Interval Mathematics

Dawood, Hend, and Yasser Dawood. Logical Aspects of Interval Dependency. Giza: Department of Mathematics, Faculty of Science, Cairo University, 2013. Abstract

By means of the most fundamental logical concepts of quantification theory, the notion of interval dependency is axiomatized and its fundamental properties are deduced.

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. 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. 

International Journal of Fuzzy Computation and Modelling (IJFCM)

Tue, 2013-04-09 17:38

Newly Announced Journal: International Journal of Fuzzy Computation and Modelling (IJFCM)

A new journal, the “International Journal of Fuzzy Computation and Modeling” (IJFCM), has been launched by Inderscience Publishers (see http://www.inderscience.com/ijfcm), The International Journal of Fuzzy Computation and Modelling (IJFCM) includes theoretical, experimental and applications of fuzzy mathematics and computation in general.

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

Tue, 2013-04-09 17:25

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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