Algebras of approximating regions

Title:	Algebras of approximating regions
Authors:	Ivo Düntsch , Dept of Computer Science , Brock University , St Catherines, Ontario, L2S 3A1, Canada Ewa Orlowska, National Institute of Telecommunications , Warsaw, Poland Hui Wang , School of Information and Software Engineering , University of Ulster
Status:	Fundamenta Informaticae 46 (2001), 71-82
Abstract:	It is rarely the case that spatial regions can be determined up to their true boundaries, if, indeed, they have such boundaries; in most cases, we can only observe regions up to a certain granularity. Often, this is a desirable feature, since too much detail can disturb the view, and we will not be able to see the forest for the trees, if our desire is to see the forest. Having as our basic assumption that regions can (or need to) be observed only approximately, we want to find an operationalisation of the domain of regions, which is broad enough to express the properties which we want to study, and, at the same time, has enough mathematical structure to serve as a reasoning mechanisms without being overly restrictive to our intuition. This paper is organised as follows: Firstly, we will define the class of approximation algebras which is then shown to be equipollent to a class of well known algebraic structures. Secondly, we suggest a way to generalise the relations "contact" and "part of" of regions to the approximate case. Finally, we will give an outlook to future work.