﻿ The Law of Importation in Mathematical Fuzzy Logics-西南交通大学数学学院

# The Law of Importation in Mathematical Fuzzy Logics

2022-12-06 数学学院 点击：[]

陕西师范大学周红军教授学术报告

报告人：周红军教授 陕西师范大学数学与统计学院

报告题目：The law of importation in mathematical fuzzy logics

报告时间：2022127日（星期三）19:00-21:00

报告地点：腾讯会议：984-634-300

报告内容简介：

The law of importation (LI) x→(y→ z)=(x Ä y)→ z between implication → and conjunction Ä proves to be an important property in mathematical fuzzy logic at both sides of theory and application. One open problem repeatedly mentioned in literature in recent decades is to find all possible pairs of fuzzy implications and t-norms/uninorms satisfying (LI). In this talk we will provide first a survey on known solutions to (LI) in the literature, where we will elaborate on the Massanet-Torrens’s (N, U)-implication solutions by characterizing the compatibility between continuous fuzzy negations N and t-norms as well as uninorms U and two types of generator generated implication solutions proposed recently by the speaker. Then, as an application of (LI), we will propose two new kinds of triple I methods based on our generator generated implications and associated t-norms to solve the generalized modus ponens problem in approximate reasoning. Finally, we will outline some further studies on this topic including the algebraic structures of importation algebras which can serve as an algebraic axiomatization of (LI).

报告人简介：

周红军，博士，教授，博士生导师，毕业于陕西师范大学，美国Vanderbilt大学公派博士后。研究领域为序代数与逻辑、不确定性的数学理论等。主持国家自然科学基金4项，教育部博士点基金新教师类项目、陕西省基础研究计划项目、陕西省青年科技新星计划项目、中国科协学风传承精品项目及陕西省教育教学改革项目各1项。在《Ann. Pure Appl. Logic》《Arch. Math. Logic》《J. Mult.-Valued Logic & Soft Comput.》《IEEE Trans. Fuzzy Syst.》《Fuzzy Sets Syst.》《Intern. J. Approx. Reason.》《Inform. Sci.》《中国科学》《数学学报》等国内外学术期刊上发表论文50余篇，在科学出版社出版专著2部。获陕西高校科技成果奖一二等奖各1次。入选陕西省中青年科技创新领军人才和青年科技新星计划。任非经典逻辑与计算专委会秘书长、模糊数学与模糊系统专委会副秘书长、陕西省数学会常务理事、陕西师范大学学术委员会学术评价专门委员会委员和陕西师大学报(自然科学版)编委。

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