For fuzzy relation inequality system B ≤R A≤ B ,after its fuzzy relation R is obtaind using sign matrix method, fuzzy mapping R is changed into R * as the new input of fuzzy relation in the preparatory system.

In order to reduce the real decision systems coming with discrete data as well as continuous data,even fuzzy data,a new rough set theory model based on fuzzy equation relation was established.

The irrationality of the relative reduction algorithm of rough set model based on fuzzy equation relation was pointed out and the notion of relative reduction was redefined and an improved binary version of particle swarm optimization (PSO) algorithm was used to compute the relative reduction of the hybrid decision systems.

Decomposition of rough sets based on fuzzy equivalence relation;

An analogism of fluvial process is presented according to the weight of primary factors and fuzzy equivalence relation.

A method based on fuzzy equivalence relation is applied to implement target classification and a synthetic algorithm is presented to fulfill multi-layer structure among groups by using the nearest-neighbor method and field knowledge.