zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Analysis of the error in the standard approximation used for multiplication of triangular and trapezoidal fuzzy numbers and the development of a new approximation. (English) Zbl 0915.04003
Summary: Triangular and trapezoidal fuzzy numbers are commonly used in many applications. It is well known that the operators used for the nonlinear operations such as multiplication, division, and inverse are approximations to the actual operators. It is also commonly assumed that the error introduced by the approximations is small and acceptable. This paper examines the error of approximation for repeated use of the multiplication operand and shows it can be sufficiently large in simple circumstances to produce erroneous results. The computational complexity of the multiplication operation is analyzed and shown to be sufficiently complex that a computationally simpler approximation is needed. As a consequence, the error produced by the approximation for the multiplication operation is analyzed and a new approximation developed that is accurate for a large range of problems. An error expression is developed for the new approximation that can be used to determine when it is producing unacceptable results.

03E72Fuzzy set theory
Full Text: DOI