Cluster differences scaling with a within-clusters loss component and a fuzzy successive approximation strategy to avoid local minima

Cluster differences scaling is a method for partitioning a set of objects into classes and simultaneously finding a low-dimensional spatial representation ofK cluster points, to model a given square table of dissimilarities amongn stimuli or objects. The least squares loss function of cluster differences scaling, originally defined only on the residuals of pairs of objects that are allocated to different clusters, is extended with a loss component for pairs that are allocated to the same cluster. It is shown that this extension makes the method equivalent to multidimensional scaling with cluster constraints on the coordinates. A decomposition of the sum of squared dissimilarities into contributions from several sources of variation is described, including the appropriate degrees of freedom for each source. After developing a convergent algorithm for fitting the cluster differences model, it is argued that the individual objects and the cluster locations can be jointly displayed in a configuration obtained as a by-product of the optimization. Finally, the paper introduces a fuzzy version of the loss function, which can be used in a successive approximation strategy for avoiding local minima. A simulation study demonstrates that this strategy significantly outperforms two other well-known initialization strategies, and that it has a success rate of 92 out of 100 in attaining the global minimum.     

The Comparative Set Fallacy

This paper argues for the validity of inferences that take the form of: A is more X than B; therefore A and B are both X. After considering representative counterexamples, it is claimed that these inferences are valid if and only if the comparative terms in the inference are taken from no more than one comparative set, where a comparative set is understood to be comprised of a positive, comparative, and superlative, represented as {X, more X than, most X}. In all instances where arguments appearing to be of this form are invalid, it is the case that the argument has fallaciously taken terms from more than one comparative set. The fallacy of appealing to more than one comparative set in an inference involving comparative terms is shown to be analogous to the fallacy of equivocation in argumentation. The paper concludes by suggesting a conflation of logical issues with grammatical issues is the core difficulty leading some to consider inferences in the form of A is more X than B; therefore A and B are X to be invalid.     

Fuzzy Identities for an Inclusive Anglohispanic Dialogue

When constructed in linear terms, cultures and identities misrepresent other people, constructing crisp boundaries that separate groups as if completely different. To demonstrate the negative impact of such views, I analyze cultural texts such as songs, films, and Web pages, showing the intercultural complexity existing in different constructions of Mexicanness as part of the dialogue arising in the political, social, and cultural interaction between Mexico and the United States. I emphasize the contrast between examples that reinforce identities that can be interpreted as fuzzy and inclusive, against those promoting and generating discrimination and exclusion.     

Help or hinder? When recommendation signage expands consideration sets and heightens decision difficulty

This research examines whether recommendation signage helps or hinders the consumer when faced with choosing from large product assortments. In spite of frequent usage and retailer intuition suggesting that providing recommendation signs (e.g., “Best Seller,” “Award Winner”) should help consumers in the choice process, we propose that signs can hinder choice for consumers with more developed preferences by adding to the complexity and difficulty of the decision process. In three experiments using horizontally differentiated products in multiple categories, we provide evidence that recommendation signs create preference conflict for consumers with more developed preferences, leading these consumers to form larger consideration sets and ultimately experience more difficulty from the decision-making process. In addition, we show that these effects are mitigated for consumers with less developed preferences and when the choice is from a small assortment. The results suggest that recommendation signage may not be an effective tool for aiding choice from large assortments; instead signage can exacerbate the difficulties associated with having too many choices, with implications on purchase quantity.     

A Note on Prototypes,Convexity and Fuzzy Sets

The work on prototypes in ontologies pioneered by Rosch [10] and elaborated by Lakoff [8] and Freund [3] is related to vagueness in the sense that the more remote an instance is from a prototype the fewer people agree that it is an example of that prototype. An intuitive example is the prototypical “mother”, and it is observed that more specific instances like ”single mother”, “adoptive mother”, “surrogate mother”, etc., are less and less likely to be classified as “mothers” by experimental subjects. From a different direction Gärdenfors [4] provided a persuasive account of natural predicates to resolve paradoxes of induction like Goodman’s “Grue” predicate [5]. Gärdenfors proposed that “quality dimensions” arising from human cognition and perception impose topologies on concepts such that the ones that appear “natural” to us are convex in these topologies. We show that these two cognitive principles — prototypes and predicate convexity — are equivalent to unimodal (convex) fuzzy characteristic functions for sets. Then we examine the case when the fuzzy set characteristic function is not convex, in particular when it is multi-modal. We argue that this is an indication that the fuzzy concept should really be regarded as a super concept in which the decomposed components are subconcepts in an ontological taxonomy.     

刻板印象的自动激活实验研究

本研究应用模糊主次评判方法配合语义启动技术进行实验。结果表明;在年龄刻板印象上存在自动激活,而且没有性别差异;用不同性质的启动词来激活与年龄有关的刻板印象,激活后的刻板印象对年龄的判断有不同的影响,而且被试没有一个人意识到这点,表明内隐刻板印象的存在;人的判断具有模糊性,模糊主次评判方法有助于社会认知领域的量化研究,这是一个全新的尝试。     

模糊分组的时间层次网络结构研究

本研究通过两个实验来对连续性的时间顺序标码的层次网络结构的性质进行了探讨。研究结果表明,连续性的时间顺序标码是按照层次网络的结构组织起来的,若干项目组成一个小组,若干小组组成更大的组。连续性的时间标码层次网络的形成具有自动性、内隐性的特点。连续性的时间顺序标码的层次网络结构是主观的、模糊的。两个相邻的小组的项目之间出现了距离效应,而两个相邻的大组的项目之间则出现了越界效应,由于两个大组的项目的平均距离大于两个小组的项目的平均距离,越界效应大于距离效应。