The Fuzzy Relationship And Expression Of Fuzzy Measure And Its Related Structure

Dubois,Prade and Rico studied the relation between capacity and possibility measure ranging on a finite totally ordered set.We prove that the fuzzy measure taking values in De Morgan algebra can be expressed not only by the infimum of some possibility measures but also by the supremum of some necessity measures.Secondly,Yager studied the fuzzy relationship between attribute variables.We use MBS structure which used to represent the uncertainty of attribute values in-spired by Yager,to determine the fuzzy relationship between attribute variables.Finally,a new D-S decision model is proposed in this thesis.This thesis makes two parts of promotion and innovation for the works of Dubois and Yager.1.This thesis studies the capacity ranging on De Morgan algebra and con-structs two types of possibility distributions by permutation and inner Mobius transform.We prove that capacity ranging on De Morgan algebra can be repre-sented by a infimum of possibility measures.We also construct a type of necessity distributions by outer Mobius transform and prove that supremum of necessity measure can represent capacity ranging on De Morgan algebra.On the other hand,this thesis study these results by using lattice measure.2.The work done by Yager is generalized,and the uncertainty of attributes is represented by MBS structure,then we establish the fuzzy relations based on MB-S.Inspired by Yager,we propose a D-S structure decision model to help decision makers for analyzing.