Ratio Judgments Research Articles

Construction and Application of Index System for Integration of Red Cultural Resources and Ideological and Political Education Based on Fuzzy Judgment Method

This article states the fuzzy judgment method of the established index system around the history resources and red cultural resources. Firstly, in the second part, it summarizes the system of red culture in ideology and politics and the concepts of various resources of red culture. Then, in the third part, through the construction of the judgment index system, three judgment methods of the index system are put forward, which are the rank sum ratio judgment method, comprehensive index judgment method, and analytic hierarchy process (AHP) judgment method, and the weight judgment calculation of the index system is put forward. Finally, the fourth part puts forward the red cultural resource judgment method of the index system weight, but universities should enhance the cultural heritage of resource system. Besides this theory, the article also analyzes the necessity and effectiveness of the integration of red culture in the new era. This will help to investigate and test the current situation of red culture integrating into the local university foundation. Red culture is the culture formed under the red background, that is, the revolutionary war era. The special background of the times endows red culture with unique vitality, which makes it a unique component of China’s advanced culture. Red culture has been finally condensed into a representative culture with Chinese characteristics, which contains endless spiritual wealth.

Rethinking the Ranks of Visual Channels.

Data can be visually represented using visual channels like position, length or luminance. An existing ranking of these visual channels is based on how accurately participants could report the ratio between two depicted values. There is an assumption that this ranking should hold for different tasks and for different numbers of marks. However, there is surprisingly little existing work that tests this assumption, especially given that visually computing ratios is relatively unimportant in real-world visualizations, compared to seeing, remembering, and comparing trends and motifs, across displays that almost universally depict more than two values. To simulate the information extracted from a glance at a visualization, we instead asked participants to immediately reproduce a set of values from memory after they were shown the visualization. These values could be shown in a bar graph (position (bar)), line graph (position (line)), heat map (luminance), bubble chart (area), misaligned bar graph (length), or 'wind map' (angle). With a Bayesian multilevel modeling approach, we show how the rank positions of visual channels shift across different numbers of marks (2, 4 or 8) and for bias, precision, and error measures. The ranking did not hold, even for reproductions of only 2 marks, and the new probabilistic ranking was highly inconsistent for reproductions of different numbers of marks. Other factors besides channel choice had an order of magnitude more influence on performance, such as the number of values in the series (e.g., more marks led to larger errors), or the value of each mark (e.g., small values were systematically overestimated). Every visual channel was worse for displays with 8 marks than 4, consistent with established limits on visual memory. These results point to the need for a body of empirical studies that move beyond two-value ratio judgments as a baseline for reliably ranking the quality of a visual channel, including testing new tasks (detection of trends or motifs), timescales (immediate computation, or later comparison), and the number of values (from a handful, to thousands).

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children's numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.

No mark is an island: Precision and category repulsion biases in data reproductions.

Data visualization is powerful in large part because it facilitates visual extraction of values. Yet, existing measures of perceptual precision for data channels (e.g., position, length, orientation, etc.) are based largely on verbal reports of ratio judgments between two values (e.g., [7]). Verbal report conflates multiple sources of error beyond actual visual precision, introducing a ratio computation between these values and a requirement to translate that ratio to a verbal number. Here we observe raw measures of precision by eliminating both ratio computations and verbal reports; we simply ask participants to reproduce marks (a single bar or dot) to match a previously seen one. We manipulated whether the mark was initially presented (and later drawn) alone, paired with a reference (e.g. a second '100%' bar also present at test, or a y-axis for the dot), or integrated with the reference (merging that reference bar into a stacked bar graph, or placing the dot directly on the axis). Reproductions of smaller values were overestimated, and larger values were underestimated, suggesting systematic memory biases. Average reproduction error was around 10% of the actual value, regardless of whether the reproduction was done on a common baseline with the original. In the reference and (especially) the integrated conditions, responses were repulsed from an implicit midpoint of the reference mark, such that values above 50% were overestimated, and values below 50% were underestimated. This reproduction paradigm may serve within a new suite of more fundamental measures of the precision of graphical perception.

