## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2011

#### Abstract

In this book the authors study the properties of natural class of intervals built using (–∞, ∞) and (∞, –∞). These natural class of intervals behave like the reals R, as far as the operations of addition, multiplication, subtraction and division are concerned. Using these natural class of intervals we build interval row matrices, interval column matrices and m × n interval matrices. Several properties about them are defined and studied. Also all arithmetic operations are performed on them in the usual way. The authors by defining so have made it easier for operations like multiplication, addition, finding determinant and inverse on matrices built using natural class of intervals. We also define polynomials with coefficients from natural class of intervals or polynomial intervals, both these concepts are one and the same, for one can be obtained from the other and vice versa. The operations of integration and differentiation are defined on these interval polynomials in a similar way as that of usual polynomials.

#### Publisher

ZIP PUBLISHING, Ohio

#### ISSN

978-1-59973-168-1

#### Language (ISO)

English

#### Keywords

TRIGONOMETRIC INTERVAL FUNCTIONS, Interval polynomials. neutrosophic logic

#### Recommended Citation

W. B. Vasantha Kandasamy, Florentin Smarandache, D. Datta, H. S. Kushwaha, P. A. Jadhav. STUDY OF NATURAL CLASS OF INTERVALS USING (–∞,∞) AND (∞, –∞). Ohio: Zip Publishing, 2011.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Applied Mathematics Commons, Number Theory Commons, Other Mathematics Commons