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Interval Type-2 Fuzzy Logic Systems and Perceptual Computers: Their Similarities and Differences

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Advances in Type-2 Fuzzy Sets and Systems

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 301))

Abstract

In this chapter, we compare the interval type-2 fuzzy logic system and perceptual computer, so as to eliminate confusion among researchers about whether or not there really are differences between them. We show that there are many more differences than similarities between them by focusing on the following six issues: inputs and membership functions, fuzzifier versus encoder, rules versus computing with words (CWW) engines, inference versus output of CWW engine, output processing versus decoder, and outputs versus recommendation plus data.

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Notes

  1. 1.

    A type-2 fuzzy set can be thought of as a type-1 fuzzy set on steroids. Its membership function no longer has a single value at each value of the primary variable, but instead is a blurred version of that function, i.e., at each value of the primary variable the membership is itself a function, called a secondary membership function (MF). When the secondary MF is a constant equal to 1, the type-2 fuzzy set is called an interval type-2 fuzzy set or an interval-valued fuzzy set; otherwise, it is called a general type-2 fuzzy set. The MF of a T2 FS is three-dimensional, with x-axis called the primary variable, y-axis called the secondary variable (or primary membership), and z-axis called the MF value (or secondary MF value). A vertical slice is a plane that is parallel to the MF-value z-axis. The footprint of uncertainty (FOU) of a T2 FS lies on the x–y plane (i.e., the primary and secondary variable plane) and includes all points on that plane for which the MF value is nonzero; it is the 2D-domain on which sit the secondary membership values. The FOU can be completely covered by T1 FSs that are called embedded T1 FSs.

  2. 2.

    TSK rules are also available in which their consequents are dynamical systems, but such rules are outside of the scope of this chapter.

  3. 3.

    The MF for a function of T1 FSs equals the union (over all values of alpha) of the MFs for the same function applied to the alpha cuts of the T1 FSs.

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Authors and Affiliations

  1. Signal and Image Processing Institute, Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, 90089-2564, USA

    Jerry M. Mendel

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  1. Jerry M. Mendel
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Correspondence to Jerry M. Mendel .

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Editors and Affiliations

  1. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Alireza Sadeghian

  2. Hughes Aircraft Electrical Engineering B, Department of Electrical Engineering - S, University of Southern California, 3740 McClintock Ave., Los Angeles, 90089-2564, California, USA

    Jerry M. Mendel

  3. Ryerson University, Victoria Street 350, Toronto, M5B 2K3, Ontario, Canada

    Hooman Tahayori

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Mendel, J.M. (2013). Interval Type-2 Fuzzy Logic Systems and Perceptual Computers: Their Similarities and Differences. In: Sadeghian, A., Mendel, J., Tahayori, H. (eds) Advances in Type-2 Fuzzy Sets and Systems. Studies in Fuzziness and Soft Computing, vol 301. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6666-6_1

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  • DOI: https://doi.org/10.1007/978-1-4614-6666-6_1

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