The Impact of “Display‐Set” Options on Decision‐Making

The way a choice set is constructed can have a significant influence on how individuals perceive and evaluate their options, and make decisions between them. Here, I examine whether a “display set” of visible but unavailable options can exert these same types of influences on whether or not to choose a single (target) item. Across a series of experiments, purchase intent is increased when the display set and target are drawn from the same category, but decreased when the display and target items are mismatched. This effect is shown to depend on perceived similarity, such that increasing display‐target similarity increases purchase intent towards the target. Furthermore, contrary to the predictions made by previous neural and behavioral research on choice sets, the relative value and/or number of display‐only items have no significant impact on these decisions. These findings reveal a novel choice behavior in commonly encountered settings such as online marketplaces. Copyright © 2016 John Wiley & Sons, Ltd.     

Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part I: Model-Based and Axiomatic Approaches

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets. We discuss here the corresponding situation for fuzzy set theory.Our emphasis will be on various approaches toward (more or less naively formed)universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets. What we give is a (critical)survey of quite a lot of such approaches which have been offered in the last approximately 35 years. The present Part I is devoted to model based and to axiomatic approaches; the forth-coming Part II will be devoted to category theoretic approaches. This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005. Presented by Jacek Malinowski     

Attribute Partitioning in Multiple Attribute Decision Making Problems for a Decision with a Purpose – a Fuzzy Approach

This work introduces a methodology to find solutions corresponding to different purposes in a multiple attribute decision‐making problem under fuzzy environment. The discernment of purpose‐based solutions becomes important when the problem is defined vaguely and solution is targeted to heterogeneous population. Depending on the purpose, for which the solution is sought, the attributes are identified and weighted in an appropriate proportion. The level of similarity between a pair of attributes plays an important role to determine the aggregated value of attributes specific to a purpose. Our work determines the similarity levels between a pair of attributes by calculating their maximum attainability in presence of each other. The achievement of an attribute in presence of another is represented as a fuzzy set in the unit interval. The crisp equivalents of the fuzzy sets in the unit interval are used to define their simultaneous satisfaction denoted as 1‐step relation. The 1‐step relation is extended to (m‐1)‐step relation to calculate the degree of attainability of the same pair of attributes in the presence of m (all) attributes. The different levels of (m‐1)‐step relations generate several partitions of the attributes corresponding to multiple purposes in the multiple attribute decision‐making problems. The degree of fulfilment of the purposes in the alternatives are numerically derived by first taking weighted average of attributes within the equivalence classes of a partition and then aggregating the values corresponding to equivalence classes through ordered weighted averaging. The methodology is illustrated with a numerical example. Copyright © 2016 John Wiley & Sons, Ltd.     

On the evaluation and application of different scales for quantifying pairwise comparisons in fuzzy sets

One of the most critical issues in many applications of fuzzy sets is the successful evaluation of membership values. A method based on pairwise comparisons provides an interesting way of evaluating membership values. That method was proposed by Saaty, almost 20 years ago, and since then has captured the interest of many researchers around the world. However, recent investigations reveal that the original scale may cause severe inconsistencies in many decision-making problems. Furthermore, exponential scales seem to be more natural for humans to use in many decision-making problems. In this paper two evaluative criteria are used to examine a total of 78 scales which can be derived from two widely used scales. The findings in this paper reveal that there is no single scale that can outperform all the other scales. Furthermore, the same findings indicate that a few scales are very efficient under certain conditions. Therefore, for a successful application of a pairwise-comparison-based method the appropriate scale needs to be selected and applied.     

Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part II: Category Theoretic Approaches

For classical sets one has with the cumulative hierarchy of sets, with axiomatizations like the system ZF, and with the category SET of all sets and mappings standard approaches toward global universes of all sets.We discuss here the corresponding situation for fuzzy set theory. Our emphasis will be on various approaches toward (more or less naively formed) universes of fuzzy sets as well as on axiomatizations, and on categories of fuzzy sets.What we give is a (critical) survey of quite a lot of such approaches which have been offered in the last approximately 35 years.Part I was devoted to model based and to axiomatic approaches; the present Part II is devoted to category theoretic approaches.This paper is a version of the invited talk given by the author at the conference Trends in Logic III, dedicated to the memory of A. MOSTOWSKI, H. RASIOWA and C. RAUSZER, and held in Warsaw and Ruciane-Nida from 23rd to 25th September 2005.     

