Distributivity And Conditional Distributivity Between Quasi-t-operators And Semi-S-uninorms

Aggregation operators play an important role in fuzzy control,fuzzy logic,image processing,artificial intelligence and so on.The distributivity and conditional distributivity of aggregation operators have become a hot topic of research.Many literatures investigate the algebraic structure of aggregation operators satisfying the properties of distributivity and conditional distributivity.Quasi-t-operators are a special class of aggregation operators,which do not satisfy the commutative law and associative law.So far,there is little relative research on the extension or the left(resp.right)distributivity of quasi-t-operators.In this paper,we mainly discuss the distributivity and conditional distributivity between quasi-t-operators and semi-S-uninorms.Firstly,we discuss the necessary and sufficient conditions for the left(resp.right)distributivity of semi-S-uninorms over quasi-t-operators,that is,the concrete algebraic structure of semi-S-uninorms and the idempotent property of quasi-t-operators satisfying the relationship of different parameters.On this basis,we obtain the necessary and sufficient conditions for the distributivity of semi-S-uninorms over quasi-t-operators.Secondly,we study the left(resp.right)distributivity of quasi-t-operators over semi-S-uninorms.In particular,under certain conditions,because we have given two different sufficient conditions for the distributivity of quasi-toperators over semi-S-uninorms from the left(resp.right),the necessary and sufficient conditions cannot be obtained.Finally,we discuss the conditional distributivity of quasit-operators over semi-S-uninorms.In particular,under certain conditions,the conditional distributivity of quasi-t-operators over semi-S-uninorms from the left(resp.right)is equivalent to the left(resp.right)distributivity of quasi-t-operators over semi-S-uninorms,and the conditional distributivity of quasi-t-operators over semi-S-uninorms is equivalent to the distributivity of quasi-t-operators over semi-S-uninorms.