Factors associated with non-invasive mechanical ventilation failure in patients with hematological neoplasia and their association with outcomes

BackgroundThe usefulness of non-invasive mechanical ventilation (NIMV) in oncohematological patients is still a matter of debate.AimTo analyze the rate of noninvasive ventilation failure and the main characteristics associated with this endpoint in oncohematological patients with acute respiratory failure (ARF).MethodsA ventilatory support protocol was developed and implemented before the onset of the study. According to the PaO2/FiO2 (P/F) ratio and clinical judgment, patients received supplementary oxygen therapy, NIMV, or invasive mechanical ventilation (IMV).ResultsEighty-two patients were included, average age between 52.1 ± 16 years old; 44 (53.6%) were male. The tested protocol was followed in 95.1% of cases. Six patients (7.3%) received IMV, 59 (89.7%) received NIMV, and 17 (20.7%) received oxygen therapy. ICU mortality rates were significantly higher in the IMV (83.3%) than in the NIMV (49.2%) and oxygen therapy (5.9%) groups (P < 0.001). Among the 59 patients who initially received NIMV, 30 (50.8%) had to eventually be intubated. Higher SOFA score at baseline (1.35 [95% CI = 1.12–2.10], P = 0.007), higher respiratory rate (RR) (1.10 [95% CI = 1.00–1.22], P = 0.048), and sepsis on admission (16.9 [95% CI = 1.93–149.26], P = 0.011) were independently associated with the need of orotracheal intubation among patients initially treated with NIMV. Moreover, NIMV failure was independently associated with ICU (P < 0.001) and hospital mortality (P = 0.049), and mortality between 6 months and 1 year (P < 0.001).ConclusionThe implementation of a NIMV protocol is feasible in patients with hematological neoplasia admitted to the ICU, even though its benefits still remain to be demonstrated. NIMV failure was associated with higher SOFA and RR and more frequent sepsis, and it was also related to poor prognosis.

A stratified process for the perception of objects: From optical transformations to 3D relief structure to 3D similarity structure to slant or aspect ratio

Previously, we developed a stratified process for slant perception. First, optical transformations in structure-from-motion (SFM) and stereo were used to derive 3D relief structure (where depth scaling remains arbitrary). Second, with sufficient continuous perspective change (≥45°), a bootstrap process derived 3D similarity structure. Third, the perceived slant was derived. As predicted by theoretical work on SFM, small visual angle (<5°) viewing requires non-coplanar points. Slanted surfaces with small 3D cuboids or tetrahedrons yielded accurate judgment while planar surfaces did not. Normally, object perception entails non-coplanar points. Now, we apply the stratified process to object perception where, after deriving similarity structure, alternative metric properties of the object can be derived (e.g. slant of the top surface or width-to-depth aspect ratio). First, we tested slant judgments of the smooth planar tops of three different polyhedral objects. We tested rectangular, hexagonal, and asymmetric pentagonal surfaces, finding that symmetry was required to determine the direction of slant (AP&P, 2019, https://doi.org/10.3758/s13414-019-01859-5). Our current results replicated the previous findings. Second, we tested judgments of aspect ratios, finding accurate performance only for symmetric objects. Results from this study suggest that, first, trackable non-coplanar points can be attained in the form of 3D objects. Second, symmetry is necessary to constrain slant and aspect ratio perception. Finally, deriving 3D similarity structure precedes estimating object properties, such as slant or aspect ratio. Together, evidence presented here supports the stratified bootstrap process for 3D object perception. Statement of significancePlanning interactions with objects in the surrounding environment entails the perception of 3D shape and slant. Studying ways through which 3D metric shape and slant can be perceived accurately by moving observers not only sheds light on how the visual system works, but also provides understanding that can be applied to other fields, like machine vision or remote sensing. The current study is a logical extension of previous studies by the same authors and explores the roles of large continuous perspective changes, relief structure, and symmetry in a stratified process for object perception.

