An understandable way to discover methods to model interval input–output samples

Xu, Shan; Li, Shenggang; Liu, Heng; Garg, Harish; Jin, Xuqin; Zhao, Jingjing

This paper shows an application of plausible reasoning methods (mainly, specialization and analogous) in mathematical modeling. Our attention is how a practitioner to determine analogously a more balanced scientific model to assist the desire during solving the entire problem. Taking interval samples modeling as a problem, we exemplify (with consideration paid to the motivation and course of discovering) how to discover, based on the classical corresponding methods, three linear regression models and two linear-like interpolation models relying on n-variable interval input-1-variable interval output samples. The rationality of these recommended models are proved, and applications of them are illuminated in detail by examples. Strategies to model further interval samples towards satisfactory are also exposed.