Uncertain Linear Complementary Problem And Its Numerical Solution

Linear complementarity problems (abbreviated as LCP) and mathematical programs with complementarity constraints have become a cross-disciplinary research field of applied mathematics and computational mathematics, which have found an extensive applications in economics, management sciences, traffic network equilibrium, energy market and engineering mechanics. So the study of LCP is attracting a great deal of theoretical and practical attention. Since there exist some uncertainties in practice, in the recent literature, models of stochastic linear complementarity problems have drawn much attention and been investigated. However, it seems that there is no any research report concerning fuzzy or fuzzy-interval LCP. In this thesis, it is intended to be studied that fuzzy and fuzzy-interval LCP models are constructed. The existence of equilibrium solution, the solutions method and the applications are studied. The main contribution in this thesis is as follows:The thesis begins with an introduction of some knowledge about LCP and uncertainty program, which presents the current and future development of uncertain LCPs.In Chapter2, we introduce some new fuzzy definitions of concepts, then, the fuzzy LCP model is constructed. A expected value (EV) method is designed and applied to solve the fuzzy LCP model. The example shows that the study of fuzzy LCP is feasible and necessary.In Chapter3, we consider LCP with multi-uncertainties in practice. Taking fuzzy and interval uncertainties into account, and some new fuzzy-interval definitions are introduced, then a fuzzy-interval model is constructed and solved. The example shows that the introduction of the multi-uncertainty LCP is feasible and necessary. Compared with previous uncertain linear complementarity problems, this model can reflect the uncertainties in practice more objectively.In Chapter4, we consider the solution existence of fuzzy linear complementarity problem contains fuzzy Ro matrix. A concept of fuzzy R0matrix is presented, the equivalent conditions for a fuzzy R0matrix are obtained. The characteristics of fuzzy Ro matrix is studied, and the ways is presented to construct fuzzy R0matrix from an arbitrary R0matrix and a zero-fuzzy matrix, or from a non R0matrix and a fuzzy R0matrix.