In this paper, associated with dominance relation, lattice theory and intuitionistic fuzzy sets theory, the lattice-valued information systems with interval-valued intuitionistic fuzzy decision are proposed and some of its properties are investigated carefully. And, an approach to knowledge reduction based on discernibility matrix in consistent lattice-valued information systems with interval-valued intuitionistic fuzzy decision is constructed and an illustrative example is applied to show its validity. Moreover, extended from the idea of knowledge reduction in consistent information systems, four types of reductions and approaches to obtaining the knowledge reductions of the inconsistent lattice-valued information systems with interval-valued intuitionistic fuzzy decision are formulated via the use of discernibility matrix. Furthermore, examples are considered to show that the approaches are useful and effective. One can obtain that the research is meaningful both in theory and in application for the issue of knowledge reduction in complex information systems.
A Model-Order Reduction Approach for Electromagnetic Problems with Nonaffine Frequency Dependence