# 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; ...

#### User activity

##### Share to:

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
• 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
Contributed by
OAIster

## Get this edition

• Set up My libraries

### How do I set up "My libraries"?

In order to set up a list of libraries that you have access to, you must first login or sign up. Then set up a personal list of libraries from your profile page by clicking on your user name at the top right of any screen.

• All (1)
• Unknown (1)
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.
None of your libraries hold this item.

## User activity

#### Tags

What are tags? Add a tag

e.g. test cricket, Perth (WA), "Parkes, Henry"

Separate different tags with a comma. To include a comma in your tag, surround the tag with double quotes.

Be the first to add a tag for this edition