Mathematics

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11 pages, 619 KiB

Open AccessFeature PaperArticle

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

by Niccolò Cao and Antonio Calcagnì

Mathematics 2022, 10(7), 1025; https://doi.org/10.3390/math10071025 - 23 Mar 2022

Viewed by 1926

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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22 pages, 1132 KiB

Open AccessArticle

The Grey Ten-Element Analysis Method: A Novel Strategic Analysis Tool

by Shervin Zakeri, Dimitri Konstantas and Naoufel Cheikhrouhou

Mathematics 2022, 10(5), 846; https://doi.org/10.3390/math10050846 - 7 Mar 2022

Cited by 3 | Viewed by 3130

Abstract

In this paper, a new strategic analysis method is introduced, called the ten-element analysis (TEA) method to determine the firm’s strategic position in the market. The new method is grounded on the computation of the reflections of the external factors on the firm’s [...] Read more.

In this paper, a new strategic analysis method is introduced, called the ten-element analysis (TEA) method to determine the firm’s strategic position in the market. The new method is grounded on the computation of the reflections of the external factors on the firm’s internal factors through the changes of the values of the internal factors throughout the time when a lack of complete information regarding the environmental factors exists. The TEA method takes ten effective key elements of the firm into account and investigates their changes through a maximum of nine periods and a minimum of two periods. To conduct the model, the paper is mainly focused on four main rubrics, including the detection of the reflection of the firm’s environmental factors on the internal factors, deriving the strategic position of the firm from the reflections, the capability of the existing strategic models in determining the strategic position from the reflections in presence of uncertainty and incomplete information of the external factors. The method is applied to a dairy company in order to find its strategic position in the market. The results showed that the output of the TEA method and SWOT analysis is similar which makes the new method reliable to employ. The TEA method is developed under the grey environment to harness the uncertainty where a new grey comparison method is introduced to compare the grey numbers. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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16 pages, 1432 KiB

Open AccessArticle

A New Model to Identify the Reliability and Trust of Internet Banking Users Using Fuzzy Theory and Data-Mining

by Hamid Bekamiri, Seyedeh Fatemeh Ghasempour Ganji, Biagio Simonetti and Seyed Amin Hosseini Seno

Mathematics 2021, 9(9), 916; https://doi.org/10.3390/math9090916 - 21 Apr 2021

Cited by 6 | Viewed by 3363

Abstract

As a result of changes in approach from traditional to virtual banking system, security in data exchange has become more important; thus, it seems essentially necessary to present a pattern based on smart models in order to reduce fraud in this field. A [...] Read more.

As a result of changes in approach from traditional to virtual banking system, security in data exchange has become more important; thus, it seems essentially necessary to present a pattern based on smart models in order to reduce fraud in this field. A new algorithm has been provided in this article to improve security and to specify the limits of giving special services to Internet banking users in order to pave appropriate ground for virtual banking. In addition to identifying behavioral models of customers, this algorithm compares the behaviors of any customer with this model and finally computes the rate of trust in customer’s behavior. The hybrid data-mining and knowledge based structure has been adapted in this algorithm according to fuzzy systems. In this research, qualitative data was gathered from interviews with banking experts, analyzed by Expert Choice to identify the most important variables of customer behavior analysis, and to analyze customer behavior and customer bank Internet transaction data for a period of one year by MATLAB and Clementine. The results of this survey indicate that the potential of the given structure to recognize the rate of trust in Internet bank user’s behavior might be at reasonable level for experts in this area. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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14 pages, 328 KiB

Open AccessArticle

Boscovich Fuzzy Regression Line

by Pavel Škrabánek, Jaroslav Marek and Alena Pozdílková

Mathematics 2021, 9(6), 685; https://doi.org/10.3390/math9060685 - 23 Mar 2021

Cited by 4 | Viewed by 3104

Abstract

We introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on [...] Read more.

We introduce a new fuzzy linear regression method. The method is capable of approximating fuzzy relationships between an independent and a dependent variable. The independent and dependent variables are expected to be a real value and triangular fuzzy numbers, respectively. We demonstrate on twenty datasets that the method is reliable, and it is less sensitive to outliers, compare with possibilistic-based fuzzy regression methods. Unlike other commonly used fuzzy regression methods, the presented method is simple for implementation and it has linear time-complexity. The method guarantees non-negativity of model parameter spreads. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

23 pages, 3014 KiB

Open AccessArticle

Using Artificial Neural Networks in Predicting the Level of Stress among Military Conscripts

by Svajone Bekesiene, Rasa Smaliukiene and Ramute Vaicaitiene

Mathematics 2021, 9(6), 626; https://doi.org/10.3390/math9060626 - 16 Mar 2021

Cited by 29 | Viewed by 7558

Abstract

The present study aims to elucidate the main variables that increase the level of stress at the beginning of military conscription service using an artificial neural network (ANN)-based prediction model. Random sample data were obtained from one battalion of the Lithuanian Armed Forces, [...] Read more.