Size and Aspect Ratio Judgments in Younger and Older Adults

Size and Aspect Ratio Judgments in Younger and Older Adults

Functional equations with division and regular operations

Functional equations are equations in which the unknown (or unknowns) are functions. We consider equations of generalized associativity, mediality (bisymmetry, entropy), paramediality, transitivity as well as the generalized Kolmogoroff equation. Their usefulness was proved in applications both in mathematics and in other disciplines, particularly in economics and social sciences (see J. Aczél, On mean values, Bull. Amer. Math. Soc. 54 (1948) 392–400; J. Aczél, Remarques algebriques sur la solution donner par M. Frechet a l’equation de Kolmogoroff, Pupl. Math. Debrecen 4 (1955) 33–42; J. Aczél, A Short Course on Functional Equations Based Upon Recent Applications to the Social and Behavioral Sciences, Theory and decision library, Series B: Mathematical and statistical methods (D. Reidel Publishing Company, Dordrecht, Boston, Lancaster, Tokyo, 1987); J. Aczél, Lectures on Functional Equations and Their Applications (Supplemented by the author, ed. H. Oser) (Dover Publications, Mineola, New York, 2006); J. Aczél, V. D. Belousov and M. Hosszu, Generalized associativity and bisymmetry on quasigroups, Acta Math. Acad. Sci. Hungar. 11 (1960) 127–136; J. Aczél and J. Dhombres, Functional Equations in Several Variables (Cambridge University Press, New York, 1991); J. Aczél and T. L. Saaty, Procedures for synthesizing ratio judgements, J. Math. Psych. 27(1) (1983) 93–102). We use unifying approach to solve these equations for division and regular operations generalizing the classical quasigroup case.

Judgments of differences and ratios of subjective heaviness.

Experimental instructions to judge differences or ratios of subjective heaviness numerically are generally assumed to produce judgments linearly proportional to the respective heaviness differences or heaviness ratios. In this study, participants were instructed to numerically judge the difference or ratio of heaviness between two weights being lifted separately, either unimanually or bimanually. Weight values were combined factorially. Patterns of factorial curves revealed that unimanual lifting triggered linear judgments of heaviness differences, whereas bimanual lifting triggered nonlinear judgments of heaviness ratios. Lifting conditions produced these judgments independently of the instruction specifications to judge differences or ratios. These results suggest the interpretation that unimanual lifting triggers linear judgments of heaviness differences by default, whereas bimanual lifting triggers nonlinear judgments of heaviness ratios learned through experience. Implications for sensory measurement are noted.

Eliciting Subjective Probabilities through Pair‐wise Comparisons

AbstractWe propose and test a novel approach for eliciting subjective joint probabilities. In the proposed approach, judges compare pairs of possible outcomes and identify which of the two is more likely and by how much. These pair‐wise comparative judgments create a matrix of ratio judgments from which the target probabilities are extracted using the rows' (or columns') geometric means. In Study 1, subjects provided direct assessments of the likelihood of joint events (e.g., sunny days and stock market gains) and also made pair‐wise comparisons of the same joint events. Subjects in Study 2 learnt the distribution of hypothetical events pairs and provided direct and ratio estimates. In both studies, the ratio estimates were significantly more accurate than the direct estimates. The results suggest that it is possible to elicit probabilistic estimates without explictly asking for probabilities and that the pair‐wise approach is a candidate for complementing or replacing traditional elicitation approaches. Copyright © 2016 John Wiley &amp; Sons, Ltd.

Advancing a Model to Account for Abnormal Spatial Relationship Perception in Bulbar Cyclotorsion.

In a previous study dated back to 2001, a small sample of cyclotropic patients were found to be affected by abnormal spatial relationship perception (aspect ratio judgment) with increased discrimination threshold of elliptical targets oriented along the horizontal axis. The angular amount of incyclodeviation correlated significantly with the discrimination threshold along the horizontal axis. Our group made a similar finding some years later in subjects suffering from Menière’s syndrome. In both cases, we advanced bulbar torsion to be responsible for the reduced sensibility to spatial relationship along the x-coordinate. Still, a possible explanation and a tentative model accounting for the results at that time had not been provided. This paper aims at making up for the gap, advancing a paradigm that explains the increased discrimination threshold in cyclotropic eyes as a function of the angular discrepancy between the horizontal coordinate on the retinal plane, corresponding to the maculopapillary axis (the “retinal horizon”), and the horizontal coordinate in the visual space (the “spatial horizon”). This angular discrepancy is posited to produce abnormal encoding of the spatial relationship of the target, leading to an unbalanced activation of the two antagonistic cellular pools responsible for the analysis of the aspect ratio at the cortical level. Such a model of the "dual horizon" seems to be able to account for the experimental finding described in the previous paper, providing a theoretical explanation for the defective sense of space in patients suffering from cyclotropia.

Test of the Ratio Judgment Hypothesis

ABSTRACT The hypothesis that we are capable of judging ratios of subjective intensities is widely used in psychology. Here, experimental results are reported that more stringently verify prior findings that people respond to sensory intensity differences while they execute the task of judging sensory intensity ratios. This verification was made on brightness and heaviness and for verbal and matching responses, suggesting that the results may be general for both sensory intensive dimensions and response systems. The results have implications for the comparisons of scores on evaluation scales based on ratio judgment.

