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Area, Perimeter and Shape of Fuzzy Geographical Entities

  • Cidália Costa Fonte
  • Weldon A. Lodwick

Abstract

This paper focuses on crisp and fuzzy operators to compute the area and perimeter of fuzzy geographical entities. The limitations of the crisp area and perimeter operators developed by Rosenfeld (1984) are discussed, as well as the advantages of the fuzzy area operator developed by Fonte and Lodwick (2004). A new fuzzy perimeter operator generating a fuzzy number is proposed. The advantage of using operators generating fuzzy numbers is then illustrated by computing the shape of a FGE, through its compactness, using the extension principle and the fuzzy area and perimeter.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Cidália Costa Fonte
    • 1
  • Weldon A. Lodwick
    • 2
  1. 1.Secção de Engenharia Geográfica, Departamento de Matemática, Faculdade de Ciências e TecnologiaUniversidade de CoimbraCoimbraPortugal
  2. 2.Mathematics DepartmentUniversity of Colorado at DenverDenverUSA

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