On Consistent Subsets of Large Sets of Satisfiable Sentences

We extend some results of Adam Kolany to show that large sets of satisfiable sentences generally contain equally large subsets of mutually consistent sentences. In particular, this is always true for sets of uncountable cofinality, and remains true for sets of denumerable cofinality if we put appropriate bounding conditions on the sentences. The results apply to both the propositional and the predicate calculus. To obtain these results, we use delta sets for regular cardinals, and, for singular cardinals, a generalization of delta sets. All of our results are theorems in ZFC.     

应用层次析分法和模糊综合评判研究保健品消费心理

将层次分析方法与模糊综合评判理论相结合,以营养成分、包装情况、价格因素、广告宣传、售后服务为一级评判指标,以保健品专卖店、大型超市、小型超市、杂货店、厂家邮购五种销售渠道为二级评价指标,给出一种模糊判断的权重计算方法,建立了保健品消费心理的层次模糊决策模型。应用该模型对长春地区消费者的保健品消费心理进行了测试,结果表明：测试结果与实际销售情况相符。说明应用该方法建立起来的模型在了解消费者对保健品的消费心理方面是可行的,同时也为新型保健品的开发和市场推广提供了一定的依据。     

Ambiguous comparative judgment: Fuzzy set model and data analysis

Abstract:  This paper proposed two types of fuzzy set models for ambiguous comparative judgments, which did not always hold transitivity and comparability properties. The first type of model was a fuzzy theoretical extension of the additive difference model for preference that was used to explain ambiguous preference strength. The second was a fuzzy logic model for explaining ambiguous preference in which preference strength was bounded, such as a probability measure. In both models, multi-attribute weighting parameters and all attribute values were assumed to be asymmetric fuzzy L-R numbers. For each model, a method of parameter estimation using fuzzy regression analysis was proposed. Numerical examples were also provided for comparison. Finally, the theoretical and practical implications of the proposed models were discussed.     

On Judgments of Approximately Equal

Although precision is often important in quantitative judgment, sometimes, it is valuable to recognize that two quantities are roughly the same. Fuzzy‐trace theory suggests that approximately equal judgments rely on gist representations (i.e., meaningful fuzzy categories of quantity). We conducted three experiments to investigate approximately equal judgments with number pairs presented in different formats, both with and without semantic content (breast cancer statistics). In each study, the ratio of the smaller divided by larger number predicted approximately equal judgments. Experiment 1 also examined how knowledge of breast cancer, presentation format (frequencies vs. percentages), and differences in gist comprehension of breast cancer information influence fuzzy equality judgments. As predicted by the fuzzy‐trace theory concept of denominator neglect, approximately equal judgments were more sensitive, as measured by signal detection theory (SDT) analyses, when presented as percentages. In both experiments with breast cancer statistics, people were more likely to judge number pairs approximately equal when they were embedded in sentences about breast cancer, and breast cancer knowledge predicted increased perception of equality, when appropriately consistent with reliable sources, and increased judgment sensitivity. In Experiment 2, a simple intervention focusing on gist meaning increased source‐consistent approximately equal judgments, increased SDT judgment sensitivity, and decreased SDT response bias. In Experiment 3, using number pairs devoid of semantic context spanning four orders of magnitude, we further examined ratio similarity. Overall, more knowledgeable judges and those who better understood the gist of meaningful numbers were more likely to judge literally different numbers as “approximately equal” rather than make precise discriminations that were meaningless. Copyright © 2017 John Wiley & Sons, Ltd.     

A Fuzzy Topsis Method for Prioritized Aggregation in Multi‐Criteria Decision Making Problems

Aggregation in a decision making environment requires the fusion of opinions of a group of decision makers. The group of decision makers are required to analyse a set of interrelated criteria that are usually measured on a linguistic scale. This process requires, in many instances, to capture experts experience, intuition and thinking that are traditionally expressed in a linguistic fashion rather than a numerical fashion. Furthermore, the necessity of considering the relationship between the criteria to the overall decision must be considered by the group of decision makers. This paper extends the application of fuzzy numbers, fuzzy relative importance scores (FRIS), fuzzy relative weights (FRW) and the fuzzy technique of order preference by similarity to ideal solution (TOPSIS) in prioritized aggregation. This extension provides a mean to systematically aggregate a group of decision makers' views for a set of interrelated criteria that are measured on a linguistic scale. First, an overview of the application of fuzzy numbers and the characteristics of aggregating fuzzy numbers in multi‐criteria decision making problems are presented. Then, the application of TOPSIS in fuzzy environments is presented. Next, past research is highlighted to present prioritized aggregation and the different aggregation operators' classes. Subsequently, a new prioritized aggregation method is presented. This method utilizes fuzzy TOPSIS with prioritized aggregation in fuzzy environments. Finally, the fuzzy prioritized aggregation method presented in this paper is applied on an actual case study. According to the results, the method presented in this paper provides a systematic approach to capture the uncertainty and imprecision associated with quantifying linguistic measurements in multi‐criteria decision making problems. Furthermore, it considers the relationship between the set of linguistically measured criteria undergoing prioritized aggregation in a fuzzy environment. Lastly, findings, conclusions and future work are presented. Copyright © 2016 John Wiley & Sons, Ltd.     

