English, Article edition: ON THE PROPERTIES OF A GENERALIZED CLASS OF T-NORMS IN INTERVAL-VALUED FUZZY LOGICS BART VAN GASSE; CHRIS CORNELIS; GLAD DESCHRIJVER; ...

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Bookmark: http://trove.nla.gov.au/version/133053
Physical Description
  • article
Language
  • English

Edition details

Title
  • ON THE PROPERTIES OF A GENERALIZED CLASS OF T-NORMS IN INTERVAL-VALUED FUZZY LOGICS
Author
  • BART VAN GASSE
  • CHRIS CORNELIS
  • GLAD DESCHRIJVER
  • ETIENNE E. KERRE
Physical Description
  • article
Notes
  • Since it does not generate any MTL-algebra (prelinear residuated lattice), the lattice $\mathcal{L}^I$ of closed subintervals of [0, 1] falls outside the mainstream of research on formal fuzzy logics. However, due to the intimate connection between logical connectives on $\mathcal{L}^I$ and those on [0, 1], many relevant logical properties can still be maintained, sometimes in a slightly weaker form. In this paper, we focus on a broad class of parametrized t-norms on $\mathcal{L}^I$. We derive their corresponding residual implicators, and examine commonly imposed logical properties. Importantly, we formally establish one-to-one correspondences between â¨-definability (respectively, weak divisibility) for t-norms of this class and strong â¨-definability (resp., divisibility) for their counterparts on [0, 1].
  • Formal fuzzy logic, interval-valued fuzzy sets, triangular norms, residuated lattices
  • RePEc:wsi:nmncxx:v:02:y:2006:i:01:p:29-41
Language
  • English
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