Research On The Migrativity Of Two Classes Of Uninorms

Aggregation functions are mathematical models describing the process of information aggregation.They play important roles in approximate reasoning,fuzzy sets and fuzzy logic.In order to meet the needs of different fields,people have constructed a large number of different types of aggregation functions.As an important aggregation function,uninorms have good algebraic properties.As an important property of binary aggregation functions,migrativity has good application value in information aggregation,image processing and decision-making.The characterization of migrativity between common classes of uninorms has always been a hot topic of research.This thesis investigates the migrativity between two classes of uninorms.The main arrangements are as follows:Chapter 1 reviews the research background and current status of migrativity,introduces the main content and research significance of this thesis.Chapter 2 reviews the definitions and important properties of t-norms,t-conorms and uninorms.Common classes of uninorms and related lemmas for uninorms with continuous underlying operators are recalled.Chapter 3 discusses the migrativity of two classes of uninorms.The first class refers to a class of conjunctive uninorms locally internal on the boundary,while rhe second class refers to a class of uninorms locally internal in the region A(e)=[0,1]2\([0,e]2 ∪[e,1]2)having continuous underlying operators.We discuss the migrativity of these two classes of uninorms in different situations and provide necessary and sufficient conditions for the relevant migrativity equality to hold.Finally,we compare and summarize the results of this thesis with the migrativity conclusions of other common uninorms.Chapter 4 summary and prospects for future work.