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Soft Computing

, Volume 6, Issue 2, pp 124–140 | Cite as

A granular counterpart to the gradient operator

  • S. Dick
  • W. Rodriguez
  • A. Kandel
Original paper

Abstract

 We introduce the linguistic gradient operator, a granular counterpart to the gradient operator in classical calculus. A multiple-input single-output Mamdani fuzzy rulebase is treated as a function in a linguistic state space, defined by the Cartesian product of the antecedent linguistic variables in the rulebase. The value of the consequent linguistic variable is treated as a function in this space, and thus represents the fuzzy rulebase. The linguistic gradient operator takes the consequent function and produces an N-vector of linguistic values, which are approximations to the N first partial derivatives of the consequent function. This vector points in the direction of the greatest local increase of the consequent function, and thus shows how a rule relates to its “neighboring” rules in rule space. Two Examples demonstrate that the linguistic gradient is a linguistic analogue of the classical gradient operator.

Keywords Linguistic gradient, Qualitative reasoning, Linguistic variables, Granular computing, Computing with words 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • S. Dick
    • 1
  • W. Rodriguez
    • 1
  • A. Kandel
    • 1
  1. 1.Department of Computer Science and Engineering, University of South Florida, 4202E. Fowler Avenue, ENB 118, Tampa, FL, USA, 33620 E-mail: dick@csee.usf.edu, kandel@csee.usf.eduUS

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