### Journals Information

**
Mathematics and Statistics Vol. 11(4), pp. 685 - 692 DOI: 10.13189/ms.2023.110410 Reprint (PDF) (759Kb) **

## Alternative Algebra for Multiplication and Inverse of Interval Number

**Mashadi ^{1}, Abdul Hadi ^{1}, Sukono ^{2}^{,*}**

^{1}Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Riau, Indonesia

^{2}Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia

**ABSTRACT**

Recently, there are a lot of arithmetic interval forms. One of them only defines nonnegative interval numbers, whereas another one defines all forms of intervals. However, there are not many differences among the many arithmetic forms that were provided, particularly for addition and subtraction. For multiplication, division or inverse, there are many types of operations offered. But the problem is how to determine inverse of an interval number. There are many alternative offers to determine inverse of an interval number . But only for certain cases and for many cases, we have which is not equal to interval number . Based on these conditions, in this article an analysis of the issues with several existing interval algebras will be given and based on the analysis an alternative will be proposed to determine the form of multiplication and inverse from an interval number, which begins to define the positivity of an interval number with mid-point and then we construct algebra operations especially for multiplication. From the multiplication operation, we can construct the inverse form of an interval number . Furthermore, it is proven that for numbers of interval where , there is an interval number , so that it applies .

**KEYWORDS**

Interval Arithmetic, Interval Matrix, Inverse of Interval Number

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Mashadi , Abdul Hadi , Sukono , "Alternative Algebra for Multiplication and Inverse of Interval Number," Mathematics and Statistics, Vol. 11, No. 4, pp. 685 - 692, 2023. DOI: 10.13189/ms.2023.110410.

(b). APA Format:

Mashadi , Abdul Hadi , Sukono (2023). Alternative Algebra for Multiplication and Inverse of Interval Number. Mathematics and Statistics, 11(4), 685 - 692. DOI: 10.13189/ms.2023.110410.