Assisting the decision making-A generalization of choice models to handle the binary choices

Muhammad Arshad; Salman A. Cheema; Juan L.G. Guirao; Juan M. Sánchez; Adrián Valverde; Muhammad Arshad; Salman A. Cheema; Juan L.G. Guirao; Juan M. Sánchez; Adrián Valverde

doi:10.3934/math.2023159

AIMS Mathematics

2023, Volume 8, Issue 2: 3083-3100. doi: 10.3934/math.2023159

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Assisting the decision making-A generalization of choice models to handle the binary choices

1.
Department of Applied Sciences, School of Science, National Textile University, Faisalabad, Pakistan, 37610
2.
Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina 30203-Cartagena, Spain
3.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 04 July 2022 Revised: 17 September 2022 Accepted: 25 September 2022 Published: 15 November 2022
MSC : 74H10, 74B05, 35Q74, 35J05, 33C55

This research fundamentally aims at providing a generalized framework to assist the launch of paired comparison models while dealing with discrete binary choices. The purpose is served by exploiting the fundaments of the exponential family of distributions. The proposed generalization is proved to cater to seven paired comparison models as members of this newly developed mechanism. The legitimacy of the devised scheme is demonstrated through rigorous simulation-based investigation as well as keenly persuaded empirical evaluations. A detailed analysis, covering a wide range of parametric settings, through the launch of Gibbs Sampler—a notable extension of Markov Chain Monte Carlo methods, is conducted under the Bayesian paradigm. The outcomes of this research substantiate the legitimacy of the devised general structure by not only successfully retaining the preference ordering but also by staying consistent with the established theoretical framework of comparative models.
- choice behaviors,
- comparative models,
- exponential family of distributions,
- paired comparison
Citation: Muhammad Arshad, Salman A. Cheema, Juan L.G. Guirao, Juan M. Sánchez, Adrián Valverde. Assisting the decision making-A generalization of choice models to handle the binary choices[J]. AIMS Mathematics, 2023, 8(2): 3083-3100. doi: 10.3934/math.2023159

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Abstract

This research fundamentally aims at providing a generalized framework to assist the launch of paired comparison models while dealing with discrete binary choices. The purpose is served by exploiting the fundaments of the exponential family of distributions. The proposed generalization is proved to cater to seven paired comparison models as members of this newly developed mechanism. The legitimacy of the devised scheme is demonstrated through rigorous simulation-based investigation as well as keenly persuaded empirical evaluations. A detailed analysis, covering a wide range of parametric settings, through the launch of Gibbs Sampler—a notable extension of Markov Chain Monte Carlo methods, is conducted under the Bayesian paradigm. The outcomes of this research substantiate the legitimacy of the devised general structure by not only successfully retaining the preference ordering but also by staying consistent with the established theoretical framework of comparative models.

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