Whys and Hows of the Parameterized Interval Analyses: A Guide for the Perplexed
Isaac E. Elishakoff · International Journal for Computational Methods in Engineering Science and Mechanics · 2013
Novel elements of the parameterized interval analysis developed in [1 Elishakoff, I. and Miglis, Y. 2012. Overestimation-Free Computational Version of Interval Analysis. International Journal for Computational Methods of Engineering Science and Mechanics, 13: 319–328. [Taylor & Francis Online] , [Google Scholar], 2 Elishakoff, I. and Miglis, Y. 2012. Novel Parametrized Intervals May Lead to Sharp Bounds. Mechanics Research Communications, 44: 1–8. [Crossref], [Web of Science ®] , [Google Scholar]] are emphasized in this response, to Professor E.D. Popova, or possibly to others who may be perplexed by the parameterized interval analysis. It is also shown that the overwhelming majority of comments by Popova [3 Popova, E. D. and On. Overestimation-free Computational Version of Interval Analysis. International Journal for Computational Methods of Engineering Science and Mechanics (this issue), [Google Scholar]] are based on a misreading of our paper [1 Elishakoff, I. and Miglis, Y. 2012. Overestimation-Free Computational Version of Interval Analysis. International Journal for Computational Methods of Engineering Science and Mechanics, 13: 319–328. [Taylor & Francis Online] , [Google Scholar]]. Partial responsibility for this misreading can be attributed to the fact that explanations provided in [1 Elishakoff, I. and Miglis, Y. 2012. Overestimation-Free Computational Version of Interval Analysis. International Journal for Computational Methods of Engineering Science and Mechanics, 13: 319–328. [Taylor & Francis Online] , [Google Scholar]] were laconic. These could have been more extensive in view of the novelty of our approach [1 Elishakoff, I. and Miglis, Y. 2012. Overestimation-Free Computational Version of Interval Analysis. International Journal for Computational Methods of Engineering Science and Mechanics, 13: 319–328. [Taylor & Francis Online] , [Google Scholar], 2 Elishakoff, I. and Miglis, Y. 2012. Novel Parametrized Intervals May Lead to Sharp Bounds. Mechanics Research Communications, 44: 1–8. [Crossref], [Web of Science ®] , [Google Scholar]]. It is our duty, therefore, to reiterate, in this response, the whys and hows of parameterization of intervals, introduced in [1 Elishakoff, I. and Miglis, Y. 2012. Overestimation-Free Computational Version of Interval Analysis. International Journal for Computational Methods of Engineering Science and Mechanics, 13: 319–328. [Taylor & Francis Online] , [Google Scholar]] to incorporate the possibly available information on dependencies between various intervals describing the problem at hand. This possibility appears to have been discarded by the standard interval analysis, which may, as a result, lead to overdesign, leading to the possible divorce of engineers from the otherwise beautiful interval analysis.