報告題目：On convex MV-algebras
報告人：史福貴 教授（北京理工大學(xué)）
報告時間： 2024年5月15日（周三）下午14：00-15：00
主持人：朱萍 教授
報告地點：北京郵電大學(xué)沙河校區(qū)理學(xué)樓520
報告摘要：
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.
專家簡介：
史福貴，北京理工大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院二級教授，博士生導(dǎo)師，主要從事模糊集理論，模糊拓撲，模糊擬陣，模糊凸空間和凸代數(shù)等的研究，發(fā)表論文200余篇，主持國家自然科學(xué)基金四項和教育部博士點基金一項?，F(xiàn)任中國系統(tǒng)工程學(xué)會模糊數(shù)學(xué)與模糊系統(tǒng)委員會副理事長，北京運籌學(xué)會副理事長，北京數(shù)學(xué)會副監(jiān)事長，中國運籌學(xué)會理事；《Iranian Journal of Fuzzy Systems》、《Mathematics》、《數(shù)學(xué)實踐與認識》、《模糊系統(tǒng)與數(shù)學(xué)》等雜志編委。
