzyna Wegrzyn-wolskaAbstract:The aim of the article is to investigate Defuzzification functionals in the theory of Ordered Fuzzy Numbers (OFN). The model of OFN was introduced in 2002 to overcome drawbacks of classical (convex) fuzzy numbers. Each OFN is equipped with an additional feature – the orientation. New forms of Defuzzification functionals are proposed which are sensitive to the orientation change.
-
Defuzzification Functionals of Ordered Fuzzy Numbers
IEEE Transactions on Fuzzy Systems, 2013Co-Authors: Witold Kosiński, Piotr Prokopowicz, Agnieszka RosaAbstract: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.
Dimitar Petrov Filev - One of the best experts on this subject based on the ideXlab platform.
-
SLIDE: A simple adaptive Defuzzification method
IEEE Transactions on Fuzzy Systems, 1993Co-Authors: Ronald R. Yager, Dimitar Petrov FilevAbstract:We introduce a parameterized family of defuznfica- tion operators called the Semi LInear Defuzzification (SLIDE) method. This method is based upon a simple transformation of the fuzzy output set of the controller. We suggest an algorithm for the learning of the parameter from a data set. In an attempt to simplify the parameter learning we suggest a modified version of the SLIDE method which results in a simple learning algorithm. The development of the learning algorithm is based upon the use of the Kalman filter N fuzzy logic control systems (l), (2) the Defuzzification I step involves the selection of one value as the output of the controller. More specifically, starting with a fuzzy subset (possibility distribution) F over the output space X of the controller, the Defuzzification step uses this fuzzy subset to select a representative element x*. The two most often used methods of Defuzzification found in the literature are the center of area (COA) and mean of maxima (MOM) (3)-(6) methods. We recall that the MOM method takes as its defuzzified value the mean of the elements that attain the maximum membership grade in F. The COA method takes as its defuzzified value d = Ci(ui * xi), where ui = F(xi)/Cj F(xj). In (7) and (8) we formulated a general Defuzzification method via BAsic Defuzzification Distribution (BADD) transformations. The main idea of this BADD approach is to transform the possibility distribution F into a probability distribution P and then the defuzzified value is the expected value of the probability distribution. The process of transforming F into P was seen as a two-step process. The first step was to transform F into a new possibility distribution, E, and then to normalize E to obtain P. The step of obtaining E from F involved the use of a BADD transformation in which E(xi) = (F(z;))~, where 6 E (O,co). It was shown in (7) that the generalized BADD method implies the COA and MOM methods as special cases. In particular the COA method is obtained for a = 1 and the MOM is obtained for 6 = 00. When S = 0 we get a defuzzified value that is the unweighted mean of the output space, d = Xi xi. The BADD transformation has the advantage of being based on a single parameter, which allows us the potential of adaptively learning the best method of Defuzzification for a given controller. While the family of all defuzzified values that can be obtained by the generalized BADD Defuzzification method was parameterized, an undesirable property of the method was the nonlinear
-
An adaptive approach to Defuzzification based on level sets
Fuzzy Sets and Systems, 1993Co-Authors: Dimitar Petrov Filev, Ronald R. YagerAbstract:Abstract We look at the process of Defuzzification used in fuzzy logic controllers. We provide a parametrized formulation for this procedure based upon the use of level sets which we call generalized level set Defuzzification. We show that the commonly used Defuzzification procedures, mean of maxima and center of area, are special cases of this general procedure and are simply distinguished by the choice of the parameter. We provide a simple algorithm for adaptive choice of the best Defuzzification procedure.
-
A GENERALIZED Defuzzification METHOD VIA BAD DISTRIBUTIONS
International Journal of Intelligent Systems, 1991Co-Authors: Dimitar Petrov Filev, Ronald R. YagerAbstract:Defuzzification in fuzzy logic controllers concerns itself with the issue of selecting an appropriate crisp value from the fuzzy output of the controller. We provide a parametized family of Defuzzification operations. We call this family BAsic Defuzzification Distributions (BADD). We show that the commonly used methods. Mean of Maximum and Center of Area are special cases of this family. We suggest the use of these BADD transformations form the basis of a learning scheme to obtain the optimal Defuzzification method in a given application. We suggest that the parameter in the BADD family, the distinction between different Defuzzification methods, is related to the confidence we have in the rest of the controller.
