This and the next special issues of Reliable Computing contain a rich set of articles that attest to the synergism between interval analysis and fuzzy set theory. The relationships between interval analysis and fuzzy set theory are many. The most obvious relationship is arithmetic since fuzzy arithmetic is interval arithmetic on alpha-cuts (see , ). The second more basic relationship, since it is how interval and fuzzy arithmetic can be derived as well as how functions in the interval and fuzzy analysis setting (and many mathematical relationships) are deﬁned, is the extension principle (see , , ). The extension principle in interval analysis is called the united extension (see –). The third relationship is perhaps more explicit; this is fuzzy interval analysis (see , ). Here, the use of interval analysis in fuzzy set theory is direct. Of course, from the beginning (, , ) an interval [a, b] was considered as a number and this lead to interval analysis. Moveover, an interval is also a set. As a set, an interval is also a fuzzy set with rectangular membership function 1, x ∈ [a, b], µ (x)= [a, b] 0, otherwise. Therefore, from the point of view of
Reliable Computing – Springer Journals
Published: Oct 2, 2004
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera