NDLI: <formula formulatype=inline><tex Notation=TeX>$alpha$</tex></formula>-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications

Content Provider	IEEE Xplore Digital Library
Author	Mendel, J.M. Feilong Liu Daoyuan Zhai
Copyright Year	1993
Abstract	This paper 1) reviews the alpha-plane representation of a type-2 fuzzy set (T2 FS), which is a representation that is comparable to the alpha-cut representation of a type-1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operations for T2 FSs can be computed using very simple alpha-plane computations that are the set theoretic operations for interval T2 (IT2) FSs; 3) reviews how the centroid of a T2 FS can be computed using alpha-plane computations that are also very simple because they can be performed using existing Karnik Mendel algorithms that are applied to each alpha-plane; 4) shows how many theoretically based geometrical properties can be obtained about the centroid, even before the centroid is computed; 5) provides examples that show that the mean value (defuzzified value) of the centroid can often be approximated by using the centroids of only 0 and 1 alpha -planes of a T2 FS; 6) examines a triangle quasi-T2 fuzzy logic system (Q-T2 FLS) whose secondary membership functions are triangles and for which all calculations use existing T1 or IT2 FS mathematics, and hence, they may be a good next step in the hierarchy of FLSs, from T1 to IT2 to T2; and 7) compares T1, IT2, and triangle Q-T2 FLSs to forecast noise-corrupted measurements of a chaotic Mackey-Glass time series.
Sponsorship	IEEE Computational Intelligence Society
Starting Page	1189
Ending Page	1207
Page Count	19
File Size	1102830
File Format	PDF
ISSN	10636706
Volume Number	17
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-10-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Embedded computing Integral equations Frequency selective surfaces Uncertainty type-2 fuzzy sets (T2 FSs) $\alpha$-Plane centroid Mackey–Glass time series quasi-type-2 fuzzy logic systems (Q-T2 FLSs) set theoretic operations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Artificial Intelligence Control and Systems Engineering Computational Theory and Mathematics

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