Definition of G-intuitionistic fuzzy equivalent relation is given.

On Properties of the Cut-sets of Intuitionistic Fuzzy Relations

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.

With these values the authors can construct fuzzy equivalence relations among objects.

And then the relative quality of fuzzy equivalence relations and that of transitive closure operator of fuzzy relation are studied and meanwhile their relations are also researched.