Representation of Indifference and Preference Ordering Between Random Variables by Coherent Upper and Lower Conditional Previsions Defined by Hausdorff Outer and Inner Measures

Coherent lower and upper conditional previsions defined by Hausdorff inner and outer measures are proposed to represent respectively a partial strict order and a complete indifference relations between random variables. The two binary relations can describe the activity of the conscious human thought ruled by the antisymmetric property and the unconscious human thought which is governed by the symmetric principle and the generalization principle.