报告题目：Uninorms and their extension
In this talk, we first show an extension of uninorms called semi-uninorms, talk about the residual operators of semi-uninorms and the induced semi-uninorms by implications on a complete lattice. Then, we talk about the distributivity and conditional distributivity of semi-uninorms and continuous t-conorms, which closely relates an open problem recalled by Klement in the Linz2000 closing session. Furthermore, by weakening the neutral element condition of semi-uninorms, we introduce weak-neutral semiuninorms (shortly, wn-semiuninorms). After analyzing their structure, several classes of wn-semiuninorms are presented. Particularly, based on a kind of monotone unary functions which are not necessarily continuous and strictly monotone, we introduce representable wn-semiuninorms. We show that there is no idempotent proper wn-semiuninorm. Each representable wn-semiuninorm is Archimidean but not strictly monotone, and its additive generator is unique up to a positive multiplicative constant under some conditions.