Modeling user experience: A case study on a mobile device

User experience (UX) consists of all aspects of interactions between a user and a product. Recently, many studies have been conducted to define the UX concept, but few studies have attempted to quantify UX. This paper proposed quantification models that integrate major elements of UX into a single index. A variety of models were proposed and evaluated including compensatory (i.e. simple linear, polynomial and S-shaped value) and non-compensatory (i.e. conjunctive and disjunctive) models. A case study with a commercial tablet PC was conducted in which a total of 26 subjects participated in a laboratory environment. Each participant performed a pretest ensuring the ability to make ratio judgments and then evaluated predefined dimensions with the modified magnitude estimation procedure. A total of 22 hierarchical dimensions were evaluated such as overall UX, its elements (i.e. usability, affect and user value) and sub-elements. Both compensatory and non-compensatory models had high performance in terms of goodness of fit. The results of this study are expected to help product or service designers develop indices representing an overall UX value. Relevance to industryThis study proposed quantification models that aggregate elements of UX. Although the UX index has been controversial, the single value developed by the models can be expected to help decision-makers understand about products or services intuitively.

An Empirical Model of Slope Ratio Comparisons

Comparing slopes is a fundamental graph reading task and the aspect ratio chosen for a plot influences how easy these comparisons are to make. According to Banking to 45°, a classic design guideline first proposed and studied by Cleveland et al., aspect ratios that center slopes around 45° minimize errors in visual judgments of slope ratios. This paper revisits this earlier work. Through exploratory pilot studies that expand Cleveland et al.'s experimental design, we develop an empirical model of slope ratio estimation that fits more extreme slope ratio judgments and two common slope ratio estimation strategies. We then run two experiments to validate our model. In the first, we show that our model fits more generally than the one proposed by Cleveland et al. and we find that, in general, slope ratio errors are not minimized around 45°. In the second experiment, we explore a novel hypothesis raised by our model: that visible baselines can substantially mitigate errors made in slope judgments. We conclude with an application of our model to aspect ratio selection.

The ordered multiplicative modular geometric operator

The aim of this paper is to investigate an ordered multiplicative modular geometric operator and its relevant properties. The ordered multiplicative modular geometric operator is a generalized form of the ordered weighted geometric operator which has been designed incorporating the advantages of the geometric mean to deal with ratio judgments and the advantages of the ordered weighted averaging (OWA) operator to represent the concept of fuzzy majority in the process of information aggregation. Besides, the ordered multiplicative modular geometric operator can be seen as a symmetrized multiplicative modular aggregation function, characterized by comonotone multiplicative modularity. It is worth pointing that lots of the existing operators (such as the ordered weighted geometric operator, the weighted geometric operator, the ordered weighted maximum, and the Max and Min operators) can be regarded as the special cases of the ordered multiplicative modular geometric operator, which is of value in developing the theory of geometric operators.

How should we use the visual analogue scale (VAS) in rehabilitation outcomes? II: Visual analogue scales as ratio scales: An alternative to the view of Kersten et al.

