Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

Inclusion properties for random relations under the hypotheses of stochastic independence and non-interactivity

S. Chen*, F. Tonon
University of Utah, Department of Geology and Geophysics, 135 South 1460 East, Salt Lake City, UT 84112, USA

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This paper investigates whether random set inclusion is preserved by non-interactivity and by stochastic independence. Let (X1, x1), (X2, x2) be two random sets on U1 and U2, respectively, and let (Y1, y1), (Y2, y2) be two consonant inclusions of theirs. Let (Z1, z1) be the random relation on U1 × U2 obtained from (X1, x1) and (X2, x2) under the hypothesis of stochastic independence, and let (Z2, z2) ((Z3, z3), resp.) be the random relation on U1 × U2 obtained from (Y1, y1), (Y2, y2) under the hypothesis of non-interactivity (stochastic independence, resp.). We prove that these hypotheses do not imply that (Z1, z1) ⊆ (Z2, z2), but imply that (Z1, z1) ⊆ (Z3, z3).

Keywords:  Random set; Relation; Inclusion; Non-interactivity; Stochastic independence

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