Invariance to various transformations is key to object recognition but existing definitions of invariance are somewhat confusing while discussions of invariance are often confused. In this report, we provide an operational definition of invariance by formally defining perceptual tasks as classification problems. The definition should be appropriate for physiology, psychophysics and computationa...

Investigating sources of withinand between-group differences and measurement invariance (MI) across groups is fundamental to any meaningful group comparison based on observed test scores. It is shown that by placing certain restrictions on the multigroup confirmatory factor model, it is possible to investigate the hypothesis that withinand between-group differences are due to the same factors. ...

Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regar...

We give some sufficient conditions such that a crisp, interval, triangular, trapezoidal, parametric approximation of a fuzzy number, with or without additional requirements, to have the properties of invariance to translations or scale invariance.