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.     

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.     

The lure of choice

We report three studies demonstrating the ‘lure of choice’ people prefer options that allow them to take further choices over those that do not, even when the extra choices cannot improve the ultimate outcome. In Studies 1 and 2, participants chose between two options: one solitary item, and a pair of items between which they would then make a further choice. Consistent with the lure of choice, a given item was more likely to be the ultimate choice when it was initially part of a choice pair than when it was offered on its own. We also demonstrate the lure of choice in a four‐door version of the Monty Hall problem, in which participants could either stick with their original choice or switch to one of two unopened doors. Participants were more likely to switch if they could first ‘choose to choose’ between the two unopened doors (without immediately specifying which) than if they had to choose one door straightaway. We conclude by suggesting that the lure of choice is due to a choice heuristic that is very reliable in the natural world, but much less so in a world created by marketers. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

A Contextual-Hierarchical Approach to Truth and the Liar Paradox

This paper presents an approach to truth and the Liar paradox which combines elements of context dependence and hierarchy. This approach is developed formally, using the techniques of model theory in admissible sets. Special attention is paid to showing how starting with some ideas about context drawn from linguistics and philosophy of language, we can see the Liar sentence to be context dependent. Once this context dependence is properly understood, it is argued, a hierarchical structure emerges which is neither ad hoc nor unnatural.     

Innovative method to evaluate quality management system audit results’ using single value neutrosophic number

Using Quality Management System (QMS) enables the organization to fulfil its purpose and mission to meet customers and regulatory requirements and improve its effectiveness and efficiency on a continuous basis, Quality Audit is very critical tool to ensure that the standards, policies and/or procedures are applied in the organization as planned in QMS, in real world applications, the results of the Quality Audit process depend on the auditors’ human judgments that characterized with doubts sometimes, estimating values another times, and using general impressions in his judgment, which motivate to introduce for the first time the Neutrosophic Quality Audit (NQA) model which can be extended to manage and audit in the future. NQA will be used to enhance the way of evaluating the quality audit results while many uncertainty aspects and indeterminacy do exist, the proposed model using Single Value Neutrosophic Numbers (SVNN) which is an instance of neutrosophic set, to overcome the weakness of using a crisp value to present the result of the audit findings, in addition, using Simplified Neutrosophic Weighted Geometric Average Operator (SNWGAO), and cosine similarity degree, an illustrative example is provided to validate the proposed model.