Some Research On Associative Aggregation Operators

The process of putting different information together into a single value is called aggregation.The function used in this process is called aggregation operator.A high level of attention is focus on the aggregation operators satisfying associativity.In this context,we mainly introduce the solution of functional equations involving associative aggregation operators and the results of associative aggregation operators on bounded lattices.More precisely,this paper contains the following contents:(1)We mainly devote to solve the distributivity equations between 2-uninorms and semi-t-operators,without the assumption that semi-t-operator is continuous.Previous results about t-norms,t-conorms,uninorms and nullnorms over t-norms,tconorms,nullnorms and semi-t-operators can be obtained as simple corollaries.(2)Firstly,we give the solution of t-norms,t-conorms,uninorms,T-uninorms and semit-operators distribute over S-uninorms.Moreover,we describe t-norms,T-uninorms and semi-t-operators that are conditional distributive over S-uninorms.(3)We extend modular condition for aggregation operators to modular condition for uni-nullnorms.Modularity condition between disjunctive(resp.conjunctive)uninullnorms and some most studied classed of binary aggregation operators(i.e.,tnorms,t-conorms,uninorms and semi-t-operators)are discussed.Since uni-nullnorms are extensions of nullnorms and uninorms,previous results about modularity condition for nullnorms and uninorms can be obtained as simple corollaries.(4)We study semi-t-operators on bounded lattices and show the existence of semit-operators using some constructive approaches.A partial order relation is also defined based on the semi-t-operator and some properties of this relation are examined.Finally,we apply to the semi-t-operators on interval-valued.