NDLI: A simple fuzzy rule-based system through vector membership and kernel-based granulation

Content Provider	IEEE Xplore Digital Library
Author	Angelov, P. Yager, R.
Copyright Year	2010
Description	Author affiliation: Machine Intelligence Institute, Iona College, New Rochelle, New York, USA (Yager, R.) \|\| Department of Communication Systems, Infolab21, Lancaster University, LA1 4WA, UK (Angelov, P.)
Abstract	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 all̲ 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.
Starting Page	349
Ending Page	354
File Size	593353
Page Count	6
File Format	PDF
ISBN	9781424451630
DOI	10.1109/IS.2010.5548369
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2010-07-07
Publisher Place	United Kingdom
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy systems Knowledge based systems Virtual manufacturing Humans Fuzzy reasoning Intelligent systems Takagi-Sugeno model Mathematical model Predictive models Control system synthesis kernel-based representation fuzzy rule-based systems Zadeh-Mamdani and Takagi-Sugeno fuzzy systems memebership functions granulation
Content Type	Text
Resource Type	Article

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