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Producing Fuzzy Inclusion and Entropy Measures

In: Computation, Cryptography, and Network Security

Author

Listed:
  • Athanasios C. Bogiatzis

    (Democritus University of Thrace, Department of Civil Engineering, Section of Mathematics and Informatics)

  • Basil K. Papadopoulos

    (Democritus University of Thrace, Department of Civil Engineering, Section of Mathematics and Informatics)

Abstract

Inclusion and entropy measurements are significant for a variety of applications in fuzzy logic area. Several authors and researchers have tried to axiomatize fuzzy inclusion and entropy indicators. Others have introduced such measures based on specific desired properties. Significant results have been obtained; results that have led to a number of alternative solutions concerning several different applications. Apart from these interesting and innovative ideas, open matters of further discussion and research have occurred in these studies as well. Following the work of these authors, we propose an alternative axiomatization of fuzzy inclusion based on an already existing one. This allows us to introduce a category of subsethood and entropy measures which contains well-known indicators as well as new ones.

Suggested Citation

  • Athanasios C. Bogiatzis & Basil K. Papadopoulos, 2015. "Producing Fuzzy Inclusion and Entropy Measures," Springer Books, in: Nicholas J. Daras & Michael Th. Rassias (ed.), Computation, Cryptography, and Network Security, pages 51-74, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-18275-9_3
    DOI: 10.1007/978-3-319-18275-9_3
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