Is the conventional interval arithmetic correct
Andrzej Piegat, Marek Landowski · Applied Computer Science · 2012
Interval arithmetic as part of interval mathematics and Granular Computing is unusually im- portant for development of science and engineering in connection with necessity of taking into account uncertainty and approximativeness of data occurring in almost all calculations. Interval arithmetic also conditions development of Artificial Intelligence and especially of automatic think- ing, Computing with Words, grey systems, fuzzy arithmetic and probabilistic arithmetic. However, the mostly used conventional Moore-arithmetic has evident weak-points. These weak-points are well known, but nonetheless it is further on frequently used. The paper presents basic operations of RDM-arithmetic that does not possess faults of Moore-arithmetic. The RDM-arithmetic is based on multi-dimensional approach, the Moore-arithmetic on one-dimensional approach to interval calculations. The paper also presents a testing method, which allows for clear checking whether results of any interval arithmetic are correct or not. The paper contains many examples and illustrations for better understanding of the RDM-arithmetic. In the paper, because of volume limitations only operations of addition and subtraction are discussed. Operations of multiplica- tion and division of intervals will be presented in next publication. Author of the RDM-arithmetic concept is Andrzej Piegat.