第一百三十六期科技大讲堂：Ranking and Total Ordering on Sets of Fuzzy Numbers

报告人：王震源 教授

单位：University of Nebraska at Omaha, USA

报告时间：2018年7月5日10:00—12:00

报告地点：第三会议室

报告题目：Ranking and Total Ordering on Sets of Fuzzy Numbers

报告概要：Ranking and totally ordering fuzzy numbers are indispensable tools for decision making in fuzzy environment. Regarding real numbers as special fuzzy numbers, any ranking or total ordering defined on sets of fuzzy numbers must coincide with the natural ordering of real numbers. In this work, a general method to establish ranking and total ordering on sets, which is not necessarily countable, of fuzzy numbers is proposed based on using reference systems. The most common reference system is just the set of all real numbers with their natural ordering. Sometimes, more reference systems formed by existing ranked or totally ordered sets are needed. We also propose several criteria of the goodness, such as the geometric intuitiveness and the continuity, for rankings and total orderings on sets of fuzzy numbers. In addition, the concept of fuzzy integers is introduced in this work. The rankings on sets of fuzzy integers are also discussed. Based on newly established Decomposition Theorem IV, we may define total orderings on the set of all fuzzy numbers. This new decomposition theorem can also lead to an important conclusion on the cardinality of the set consisting of all fuzzy numbers.（赵放）

报告人简介：

王震源：1962年毕业于复旦大学数学系，1991年获美国纽约州立大学(Binghamton)博士学位。从1962年开始，王震源任教于河北大学。1979至1981年，以访问学者身份在法国巴黎第六大学概率计算实验室和人工智能实验室从事非可加测度的研究。回河北大学后，历任副教授（1983-1986）、教授（1986-2000）、数学系系主任（1985-1990）。自1989年起，先后在美国宾厄姆顿大学(SUNY- Binghamton) 系统科学系、新墨西哥州立大学数学系、得克萨斯大学 (El Paso) 数学系、以及香港中文大学计算机科学和工程学系分别任客座教授/研究员。王震源自2001年起任教于美国内布拉斯加大学(Omaha)，现为该校数学系终身教授。

王震源曾获河北省科技进步一等奖(1985)、国家科委和劳动人事部颁发的国家级具有突出贡献的中青年科技专家称号(1986)、ISI (美国科学信息研究院, SCI发布者)的经典引文奖(2000)、美国内布拉斯加大学杰出研究和创造性工作奖(2007)等奖励和荣誉称号。他已发表科学论文一百六十余篇，并出版三部专著：Fuzzy Measure Theory（Plenum，1992）、Generalized Measure Theory （Springer, 2008）、Nonlinear Integrals and Their Applications in Data Mining （World Scientific，2010）。他是 Fuzzy Sets and Systems 等国际杂志的编委。王震源曾任第七、八、九届全国政协委员。