On the Structure of the Non-dominated Set for Bicriteria Programmes

In multiple-objective programming, a knowledge of the structure of the non-dominated set can aid in generating efficient solutions. We present new concepts which allow for a better understanding of the structure of the set of non-dominated solutions for non-convex bicriteria programming problems. In particular, a means of determining whether or not this set is connected is examined. Both supersets and newly defined subsets of the non-dominated set are utilized in this investigation. Of additional value is the use of the lower envelope of the set of outcomes in classifying feasible points as (properly) non-dominated solutions.     

Sets and Classes as Many

In this paper the view is developed that classes should not be understood as individuals, but, rather, as classes as many of individuals. To correlate classes with individuals labelling and colabelling functions are introduced and sets identified with a certain subdomain of the classes on which the labelling and colabelling functions are mutually inverse. A minimal axiomatization of the resulting system is formulated and some of its extensions are related to various systems of set theory, including nonwellfounded set theories.     

The Structure of the Ordinals and the Interpretation of ZF in Double Extension Set Theory

Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to ₀ formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals.     

Closing the gap between behavior and models in route choice: The role of spatiotemporal constraints and latent traits in choice set formation

A considerable gap exists between the behavioral paradigm of choice set formation in route choice and its representation in route choice modeling. While travelers form their viable choice set by retaining routes that satisfy spatiotemporal constraints, existing route generation techniques do not account for individual-related spatiotemporal constraints. This paper reduces the gap by proposing a route choice model incorporating spatiotemporal constraints and latent traits. The proposed approach combines stochastic route generation with a latent variable semi-compensatory model representing constraint-based choice set formation followed by compensatory choice. The model is applied to data focusing on habitual commuting route choice behavior in morning peak hours. Results show (i) the possibility of inferring spatiotemporal constraints from considered routes, (ii) the importance of incorporating spatiotemporal constraints and latent traits in route choice models, and (iii) the linkage between spatiotemporal constraints and time saving, spatial and mnemonic abilities.     

Question Design Affects Students' Sense-Making on Mathematics Word Problems

Mathematics word problems provide students with an opportunity to apply what they are learning in their mathematics classes to the world around them. However, students often neglect their knowledge of the world and provide nonsensical responses (e.g., they may answer that a school needs 12.5 buses for a field trip). This study examined if the question design of word problems affects students' mindset in ways that affect subsequent sense-making. The hypothesis was that rewriting standard word problems to introduce inherent uncertainty about the result would be beneficial to student performance and sense-making because it requires students to reason explicitly about the context described in the problem. Middle school students (N = 229) were randomly assigned to one of three conditions. In the standard textbook condition, students solved a set of six word problems taken from current textbooks. In the modified yes/no condition, students solved the same six problems rewritten so the solution helped answer a “yes” or “no” question. In the disfluency control condition, students solved the standard problems each rewritten in a variety of fonts to make them look unusual. After solving the six problems in their assigned condition, all students solved the same three “problematic” problems designed to assess sense-making. Contrary to predictions, results showed that students in the modified yes/no condition solved the fewest problems correctly in their assigned condition problem set. However, consistent with predictions, they subsequently demonstrated more sense-making on the three problematic problems. Results suggest that standard textbook word problems may be able to be rewritten in ways that mitigate a “senseless” mindset.     

Can spatialisation be extended to episodic memory and open sets?

The SPoARC effect (Spatial Positional Associated Response Codes) has only been observed in working memory (WM) using closed sets. It is interpreted as showing that individuals spatialise to-be-remembered items in a left-to-right fashion, using spatialisation as context. Given that context is crucial for episodic memory (EM), we tested if this effect could be observed in EM by using 15-word lists taken from an open set. After each list, 30 probes were sequentially displayed to test recognition. The left/right-hand key assignment for yes/no answers was varied. No SPoARC effect was observed. However, as all previous SPoARC experiments had used short lists and closed sets, it was not possible to know if this absence of SPoARC was due to the open set feature or the length of the lists. A second experiment was thus run using open sets and short 5-word lists, which do not necessitate EM to be remembered. A SPoARC effect was observed indicating that Experiment 1 result was due to the involvement of supra-span lists and that SPoARC effects do not extend to EM with open sets. Experiment 2 also enabled us to generalise the SPoARC effect to open sets in WM for the first time.     

消费者基于选择集的情境效应

消费者基于选择集的情境效应颠覆了传统的理性选择理论,表明了情境对消费者偏好和选择的系统性影响。情境效应主要的类型有吸引效应和折衷效应。情境效应具有感知偏差、风险和负面情绪规避以及信息推理等方面的内在机理。选择集结构和特征及消费者等因素都对情境效应产生影响,而情境效应会影响消费者偏好的构建。未来情境效应研究将会向复杂属性组合、复杂购买情境和新情境效应的发现等方面拓展。     

Elementary Extensions of External Classes in a Nonstandard Universe

In continuation of our study of HST, Hrbaek set theory (a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the st--language, and Saturation for well-orderable families of internal sets), we consider the problem of existence of elementary extensions of inner "external" subclasses of the HST universe.We show that, given a standard cardinal , any set R * generates an "internal" class S(R) of all sets standard relatively to elements of R, and an "external" class L[S(R)] of all sets constructible (in a sense close to the Gödel constructibility) from sets in S(R). We prove that under some mild saturation-like requirements for R the class L[S(R)] models a certain -version of HST including the principle of +-saturation; moreover, in this case L[S(R)] is an elementary extension of L[S(R)] in the st--language whenever sets R R satisfy the requirements.