The commentary by Kersten et al. (1) contains faulty assertions that could have destructive consequences for pain measurement. They erroneously claim, as do others (2, 3), that an 11 point numerical rating scale (NRS) and a visual analogue scale (VAS) have equivalent formats and that both scales provide only ordinal but not interval or ratio scale measurement. Yet NRS and VAS are certainly not equivalent. Considerable research has shown at least some types of VAS are ratio scales and have psychometric properties that are superior to that of the 11 point NRS. Contrary to Kersten et al.’s assertion (1), 5 separate studies, including those directed toward moderate (4) and severe clinical pain (5) and those directed toward both experimental and clinical pain (6–8) demonstrated ratio scale properties for at least one type of VAS. Common to these studies is the demonstration that separate judgments of ratios or proportions of pain intensity are in quantitative agreement with VAS ratings of pain. In addition, the studies that include both clinical and experimental pain show reliable stimulus-response power functions and a zero point for the VAS scale, further validating its ratio properties (6–8). This approach is in contrast to some studies that only use cross sectional or Rasch analysis of clinical pain ratings to examine ordinal, interval, or ratio level of measurement (9). If a VAS is a ratio scale, then it must have interval properties as well and parametric statistics are appropriate for data analysis. Besides ratio scale level of measurement, VAS also fulfill other criteria for adequate measurement (10, 11), including high test-retest reliability and repeatability (12), internally consistent measures of clinical and experimental pain (6–8, 11), sensitivity to variables that increase or decrease pain (11,13), capacity to measure multiple dimensions of pain (6–8, 11, 14), strong association with measures of pain-related activity in the human brain (15), and in the case of mechanical or electronic VAS, simplicity and ease of use (8, 16, 17). The latter property is in direct contradiction to Kersten et al.’s (1) assertion, based on a single study, that “patients find it difficult to judge how to rate their pain on the VAS line” (18). This particular study fails to provide any information as to how individuals were instructed in use of the scale. Difficulty of use is a likely problem in the absence of good instructions. “Ease of use” is a consistent feature of VAS when adequate instructions are given, as described in the Methods section of research reports, and when mechanical or electronic scales are provided (16, 17). Pencil-and-paper versions of VAS are more difficult to use in cognitively impaired individuals (19). On the other hand, studies that include over a thousand participants find that the vast majority of participants can easily use VAS when properly instructed (11 and references therein). It is not widely recognized that VAS have measurement properties that are superior to the commonly used 11 point NRS. Unlike VAS, the 11 point-NRS has been demonstrated to lack ratio scale properties because it has no distinct zero point, inaccurately predicts separate judgments of ratios of pain intensity (6, 8) and has been repeatedly shown to evoke artificially high ratings at the lower end of the scale (8, 20). The notion that NRS ratings can substitute for VAS ratings because they are highly correlated with each other would be misguided. For example, one study demonstrated that both scales display monotonic functions of stimulus intensity and are likely to be highly correlated, yet the 11 point-NRS stimulus-response curve was displaced above the VAS curve (8). Only the VAS stimulus-response curve reflected accurate ratios or proportions of pain intensity and demonstrated a zero point (8). Given known psychometric features of VAS, the claim of lack of interval or ratio scale properties of VAS (1) is not supported by the evidence, as are past recommendations of use of 11 point NRS over VAS in clinical trials (19, 21).

The procedure for synthesizing ratio judgements

We study the paper of Aczel and Saaty of the axiomatic method for synthesizing ratio judgements. The purpose for this technical note is to point out a direction that the property for finite operation may be derived from the property of binary operation.

An Empirical Study of Equivalence Judgments vs. Ratio Judgments in Decision Analysis*

AbstractTwo commonly used elicitation modes on strength of preference, equivalence and ratio judgments, were compared in an experiment. The result from the experiment showed that ratio judgments were less effective than equivalence judgments. Based on an iterative design for eliciting multiattribute preference structures, equivalence judgments outperformed ratio judgments in estimating single‐attribute measurable value functions, while being nearly more effective than ratio judgments in assessing multiattribute preference structures. The implications of the results from the experiment are that multiattribute decision‐making techniques should take advantage of the decision maker's inclination of making effective equivalence trade‐off judgments, and that useful techniques should be devised to incorporate different commonly used techniques, such as multiattribute utility theory and the Analytic Hierarchy Process, to elicit and consolidate equivalence trade‐off judgments.

Preference ratios in multiattribute evaluation (PRIME)-elicitation and decision procedures under incomplete information

This paper presents the preference ratios in multiattribute evaluation (PRIME) method which supports the analysis of incomplete information in multiattribute weighting models. In PRIME, preference elicitation and synthesis is based on 1) the conversion of possibly imprecise ratio judgments into an imprecisely specified preference model, 2) the use of dominance structures and decision rules in deriving decision recommendations, and 3) the sequencing of the elicitation process into a series of elicitation tasks. This process may be continued until the most preferred alternative is identified or, alternatively, stopped with a decision recommendation if the decision maker is prepared to accept the possibility that the value of some other alternative is higher. An extensive simulation study on the computational properties of PRIME is presented. The method is illustrated with a re-analysis of an earlier case study on international oil tanker negotiations.

A modified procedure for synthesising ratio judgements in the analytic hierarchy process

The analytic hierarchy process (AHP) has been widely applied to solve problems arising in group decision making, by synthesising different or conflicting judgements. However, directly synthesising conflicting judgements by calculating the geometric mean of preference weights (ratios) in AHP may not reach consensus from all members in a decision making group, especially, when those members represent the stakeholders of the decision making problem. This study proposes a new method that uses the genetic algorithm and utility function to synthesise preference weights to prevent this fallacy occurring when implementing the classical AHP approach. Using the proposed method, the final decision can be achieved with only minimally-adjusted preference weights.