The present study aims to elucidate the main variables that increase the level of stress at the beginning of military conscription service using an artificial neural network (ANN)-based prediction model. Random sample data were obtained from one battalion of the Lithuanian Armed Forces, and a survey was conducted to generate data for the training and testing of the ANN models. Using nonlinearity in stress research, numerous ANN structures were constructed and verified to limit the optimal number of neurons, hidden layers, and transfer functions. The highest accuracy was obtained by the multilayer perceptron neural network (MLPNN) with a 6-2-2 partition. A standardized rescaling method was used for covariates. For the activation function, the hyperbolic tangent was used with 20 units in one hidden layer as well as the back-propagation algorithm. The best ANN model was determined as the model that showed the smallest cross-entropy error, the correct classification rate, and the area under the ROC curve. These findings show, with high precision, that cohesion in a team and adaptation to military routines are two critical elements that have the greatest impact on the stress level of conscripts. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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25 pages, 2582 KiB

Open AccessEditor’s ChoiceArticle

Comprehensive Assessment of Distance Learning Modules by Fuzzy AHP-TOPSIS Method

by Svajone Bekesiene, Aidas Vasilis Vasiliauskas, Šárka Hošková-Mayerová and Virgilija Vasilienė-Vasiliauskienė

Mathematics 2021, 9(4), 409; https://doi.org/10.3390/math9040409 - 19 Feb 2021

Cited by 24 | Viewed by 5242

Abstract

This survey is focussed on distance learning studies, where there can be met a lot of technical obstacles, which creates complications in decision making. To get an ideal solution for these kinds of problems, the Fuzzy TOPSIS (Technique for Order Preference by Similarities [...] Read more.

This survey is focussed on distance learning studies, where there can be met a lot of technical obstacles, which creates complications in decision making. To get an ideal solution for these kinds of problems, the Fuzzy TOPSIS (Technique for Order Preference by Similarities to Ideal Solution) is one of the best solutions. Therefore, this paper presents the distance learning quality assessment surveys when the Fuzzy AHP (Analytic Hierarchy Process) and TOPSIS methods are used. Research results describe the application of the Fuzzy AHP—TOPSIS hybrid method. MCDM (Multi-Criteria Decision Making) programs with MATLAB (R2020b) mathematical package were written to calculate the evaluation results for three distance learning courses. In the practical implementation of the proposed distance learning module evaluation methodology, the experts’ evaluation method was applied. Thirty-four judges were chosen with specific knowledge and skills and with very different competencies to assess three alternatives by fourteen criteria. Following the experts’ evaluation, a statistical analysis method was used to process the data. After applying the complex evaluation, the comparative analysis method was used to summarize the obtained results. This work further provides useful guidelines for the development of an easily understandable hierarchy of criteria model that reflects the main goal of study quality assessment. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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21 pages, 1685 KiB

Open AccessArticle

Accurate Prediction of Concentration Changes in Ozone as an Air Pollutant by Multiple Linear Regression and Artificial Neural Networks

by Svajone Bekesiene, Ieva Meidute-Kavaliauskiene and Vaida Vasiliauskiene

Mathematics 2021, 9(4), 356; https://doi.org/10.3390/math9040356 - 10 Feb 2021

Cited by 26 | Viewed by 3429

Abstract

This study considers the usage of multilinear regression and artificial neural network modelling to forecast ozone concentrations with regard to weather-related indicators (wind speed, wind direction, relative humidity and temperature). Initial data were obtained by measuring the meteorological parameters using the PC Radio [...] Read more.

This study considers the usage of multilinear regression and artificial neural network modelling to forecast ozone concentrations with regard to weather-related indicators (wind speed, wind direction, relative humidity and temperature). Initial data were obtained by measuring the meteorological parameters using the PC Radio Weather Station. Ozone concentrations near high-voltage lines were measured using RS1003 and at a 220 m distance using ML9811. Neural network models such as the multilayer perceptron and radial basis function neural networks were constructed. The prognostic capacities of the designed models were assessed by comparing the result data by way of the square of the coefficient of multiple correlations (R²) and mean square error (MSE) values. The number of hidden neurons was optimised by decreasing an error function that recorded the number of units in the hidden layers to the precision of the expanded networks. The neural software IBM SPSS 26v was used for artificial neural network (ANN) modelling. The study demonstrated that the linear regression modelling approach was lacking in its capacity to predict the investigated ozone concentrations by used parameters, whereas the use of an ANN offered more precise outcomes. The conducted tests’ results established the strength of the designed artificial neural network models with irrelevant differences between detected and forecasted data. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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17 pages, 306 KiB

Open AccessArticle

Non-Parametric Probability Distributions Embedded Inside of a Linear Space Provided with a Quadratic Metric

by Pierpaolo Angelini and Fabrizio Maturo

Mathematics 2020, 8(11), 1901; https://doi.org/10.3390/math8111901 - 31 Oct 2020

Cited by 8 | Viewed by 2376

Abstract

There exist uncertain situations in which a random event is not a measurable set, but it is a point of a linear space inside of which it is possible to study different random quantities characterized by non-parametric probability distributions. We show that if [...] Read more.

There exist uncertain situations in which a random event is not a measurable set, but it is a point of a linear space inside of which it is possible to study different random quantities characterized by non-parametric probability distributions. We show that if an event is not a measurable set then it is contained in a closed structure which is not a

σ

-algebra but a linear space over

R

. We think of probability as being a mass. It is really a mass with respect to problems of statistical sampling. It is a mass with respect to problems of social sciences. In particular, it is a mass with regard to economic situations studied by means of the subjective notion of utility. We are able to decompose a random quantity meant as a geometric entity inside of a metric space. It is also possible to decompose its prevision and variance inside of it. We show a quadratic metric in order to obtain the variance of a random quantity. The origin of the notion of variability is not standardized within this context. It always depends on the state of information and knowledge of an individual. We study different intrinsic properties of non-parametric probability distributions as well as of probabilistic indices summarizing them. We define the notion of

α

-distance between two non-parametric probability distributions. Full article

(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)

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