A Decision Support System for Prioritizing Investments in an Energy Efficiency Program in Favelas in the City of Rio de Janeiro

This study proposes an integrated qualitative and quantitative assessment of expert opinions aiming at ranking a set of five shantytowns (favelas) located in the city of Rio de Janeiro. These communities are candidates for investments in an energy efficiency program implemented by the local electric utility company. The city, state, and federal governments want to eliminate domination of these areas by organized criminal gangs and present the city as a peaceful metropolis while hosting two big sports events: the soccer World Cup in 2014 and the Olympic Games in 2016. In recent years, some favelas were chosen to be prototypes for an ambitious project to reshape Rio de Janeiro. This involves first sending in special tactics police to drive drug gangs out, then installing the Pacifying Police Unit in the favela. Once security has been established, it is possible to improve general living conditions in these areas, including by providing public services such as health clinics, formal electricity connections and cable television. The core of the energy efficiency program was to convert informal customers to formal ones, because such communities were responsible for approximately 40% of the commercial losses (stolen energy) in the city. The model specification presented in this paper was set up with ten relevant criteria for decision making, identified through an in‐depth interview with the decision maker. The relative importance of the criteria and the performance of each favela regarding each criterion were measured by the Simos method. The preferences resulting from this method were translated into a nine‐point scale. The imprecision of subjective judgment was partially compensated by using a fuzzy analytical hierarchy process. Some criteria were ordinal, such as ‘Fair Relationship with the Community’ and ‘Complexity to Rebuild the Distribution Lines’, whereas other were cardinal, like ‘Percentage of Clients in Default’ and ‘Commercial Loss Due to Energy Theft’. At the end, the model was efficient in ranking the five favelas, therefore contributing to a rational and transparent approach for capital investment in social projects. Copyright © 2014 John Wiley & Sons, Ltd.     

Ranking of Drivers for Green Manufacturing Implementation Using Fuzzy Technique for Order of Preference by Similarity to Ideal Solution Method

The governments are under tremendous pressure to sustain high manufacturing growth in emerging economies. Unfortunately, the manufacturing sector consumes much energy and other resources and emits a large amount of green house gases, which increases environmental problems such as climate change and global warming. One possible solution to this problem is green manufacturing (GM) implementation in industry. However, GM implementation faces many challenges. Various motivating factors named as ‘drivers’ should be facilitated by the government and industry to make this change possible. This paper investigates the drivers for GM implementation and their ranking based on fuzzy technique for order of preference by similarity to ideal solution method using government, industry and experts perspectives. The study concluded that competitiveness, incentives, organizational resources and technology are top ranked drivers and should be facilitated by the government and industry to help implement GM. The ranking of these drivers is expected to help the government and industry to focus on few important drivers to facilitate the GM implementation with limited resources. Copyright © 2014 John Wiley & Sons, Ltd.     

Conscious thoughts from reflex-like processes: A new experimental paradigm for consciousness research

The contents of our conscious mind can seem unpredictable, whimsical, and free from external control. When instructed to attend to a stimulus in a work setting, for example, one might find oneself thinking about household chores. Conscious content thus appears different in nature from reflex action. Under the appropriate conditions, reflexes occur predictably, reliably, and via external control. Despite these intuitions, theorists have proposed that, under certain conditions, conscious content resembles reflexes and arises reliably via external control. We introduce the Reflexive Imagery Task, a paradigm in which, as a function of external control, conscious content is triggered reliably and unintentionally: When instructed to not subvocalize the name of a stimulus object, participants reliably failed to suppress the set-related imagery. This stimulus-elicited content is considered ‘high-level’ content and, in terms of stages of processing, occurs late in the processing stream. We discuss the implications of this paradigm for consciousness research.