The Relation Graph Of Three Elements And The System Analysis Of Transitivity-relationship

The fuzzy transitivity is the core of fuzzy ordering relation, and the basis of fuzzy equal relation. The research and spreading of some typical transitivity-matrices are the focus that people always concerned. The object of the research is making the relation of all kinds of fuzzy transitivity-matrices clearer.In this paper, the notions of the relation graph of three elements and general fuzzy transitivity have been introduced. The first is classified bv the groupknowledge. And it is applied to the fuzzy transitivity-relation, and then gets the map between the relation graph and the transitivity-relation. The system of formal 3-transitivity is classified and analyzed again by the new method. The result of literature is improved, and the inclusion between them is clearer.The specialty of this paper: the relation graph of three elements is one of the innovations of this paper. It is a more powerful new tool in the research of fuzzy transitivity-relation. The application of the group knowledge changes the tendency that the research method is simple in the literature, and gets the ideal result. This paper is almost gets the final object of the relation system except some relations of some single ones.The work of this paper not only enriches the research of fuzzy transitivity-matrices, but also supplies the new vision and object for the research by the given methods and principles.