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A New Distance on Generalized Fuzzy Numbers and a Glimpse on Their Properties

  • M. AmirfakhrianEmail author
  • S. Yeganehmanesh
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 641)

Abstract

Normalization is the dominant but inexact method to handle any nonnormal fuzzy sets data. This stems from the fact that normalization ignores some parts of such data in order to prepare them for being used in computational operations. A subset of such data which satisfies the property of convexity is called Generalized Fuzzy Numbers (GFN). In this paper, a new distance is presented on the set of GFNs. In the special case, when GFNs are normal (i.e. Fuzzy Numbers), the proposed distance is converted to a well-known distance which in the fuzzy literature has already been proved to be a metric. Also, some of the features of the proposed distance are studied through several examples.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsCentral Tehran Branch, Islamic Azad UniversityTehranIran

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