Interval Analysis

Dawood, Hend, and Yasser Dawood. On the Metamathematics of the Theory of Interval Numbers. Giza: Department of Mathematics, Faculty of Science, Cairo University, 2010. Abstract

The aim of this paper is to provide a metamathematical investigation of the theory of intervals with the requisite predicate calculi and axiomatic set theory.

Dawood, Hend, and Yasser Dawood. A Dependency-Aware Interval Algebra. Giza: Department of Mathematics, Faculty of Science, Cairo University, 2013. Abstract

A new dependency-aware interval arithmetic is presented and its algebraic system is investigated.

Dawood, Hend, and Yasser Dawood. On Some Order-theoretic Aspects of Interval Algebras. Giza: Department of Mathematics, Faculty of Science, Cairo University, 2014. Abstract

In this report, we study some of the order-theoretic and algebraic aspects of interval mathematics.

Dawood, Hend, and Yasser Dawood. The Form of the Uncertain: On the Mathematical Structures of Uncertainty. Giza: Department of Mathematics, Faculty of Science, Cairo University, 2016. Abstract

In this report, we investigate into the algebraic structures underlying the mathematics of uncertainty.

Dawood, Hend, and Yasser Dawood. Interval Algerbras: A Formalized Treatment. Giza: Department of Mathematics, Faculty of Science, Cairo University, 2016. Abstract

The theories of classical intervals, modal intervals, and constraint intervals are formally constructed and their mathematical structures are in-depth investigated.

Dawood, Hend, and Yasser Dawood. Investigations into a Formalized Theory of Interval Differentiation. Giza: Department of Mathematics, Faculty of Science, Cairo University, 2017. Abstract

In this report, we define an algebra of dyadic intervals. Thereupon, we present a formalization of a generalized theory of interval differentiation and investigate into some of the analytic and algebraic properties thereof.

Dawood, Hend. "Interval Mathematics as a Potential Weapon against Uncertainty." In Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems. Hershey, PA: IGI Global, 2014. Abstractinterval_mathematics_as_a_potential_weapon_against_uncertainty.pdf

This chapter is devoted to introducing the theories of interval algebra to people who are interested in applying the interval methods to uncertainty analysis in science and engineering. In view of this purpose, we shall introduce the key concepts of the algebraic theories of intervals that form the foundations of the interval techniques as they are now practised, provide a historical and epistemological background of interval mathematics and uncertainty in science and technology, and finally describe some typical applications that clarify the need for interval computations to cope with uncertainty in a wide variety of scientific disciplines.

Keywords: Interval mathematics, Uncertainty, Quantitative Knowledge, Reliability, Complex interval arithmetic, Machine interval arithmetic, Interval automatic differentiation, Computer graphics, Ray tracing, Interval root isolation.

Call for Papers: International Journal of Fuzzy Computation and Modeling (IJFCM)

Tue, 2013-04-09 17:41

Call for Papers: International Journal of Fuzzy Computation and Modeling (IJFCM)

The editorial board of the International Journal of Fuzzy Computation and Modeling (IJFCM) is pleased to announce the call for submission of papers for the first issue of the journal. 

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