| After several decades of research,the aggregation function has been widely used in many practical problems.Whether it is in mathematics or computational science,or in the field of sociology,the aggregation function is an important research tool.The uni-nullnorms studied in this article are an important class of aggregation functions.Uni-nullnorm is a special case of 2-uninorm obtained by letting a uninorm and a nullnorm sharing the same underlying t-cornorm.The widely studied t-norms,t-cornorms,uninorms and nullnorms can all be regarded as the special cases of uni-nullnorms.Therefore,uni-nullnorm is the extension of a large class of objects including these aggregation functions,so its structure and properties should be very rich.However,because the concepts of 2-uninorm and uni-nullnorm are introduced relatively late,the research on them is still lacking.On the basis of the introduction of the related concepts and the existing results of the aggregation function,in this paper,we first discuss the general characteristics of uni-nullnorms from the overall point of view,introduce the structure of uni-nullnorms,and then study the local internal properties of the conjunctive uni-nullnorm and the disjunctive uni-nullnorm on the boundary respectively.In this paper,uni-nullnorm is divided into four categories according to the different boundary types,and we discuss on what conditions a function can be defined as an uni-nullnorm as well as the relationship between uni-nullnorms and its underlying t-norms and t-conorms,Finally,the properties of disjunctive uni-nullnorms are introduced. |
