基于改进VIKOR方法的地震应急物资运输决策问题研究

地震灾害应急救援物资方案的合理选择对与减少人员伤亡,降低灾民的财产损失具有重要影响。本文针对属性权重未知情形下的地震应急物资运输方案决策问题,提出了一种Pythagorean模糊不确定语言与前景理论相结合的改进VIKOR决策方法,即PFUL-PT-VIKOR法。首先,采用Pythagorean模糊不确定语言用于描述和融合专家对地震应急物资运输方案在考虑多种属性影响下的感知信息;其次,利用主客观融合法对属性权重进行求解;然后,提出基于前景理论的改进VIKOR法并得出方案排序;最后,通过算例分析,对所提出方法的有效性和实践性给予验证。结果表明,PFUL-PT-VIKOR模型有助于增强决策专家对不确定突发情景信息感知的知识表示能力,解决属性赋权过于主观或过分依赖样本的困难,并突围了应急决策者隐性心理行为较难定量应用的思维定势,增强了模型的现实适用性,为地震应急物资是否合理运输提供决策支持。     

不确定环境下基于时间、费用及鲁棒性权衡的多目标项目调度优化

项目调度中的时间和费用是两个重要的指标,而在不确定环境下进度计划的鲁棒性则是保证项目平稳实施的关键。本文研究不确定环境下的多目标项目调度优化问题,以优化项目的工期、鲁棒值和成本为目标安排各活动的开始时间。基于此,作者构建多目标项目调度优化模型,将模型分解为三个子模型分析目标间的权衡关系,然后设计非劣排序遗传算法进行求解,应用精英保留策略和基于子模型权衡关系的优化策略优化算法,进行算法测试和算例参数敏感性分析。最后,应用上述方法研究一个项目实例,计算得到非劣解集,实例的敏感性分析结果进一步验证了三个目标间的权衡关系,据此提出资源的有效利用策略。本文的研究可以为多目标项目调度制定进度计划提供定量化决策支持。     

The impact of a conceptual model-based mathematics computer tutor on multiplicative reasoning and problem-solving of students with learning disabilities

The study explored the impact of Please Go Bring Me-COnceptual Model-based Problem Solving (PGBM-COMPS) computer tutoring system on multiplicative reasoning and problem solving of students with learning disabilities. The PGBM-COMPS program focused on enhancing the multiplicative reasoning and problem solving through nurturing fundamental mathematical ideas and moving students above and beyond the concrete level of operation. This is achieved by taking advantages of the constructivist approach from mathematics education and explicit conceptual model-based problem solving approach from special education. Participants were three elementary students with learning disabilities (LD). A mixed method design was employed to investigate the effect of the PGBM-COMPS program on enhancing students’ multiplicative reasoning and problem solving. It was found that the PGBM-COMPS program significantly improved participating students’ problem solving performance not only on researcher developed criterion tests but also on a norm-referenced standardized test. Qualitative and quantities data from this study indicate that, in addition to nurturing fundamental concept of composite units, it is necessary to help students to understand underlying problem structures and move toward mathematical model-based problem representation and solving for generalized problem solving skills.     

The notion of motion: covariational reasoning and the limit concept

This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided.     

Solving probability reasoning based on DNA strand displacement and probability modules

In computation biology, DNA strand displacement technology is used to simulate the computation process and has shown strong computing ability. Most researchers use it to solve logic problems, but it is only rarely used in probabilistic reasoning. To process probabilistic reasoning, a conditional probability derivation model and total probability model based on DNA strand displacement were established in this paper. The models were assessed through the game “read your mind.” It has been shown to enable the application of probabilistic reasoning in genetic diagnosis.     

Eliminating counterexamples: A Grade 8 student’s learning trajectory for contrapositive proving

This study uses a teaching experiment and retrospective analysis to develop a learning trajectory for improving a Grade 8 student’s ability to construct, critique, and validate contrapositive arguments. The study is predicated on the hypothesis that adolescents perform poorly on contrapositive reasoning tasks because they lack sufficient ways of justifying contrapositive argumentation as a viable mode of argumentation. By studying a student’s actions and comments as she develops, critiques, and validates not-the-conclusion-implies-the-conditions-are-impossible arguments for conditional claims, a promising learning trajectory for contrapositive argumentation is developed. The student’s learning trajectory demonstrates how a conception of contrapositive proving as eliminating counterexamples can be useful in developing, critiquing, and validating contrapositive arguments.     

基于区间直觉模糊不确定语言的中小企业电子商务网站建设决策方法研究

阐述中小企业在整个国民经济中的重要地位,指出电子商务对于中小企业具有天然的适应性和可行的推广性.揭示研究对象中蕴含着广泛的模糊性,应用区间直觉模糊不确定语言的必要性.介绍区间直觉模糊不确定语言的基本概念、基本运算、算术平均和加权平均、距离、期望函数、精度函数、期望函数值、精度函数值以及对象比较方法等内容.提出区间直觉模糊不确定语言决策步骤:设定方案集、指标集、专家集,确定评判矩阵,确定指标权重,计算加权平均,计算期望函数、精度函数,期望函数值、精度函数值,进行排序.以盛东商贸有限公司电子商务网站设计方案测评为例,碍出方案3优于方案2优于方案5优于方案1优于方案4的结论.     

|sinx|原函数的直接计算法

利用变限积分函数和周期函数的性质,给出了求|sinx|原函数的一种直接计算法.     

Robust output feedback cruise control for high-speed train movement with uncertain parameters

In this paper,the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated.The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers,which is subject to rolling mechanical resistance,aerodynamic drag and wind gust.Based on Lyapunov’s stability theory,the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities(LMIs),under which the high-speed train tracks the desired speed,the relative spring displacement between the two neighboring cars is stable at the equilibrium state,and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed.One numerical example is given to illustrate the effectiveness of the proposed methods.     

Possibilistic nested logic programs and strong equivalence

In this paper, the class of possibilistic nested logic programs is introduced. These possibilistic logic programs allow us to use nested expressions in the bodies and heads of their rules. By considering a possibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logic programing semantics based on answer sets for nested logic programs and the proof theory of possibilistic logic is defined. In order to define a general method for computing the possibilistic answer sets of a possibilistic nested program, the idea of equivalence between possibilistic nested programs is explored. By considering properties of equivalence between possibilistic programs, a process of transforming a possibilistic nested logic program into a possibilistic disjunctive logic program is defined. Given that our approach is an extension of answer set programming, we also explore the concept of strong equivalence between possibilistic nested logic programs. To this end, we introduce the concept of poss SE-models. Therefore, we show that two possibilistic nested logic programs are strong equivalents whenever they have the same poss SE-models.The expressiveness of the possibilistic nested logic programs is illustrated by a scenario from the medical domain. In particular, we exemplify how possibilistic nested logic programs are expressive enough for capturing medical guidelines which are pervaded by vagueness and qualitative information.