Modeling random and non-random decision uncertainty in ratings data: a fuzzy beta model

Calcagnì, Antonio; Lombardi, Luigi

doi:10.1007/s10182-021-00407-7

Cited by 3 publications

(2 citation statements)

References 80 publications

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“…It is well-accepted that mining the raters' response process can provide new insights into the mechanisms underlying rating choices [2,3]. To this end, fuzzy set theory has been widely applied in modeling the non-random and subjective components of the rating response (for a recent review, see [4]). By and large, two general approaches can be recognized in the fuzzy rating literature, namely fuzzy direct scales and fuzzy conversion scales.…”

Section: Introductionmentioning

confidence: 99%

Jointly modeling rating responses and times with fuzzy numbers: An application to psychometric data

Cao,

Calcagnì

2022

Preprint

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In several research areas, ratings data and response times have been successfully used to unfold the stage-wise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regards to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameter triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers lead to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures.

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Section: Introductionmentioning

confidence: 99%

Jointly modeling rating responses and times with fuzzy numbers: An application to psychometric data

Cao,

Calcagnì

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data

Cao

Calcagnì

2022

Mathematics

Self Cite

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In several research areas, ratings data and response times have been successfully used to unfold the stagewise process through which human raters provide their responses to questionnaires and social surveys. A limitation of the standard approach to analyze this type of data is that it requires the use of independent statistical models. Although this provides an effective way to simplify the data analysis, it could potentially involve difficulties with regard to statistical inference and interpretation. In this sense, a joint analysis could be more effective. In this research article, we describe a way to jointly analyze ratings and response times by means of fuzzy numbers. A probabilistic tree model framework has been adopted to fuzzify ratings data and four-parameters triangular fuzzy numbers have been used in order to integrate crisp responses and times. Finally, a real case study on psychometric data is discussed in order to illustrate the proposed methodology. Overall, we provide initial findings to the problem of using fuzzy numbers as abstract models for representing ratings data with additional information (i.e., response times). The results indicate that using fuzzy numbers leads to theoretically sound and more parsimonious data analysis methods, which limit some statistical issues that may occur with standard data analysis procedures.

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An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation

Ahadi,

Saadati,

Allahviranloo

et al. 2024

J Inequal Appl

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To make better decisions on approximation, we may need to increase reliable and useful information on different aspects of approximation. To enhance information about the quality and certainty of approximating the solution of an Apollonius-type quadratic functional equation, we need to measure both the quality and the certainty of the approximation and the maximum errors. To measure the quality of it, we use fuzzy sets, and to achieve its certainty, we use the probability distribution function. To formulate the above problem, we apply the concept of Z-numbers and introduce a special matrix of the form $\mathrm{diag}(A, B, C)$ diag ( A , B , C ) (named the generalized Z-number) where A is a fuzzy time-stamped set, B is the probability distribution function, and C is a degree of reliability of A that is described as a value of $A\ast B$ A ∗ B . Using generalized Z-numbers, we define a novel control function to investigate H–U–R stability to approximate the solution of an Apollonius-type quadratic functional equation with quality and certainty of the approximation.

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Modeling random and non-random decision uncertainty in ratings data: a fuzzy beta model

Cited by 3 publications

References 80 publications

Jointly modeling rating responses and times with fuzzy numbers: An application to psychometric data

Jointly modeling rating responses and times with fuzzy numbers: An application to psychometric data

Jointly Modeling Rating Responses and Times with Fuzzy Numbers: An Application to Psychometric Data

An application of decision theory on the approximation of a generalized Apollonius-type quadratic functional equation

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