| The migrativity is a very important property of aggregation functions,and it is widely used in decision-making and image processing.So far,many profound result-s on migrativity of aggregation functions have been obtained.The thesis chooses to study the mutual migrativity properties between two newly-born subclasses of aggregation functions,namely,overlap functions and uni-nullnorms,including the migrativity properties of overlap functions over uni-nullnorms and the migrativity properties of uni-nullnorms over overlap functions.The main results are characteri-zations of solutions to the migrativity functional equation for all possible combina-tions of overlap functions and uni-nullnorms.The.concrete content is as follows:1:Migrativity properties of overlap functions over uni-nullnorms.Firstly,we investigate the migrativity properties of overlap functions over triangular norms and triangular conorms,and give the characterizations of overlap functions,triangular norms and triangular conorms.Next,we focus on the characterization of migrativity functional equation of overlap functions over uninorms lay in any one of the mostusual classes of uninorms.Then,we discuss the migrativity properties of overlapfunctions over nullnorms,and give the structure of overlap functions and nullnorm-s under the migrativity functional equation.At last,we discuss the migrativity properties of overlap functions over uni-nullnorins.and give the structure of overlap functions and uni-nullnorms under the migrativity functional equation.2:Migrativity properties of uni-nullnorms over overlap functions.We study the migrativity properties of conjunctive and disjumctive uni-nullnorms over over-lap functions respectively,and give the characterizations of migrativity functionalequation. |
