Solving different practical granular problems under the same system of equations
Andrzej Piegat, Marek Landowski · Granular Computing · 2017
This paper contains discussion about the paper of Kreinovich (Granular Computing 1(3):171–179, 2016) in which the author suggests the thesis that in conditions of uncertainty “solving different practical problems we get different solutions of the same system of equations with the same granules”. Authors of the present paper are of the opinion that the above thesis is result of one-dimensional approach to interval analysis prevailing at present in scientific community and also used by Kreinovich. According to this approach the direct result of any arithmetic operation $$*\in \{+,-,\times ,/\}$$ on intervals is also an interval. The main scientific contribution of the paper is showing that a granular problem analysis in an incomplete, low-dimensional space can lead to untrue conclusions because picture of the problem in this space is too poor and part of valuable, important information is lost. What is seen in the full-dimensional space of the problem space cannot be seen in an incomplete, low-dimensional space. The paper also shortly describes a multidimensional approach to interval arithmetic that is free of the above-described deficiencies.