Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Journal of Computing, Vol. 4, No 4, (2010), 447p-462p
Abstract:
An approximate number is an ordered pair consisting of a (real)
number and an error bound, briefly error, which is a (real) non-negative
number. To compute with approximate numbers the arithmetic operations
on errors should be well-known. To model computations with errors one
should suitably define and study arithmetic operations and order relations
over the set of non-negative numbers. In this work we discuss the algebraic
properties of non-negative numbers starting from familiar properties of real
numbers. We focus on certain operations of errors which seem not to have
been sufficiently studied algebraically. In this work we restrict ourselves to
arithmetic operations for errors related to addition and multiplication by
scalars. We pay special attention to subtractability-like properties of errors
and the induced “distance-like” operation. This operation is implicitly used
under different names in several contemporary fields of applied mathematics
(inner subtraction and inner addition in interval analysis, generalized
Hukuhara difference in fuzzy set theory, etc.) Here we present some new
results related to algebraic properties of this operation.