A Fuzzy Topsis Method for Prioritized Aggregation in Multi‐Criteria Decision Making Problems

Aggregation in a decision making environment requires the fusion of opinions of a group of decision makers. The group of decision makers are required to analyse a set of interrelated criteria that are usually measured on a linguistic scale. This process requires, in many instances, to capture experts experience, intuition and thinking that are traditionally expressed in a linguistic fashion rather than a numerical fashion. Furthermore, the necessity of considering the relationship between the criteria to the overall decision must be considered by the group of decision makers. This paper extends the application of fuzzy numbers, fuzzy relative importance scores (FRIS), fuzzy relative weights (FRW) and the fuzzy technique of order preference by similarity to ideal solution (TOPSIS) in prioritized aggregation. This extension provides a mean to systematically aggregate a group of decision makers' views for a set of interrelated criteria that are measured on a linguistic scale. First, an overview of the application of fuzzy numbers and the characteristics of aggregating fuzzy numbers in multi‐criteria decision making problems are presented. Then, the application of TOPSIS in fuzzy environments is presented. Next, past research is highlighted to present prioritized aggregation and the different aggregation operators' classes. Subsequently, a new prioritized aggregation method is presented. This method utilizes fuzzy TOPSIS with prioritized aggregation in fuzzy environments. Finally, the fuzzy prioritized aggregation method presented in this paper is applied on an actual case study. According to the results, the method presented in this paper provides a systematic approach to capture the uncertainty and imprecision associated with quantifying linguistic measurements in multi‐criteria decision making problems. Furthermore, it considers the relationship between the set of linguistically measured criteria undergoing prioritized aggregation in a fuzzy environment. Lastly, findings, conclusions and future work are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

数字空间表征的在线建构：来自干扰情境中数字SNARC效应的证据

尽管已有研究发现数字以空间方式表征在人类记忆系统, 但是人脑如何完成数字的空间表征尚存争议。本研究两个实验在不同比例的数字字母(实验1)和不同比例的数字汉字(实验2)混合情境中考察了数字空间表征特点及其机制, 对上述争议进行了深入研究。结果发现：(1)当数字字母比例为“1 : 1”时, 数字加工中不出现SNARC效应。当数字字母比例为“1 : 6”和“6 : 1”时, 数字加工中均出现SNARC效应。即数字字母比例与数字SNARC效应之间呈倒“U”型关系。(2)数字汉字混合情境中数字汉字比例与数字SNARC效应之间同样呈倒“U”型关系。结果说明：(1)干扰刺激与数字混合呈现会影响数字SNARC效应。(2)干扰刺激加工对数字SNARC效应的影响受到数字与干扰刺激比例的调节, 且具有跨干扰材料的稳定性。研究结果意味着数字的空间表征是人类通过统计学习在线建构的, 支持了工作记忆理论。     

《周易》自然哲学与生命实践

《周易》蕴涵的自然哲学思想,可谓是一种以生命为隐喻,宇宙论、本体论、价值论统一的生成哲学,它基于道德实践与认识实践统一的生命实践。文章根据《周易》"经"、"传"本身之内涵,按现代哲学表述方法,从源于道德之宇宙论,三才圆通之本体论,知行不二之实践论,生成整体之方法论等方面,阐明中国式自然哲学的特性与意义。指出正是这种独特的自然哲学,不仅开启了中国文化超越的价值之源,为中国古代科学提供了形而上学基础,而且应在21世纪伟大历史转型和中西对话中,共同创造人类不同文化"殊途同归"、"和而不同"的世界生成之序。     

听觉通道下负数的低水平加工引起注意的SNARC效应

采用刺激探测任务,探讨了听觉通道下负数的低水平加工能否引起注意的SNARC效应。结果表明:(1)负数的低水平加工能够产生注意的SNARC效应,即线索为绝对值小的负数时,被试对左耳目标反应更快;线索为绝对值大的负数时,被试对右耳目标反应更快。(2)负数的加工所引起听觉空间注意的转移并不依赖于负数所在的情境,而仅通过其绝对值大小与空间表征发生关联。这一结论与视觉条件下所得到的结论不一致,并支持了系统发生论假说。     

外框数目、线索数目和线索类型对返回抑制的影响

采用被试内重复测量设计和经典的线索—靶子实验范式,考查了外框数目（4和8）、线索数目（1和3）、不同线索类型（on-off线索（即线索出现后消失）、onset线索（即线索持续呈现））对返回抑制的影响,发现靶子潜在位置数目越多反应时越长,返回抑制量越小;线索数目越少反应时越长,返回抑制量越大;onset线索反应时长于on-off线索,onset线索产生的返回抑制量大于on-off线索。这表明空间工作记忆负载和记忆痕迹会影响返回抑制。     

正负数混合呈现对负数SNARC效应的影响

采用数字大小判断任务,探讨正负数混合呈现对负数SNARC效应的影响。结果发现,负数单独呈现条件下,负数出现反转的SNARC效应;负数和无加号正数混合呈现,且只对负数作反应条件下,负数有反转SNARC效应;负数和有加号正数混合呈现,且只对负数作反应条件下,负数出现反转SNARC效应;负数和无加号正数混合呈现,并对正负数分别作反应的条件下,负数有反转SNARC效应出现,而正数出现SNARC效应。说明负数空间表征受其绝对值大小的影响,绝对值较小的负数(-1、-2)表征在心理数字线的左侧,绝对值较大的负数(-8、-9)表征在数字线的右侧,且不能延伸至心理数字线左侧。     

邵康节的易学思想

本文以现代日本学者的眼光对邵雍的易学思想作了较为系统的论述。认为邵雍从宇宙观和世界观的理论基础上推演出他的历史观来 ,企图把宇宙世界的生成、万物的存在以及历史的变迁都还原为抽象的数 ,因而一方面难免陷入脱离事实、空洞推演的弊端 ,而在另方面又增加了重视义理以指导人事的内容。所以他的易学思想在古代术数与宋明理学之间 ,起了继往开来的重大作用     

遗传算法与易算算法

本文认为 ,《周易·系辞传》“天地之大德曰生” ;“生生之谓易”等以生命为本并强调生命演化的思想都与西方新兴起的遗传算法 (基因算法 )精神一致。文章在介绍了已故著名科学易学家潘雨廷先生对遗传密码的理解后 ,进而介绍了西方遗传算法的内容和结构 ,并把DNA本体看作计算硬件 ,把易数看作软件。最后比较了象数思维与遗传算法的思维 ,并提出了八卦空间     

Statistical inference of minimum rank factor analysis

For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.This work was supported, in part, by grant DMS-0073770 from the National Science Foundation.