Fuzzy ARTMAP: A Neural Network Architecture for Incremental Supervised Learning of Analog Multidimensional Maps

  • Carpenter G
  • Grossberg S
  • Zhang G
 et al. 
  • 2


    Mendeley users who have this article in their library.
  • N/A


    Citations of this article.


A complex fuzzy set is a fuzzy set whose membership function takes values in the unit circle in the complex plane. This paper investigates various operation properties and proposes a distance measure for complex fuzzy sets. The distance of two complex fuzzy sets measures the difference between the grades of two complex fuzzy sets as well as that between the phases of the two complex fuzzy sets. This distance measure is then used to define ??-equalities of complex fuzzy sets which coincide with those of fuzzy sets already defined in the literature if complex fuzzy sets reduce to real-valued fuzzy sets. Two complex fuzzy sets are said to be ??-equal if the distance between them is less than 1 - ??. This paper shows how various operations between complex fuzzy sets affect given ??-equalities of complex fuzzy sets. An example application of signal detection demonstrates the utility of the concept of ??-equalities of complex fuzzy sets in practice. ?? 2009 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • - complex fuzzy set
  • --- neural network
  • --artmap
  • --fuzzy set theory
  • -neural
  • 1
  • 2002
  • 2003
  • a connection
  • adaptive resonance theory
  • al
  • and we will not
  • argue for
  • art 1
  • art1 neural network
  • back-propagation
  • backpropagation with plummeting learn-
  • backpropagation with selective training
  • between art systems a
  • categorization
  • character process
  • character recognition
  • comparative study
  • complement of complex fuzzy
  • complex fuzzy relation
  • complex fuzzy set
  • distance measure
  • equality
  • expert
  • explained in ramot et
  • farsi optical character recognition
  • feature extraction
  • fuzzy art
  • fuzzy artmap
  • fuzzy inference
  • fuzzy relations
  • fuzzy set
  • i n t r
  • ing rate factor
  • introduction
  • learning
  • machine learning
  • medical diagnosis
  • memory search
  • moments
  • multi-
  • multilayer perceptron
  • mushroom database
  • n d
  • neural network
  • neural networks
  • o d u c
  • paper
  • pattern recognition
  • prediction
  • relation
  • self-organization
  • simplified fuzzy art map
  • simplified fuzzy artmap
  • supervised learning
  • system
  • t i o n
  • the rationale in this
  • δ-

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document


  • Gail A. Carpenter

  • Stephen Grossberg

  • Guangquan Zhang

  • Tharam Singh Dillon

  • Kaiyuan Cai

  • Jun Ma

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free