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.     

记忆集对注意焦点转换及其返回抑制的影响

采用记忆更新任务,实验1要求被试分别更新3个和4个记忆项目,并设置不转换、控制转换和抑制转换条件,考察记忆集对注意焦点转换及其返回抑制的影响;实验2操纵两次更新同一记忆项目之间对其它记忆项目更新的次数（2次、3次及3次以上）,在实验1基础上,考察返回抑制中项目抑制状态的消退过程.结论：随记忆集增加,转换代价增大,而返回抑制效应消失;当注意焦点对其它记忆项目更新2次时,之前被抑制项目的抑制状态可完全消退.     

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.     

Mathematical concepts for analyzing ambiguous situations

Abstract

We examine some mathematical tools for dealing with ambiguous situations. The main tool is the use of non-standard logic with truth-values in what is called a locale. This approach is related to fuzzy set theory, which we briefly discuss. We also consider probabilistic concepts. We include specific examples and describe the way a researcher can set up a suitable locale to analyse a concrete situation.     

Categoricity Theorems and Conceptions of Set

Two models of second-order ZFC need not be isomorphic to each other, but at least one is isomorphic to an initial segment of the other. The situation is subtler for impure set theory, but Vann McGee has recently proved a categoricity result for second-order ZFCU plus the axiom that the urelements form a set. Two models of this theory with the same universe of discourse need not be isomorphic to each other, but the pure sets of one are isomorphic to the pure sets of the other.This paper argues that similar results obtain for considerably weaker second-order axiomatizations of impure set theory that are in line with two different conceptions of set, the iterative conception and the limitation of size doctrine.