报告人简介：杨忠强，闽南师范大学二级教授，博士生导师。1990年和1994年分别在四川大学数学系和日本筑波大学数学研究所取得理学博士学位和博士（数学）学位。获陕西省政府科技进步一等奖，4次主持国金自然科学面上项目，4次主持省部级自然科学面上项目，两次获得中国国家留学基金委资助赴外研究。研究领域为无限维拓扑学，一般拓扑学，格上拓扑学，模糊数学，格论，拓扑动力系统等。在科学出版社出版专著一部，发表论文80余篇，其中高质量论文50余篇。

报告摘要：For a subset Y of the n-dimensional Euclidean space Rⁿwith |Y |≥2, let U(Y ) be the family of all fuzzy setsinRⁿ, which are upper-semicontinuous, normal and with compact supports included in Y . And let K(Y ) bea subfamily of U(Y ) consisting of all fuzzy sets which are fuzzy convex. In the set U(Y ), consider four naturalmetrics: the endograph metric D, the sendograph metric S, the L_pmetric and the L_∞metric. For a set S,let ∆(S) = {t∈[0,1]S| t(s) = 0 for all but finitely many s andsum = 1}. We can define two naturaltopologies P and C on ∆(S). There exists the natural weighted mean map φ : ∆(S) × U(Y )S→U(Rⁿ).Using these metrics and topologies, we can define 16 topologies on the set ∆(S) × U(Y )^S. In the presentpaper, we discuss the relations of these topologies and the continuity of φ with respect to these topologies.In particular, we give some characterizations of the continuity of the map φ : ∆(S) × U(Y )S→U(Rⁿ) oneach topology, and of the continuity of map φ(·,F₀) : ∆(S)→U(Rⁿ) on each topology. For K(Y ), we provealmost all results as U(Y).