TY - GEN

T1 - A simple fuzzy rule-based system through vector membership and kernel-based granulation.

AU - Angelov, Plamen

AU - Yager, Ronald

N1 - "©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE." "This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder."

PY - 2010/7/9

Y1 - 2010/7/9

N2 - It is widely recognized that the human reasoning can be approximated by fuzzy rule-based (FRB) systems which can be seen as one of the basic frameworks for representation of intelligent systems. During the last quarter of a century two particular types of FRB systems, namely Zadeh-Mamdani (ZM) and Takagi-Sugeno (TS) dominated the field. In this paper we propose an alternative type which is simpler and more intuitive while preserving the advantages of its predecessors, such as flexibility, modularity, human-intelligibility. The newly proposed concept of vector membership (VM) and kernel-based granulation (KG) of complex systems (respectively their mathematical descriptions) we see as the next, more efficient form of system modelling that is widely applicable to a plethora of applications ranging from time-series prediction, clustering, classification, control, decision support systems to other problems where conventional fuzzy rule-based systems are used. The proposed simple FRB based on VM and KG are non-parametric and fully represent the real data. Contrast this to the mere approximation of the real data distributions that is provided by Gaussian (scalar), triangular, trapezoidal etc. parametric types of membership functions that are used in currently existing types of FRB (ZM and TS). Note that even probabilistic models that are usually based on Gaussian distributions or a mixture of Gaussians or other parametric representations provide only an approximation of the real data distribution (it should be noted that particle filters are perhaps the only form of non-parametric representation that is similar in this sense to the newly proposed simple FRB with VM and KG, but they are computationally cumbersome with exponentially growing complexity). The main contribution of the proposed simple FRB with VM and KG is that while preserving all the advantages of ‘traditional’ FRB systems they avoid the well known problems related to (multiple scalar) membership functions definition, identification and update. They fully take into account and exactly represent the spatial distribution and similarity of all the real data by proposing an innovative and much simplified form of the antecedent part. At the same time, transformations to the ‘traditional’ (ZM and TS) fuzzy sets expressed by parametric membership functions per variable are also possible. In papers that will follow we will demonstrate on practical examples (including classification, prediction, decision support and other classes of problems) the benefits of this scheme. (c) IEEE Press

AB - It is widely recognized that the human reasoning can be approximated by fuzzy rule-based (FRB) systems which can be seen as one of the basic frameworks for representation of intelligent systems. During the last quarter of a century two particular types of FRB systems, namely Zadeh-Mamdani (ZM) and Takagi-Sugeno (TS) dominated the field. In this paper we propose an alternative type which is simpler and more intuitive while preserving the advantages of its predecessors, such as flexibility, modularity, human-intelligibility. The newly proposed concept of vector membership (VM) and kernel-based granulation (KG) of complex systems (respectively their mathematical descriptions) we see as the next, more efficient form of system modelling that is widely applicable to a plethora of applications ranging from time-series prediction, clustering, classification, control, decision support systems to other problems where conventional fuzzy rule-based systems are used. The proposed simple FRB based on VM and KG are non-parametric and fully represent the real data. Contrast this to the mere approximation of the real data distributions that is provided by Gaussian (scalar), triangular, trapezoidal etc. parametric types of membership functions that are used in currently existing types of FRB (ZM and TS). Note that even probabilistic models that are usually based on Gaussian distributions or a mixture of Gaussians or other parametric representations provide only an approximation of the real data distribution (it should be noted that particle filters are perhaps the only form of non-parametric representation that is similar in this sense to the newly proposed simple FRB with VM and KG, but they are computationally cumbersome with exponentially growing complexity). The main contribution of the proposed simple FRB with VM and KG is that while preserving all the advantages of ‘traditional’ FRB systems they avoid the well known problems related to (multiple scalar) membership functions definition, identification and update. They fully take into account and exactly represent the spatial distribution and similarity of all the real data by proposing an innovative and much simplified form of the antecedent part. At the same time, transformations to the ‘traditional’ (ZM and TS) fuzzy sets expressed by parametric membership functions per variable are also possible. In papers that will follow we will demonstrate on practical examples (including classification, prediction, decision support and other classes of problems) the benefits of this scheme. (c) IEEE Press

KW - fuzzy rule-based systems

KW - Zadeh-Mamdani and Takagi-Sugeno fuzzy systems

KW - memebership functions

KW - granulation

KW - kernel-based representation

U2 - 10.1109/IS.2010.5548369

DO - 10.1109/IS.2010.5548369

M3 - Conference contribution/Paper

SN - 978-1-4244-5163-0

SP - 349

EP - 354

BT - 5th IEEE International Conference Intelligent Systems (IS), 2010

PB - IEEE

T2 - 2010 IEEE International Conference on Intelligent Systems

Y2 - 1 January 1900

ER -