# Dear Colleagues

Dear Colleagues 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 [3], [4]). 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 [8], [12], [14]). The extension principle in interval analysis is called the united extension (see [5]–[7]). The third relationship is perhaps more explicit; this is fuzzy interval analysis (see [1], [2]). Here, the use of interval analysis in fuzzy set theory is direct. Of course, from the beginning ([9], [11], [13]) 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Dear Colleagues

, Volume 10 (4) – Oct 2, 2004
2 pages

/lp/springer_journal/dear-colleagues-7PjnOUpW1M
Publisher
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/B:REOM.0000032140.30155.7a
Publisher site
See Article on Publisher Site

### Abstract

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 [3], [4]). 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 [8], [12], [14]). The extension principle in interval analysis is called the united extension (see [5]–[7]). The third relationship is perhaps more explicit; this is fuzzy interval analysis (see [1], [2]). Here, the use of interval analysis in fuzzy set theory is direct. Of course, from the beginning ([9], [11], [13]) 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

### Journal

Reliable ComputingSpringer Journals

Published: Oct 2, 2004

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

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.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations

Abstract access only

18 million full-text articles

Print

20 pages / month

PDF Discount

20% off