On interval fuzzy S-implications

  • Authors:

  • B. C. Bedregal;G. P. Dimuro;R. H. N. Santiago;R. H. S. Reiser

  • Affiliations:

  • Universidade Federal do Rio Grande do Norte, Departamento de Informática e Matemática Aplicada, Campus Universitário, 59072-970 Natal, Brazil;Universidade Federal do Rio Grande, Programa de Pós-Graduação em Modelagem Computacional, Campus Carreiros, 96201-090 Rio Grande, Brazil;Universidade Federal do Rio Grande do Norte, Departamento de Informática e Matemática Aplicada, Campus Universitário, 59072-970 Natal, Brazil;Universidade Católica de Pelotas, Programa de Pós-Graduação em Informática, Rua Felix da Cunha 412, 96010-000 Pelotas, Brazil

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2010

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Abstract

This paper presents an analysis of interval-valued S-implications and interval-valued automorphisms, showing a way to obtain an interval-valued S-implication from two S-implications, such that the resulting interval-valued S-implication is said to be obtainable. Some consequences of that are: (1) the resulting interval-valued S-implication satisfies the correctness property, and (2) some important properties of usual S-implications are preserved by such interval representations. A relation between S-implications and interval-valued S-implications is outlined, showing that the action of an interval-valued automorphism on an interval-valued S-implication produces another interval-valued S-implication.