报告题目：On convex MV-algebras

报告人：史福贵 教授（北京理工大学）

报告时间： 2024年5月15日（周三）下午14：00-15：00

主持人：朱萍 教授

报告地点：24848威尼斯沙河校区理学楼520

报告摘要：

The aim of this report is to introduce convex structures on MV-algebras such that the MV-operations are convexity preserving or weak convexity preserving. Therefore, we propose the concepts of paraconvex MV-algebras and weak convex MV-algebras. We give some characterizations of weak convex MV-algebras. Further, we show that the standard MV-algebra endowed with its interval convexity is a weak convex MV-algebra. In particular, a finite MV-chain endowed with a non-trivial convex structure is a weak convex MV-algebra iff the convex structure is precisely its interval convexity. Moreover, the direct product of finite weak convex MV-algebras is still a weak convex MV-algebra. Based on this, we further get that each finite MV-algebra endowed with its interval convexity is a weak convex MV-algebra. By using ideals, we introduce the ideal convexity on an MV-algebra which turns it to be a paraconvex MV-algebra. Finally, we discuss the separation axioms on weak convex MV-algebras.

专家简介：

史福贵，北京理工大学数学与统计学院二级教授，博士生导师，主要从事模糊集理论，模糊拓扑，模糊拟阵，模糊凸空间和凸代数等的研究，发表论文200余篇，主持国家自然科学基金四项和教育部博士点基金一项。现任中国系统工程学会模糊数学与模糊系统委员会副理事长，北京运筹学会副理事长，北京数学会副监事长，中国运筹学会理事；《Iranian Journal of Fuzzy Systems》、《Mathematics》、《数学实践与认识》、《模糊系统与数学》等杂志编委。