Conditional Distributivity Equation For Uninorms With Continuous Underlying Operators And Its Inner Structure Characterization

As the mathematical model corresponding to information fusion,aggregation operators perform the combination of several inputs into a single output.In the practical applications,the construction and choice of aggregation operators is an important and difficult issue.The choice of a appropriate aggregation operator has a critical impact to information fusion which can determine the merits and demerits of fusion effect.Uninorms with continuous underlying operators as an important aggregation operators has a very wide range of applications,such as fuzzy recognition,image processing,data fusion and so on.While in the litera-ture many results about uninorms just related to the structures and some prop-erties of it under some strong conditions,or discussing some functional equations about uninorms based on the special classes,such as distributivity,migrativity and modality.This dissertation focused on the research about uninorms with continuous underlying operators.This paper mainly devoted to solving the functional equa-tions of conditional distributivity and discussing the inner structure of uninorms with continuous underlying operators.This dissertation includes two parts.In the first part,we investigate the functional equation of conditional distributivity of uninorms with continuous underlying operators and the almost complete char-acterization of such a pair?₁,₂?of uninorms is given except for only a small fraction of the unit square.In the second part,we characterize the inner structure of uninorms with continuous underlying operators given by ordinal sums,and then presents some of their properties.