On the basis of the AGM theory and kernel contraction, this thesis mainly discusses the theory of belief contraction in which new information is a general set of sentences.

The purpose of this paper is to introduce the concept of (Φ,Δ)-type probabi listic contractor in Menger PN-spaces and to study the existence and uniqueness of solutions for the nonlinear operator equations with the probabilistic contractor in Menger PN-spaces.

For better understanding and proper analysis and calculation of the locating errors,the author presents three methods in the determining of processing locating errors of components,conceptual method,constituent method,and differential method,and p.