Event-related EEG oscillations to semantically unrelated words in normal and learning disabled children

Learning disabilities (LD) are one of the most frequent problems for elementary school-aged children. In this paper, event-related EEG oscillations to semantically related and unrelated pairs of words were studied in a group of 18 children with LD not otherwise specified (LD-NOS) and in 16 children with normal academic achievement. We propose that EEG oscillations may be different in LD NOS children versus normal control children that may explain some of the deficits observed in the LD-NOS group. The EEGs were recorded using the 10/20 system. EEG segments were edited by visual inspection 1000ms before and after the stimulus, and only correct responses were considered in the analysis. Time-frequency (1-50Hz) topographic maps were obtained for the increases and decreases of power after the event with respect to the pre-stimulus average values. Significant differences between groups were observed in the behavioral responses. LD-NOS children show less number of correct responses and more omissions and false alarms than the control group. The event-induced EEG responses showed significant differences between groups. The control group showed greater power increases in the frequencies 1-6Hz than the LD-NOS group from 300 to 700ms. These differences were mainly observed in frontal regions, both to related and non-related words. This was interpreted as a deficit in attention, both to internal and external events, deficits in activation of working memory and deficits in encoding and memory retrieval in the LD-NOS children. Differences between groups were also observed in the suppression of alpha and beta rhythms in the occipital regions to related words in frequencies between 8 and 17Hz from 450 to 750ms. LD-NOS children showed shorter durations of the decreases in power than the control group. These results suggest also deficits in attention and memory retrieval. It may be concluded that LD-NOS children showed physiological differences from normal children that may explain their cognitive deficiencies.     

Creativity,Problem Solving,and Solution Set Sightedness: Radically Reformulating BVSR

Too often, psychological debates become polarized into dichotomous positions. Such polarization may have occurred with respect to Campbell's (1960) blind variation and selective retention (BVSR) theory of creativity. To resolve this unnecessary controversy, BVSR was radically reformulated with respect to creative problem solving. The reformulation began by defining (a) potential solution sets consisting of k possible solutions each described by their respective probability and utility values, (b) a set sightedness metric that gauges the extent to which the probabilities correspond to the utilities, and (c) a solution creativity index based on the joint improbability and utility of each solution. These definitions are then applied to representative cases in which simultaneous or sequential generate‐and‐test procedures scrutinize solution sets of variable size and with representative patterns of probabilities and utilities. The principal features of BVSR theory were then derived, including the implications of superfluity and backtracking. Critically, it was formally demonstrated that the most creative solutions must emerge from solution sets that score extremely low in sightedness. Although this preliminary revision has ample room for further development, the demonstration proves that BVSR's explanatory value does not depend on any specious association with Darwin's theory of evolution.     

Inferential procedures for correlation coefficients corrected for attenuation

A model and computational procedure based on classical test score theory are presented for determination of a correlation coefficient corrected for attenuation due to unreliability. Next, variance-covariance expressions for the sample estimates defined earlier are derived, based on application of the delta method. Results of a Monte Carlo study are presented in which the adequacy of the derived expressions was assessed for a large number of data forms and potential hypotheses encountered in the behavioral sciences. It is shown that, based on the proposed procedures, confidence intervals for single coefficients are reasonably precise. Two-sample hypothesis tests, for both independent and dependent samples, are also accurate. However, for hypothesis tests involving a larger number of coefficients than two—both independent and dependent—the proposed procedures require largens for adequate precision. Results of a preliminary power analysis reveal no serious loss in efficiency resulting from correction for attenuation. Implications for practice are discussed.Support for the research reported in this article was provided by the Natural Sciences and Engineering Research Council of Canada. The authors acknowledge with thanks the constructive comments of the editor and three anonymous reviewers.