Probability Theory, Advanced Mathematics and Decision-Making Applications

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (20 May 2023) | Viewed by 2620

Special Issue Editor

School of Business, Anhui University, Hefei 230601, China
Interests: fuzzy group decision making; large scale group collaborative decision making; data envelopment analysis; aggregation theory; decision support systems; bounded rationality theory; applied mathematics

Special Issue Information

Dear Colleagues,

Recently, with the development of information network technology, intelligent decision-making and evaluation has become the focus of sustainable development assessment. Intelligent decision-making and evaluation needs experts from different fields to participate in the decision-making and obtain the most effective decision results within a short period of time.

As a key factor in the process of intelligent group decision-making, the probability theory, advanced mathematics and stochastic preference information will greatly promote the rapid realization of intelligent group decision-making results. Firstly, the traditional decision-making models ignore that the group consensus level in the intelligent decision-making process is dynamic and needs to be updated constantly. Secondly, the existing research on the process of group decision-making usually ignores the internal correlation of stochastic preference information. Finally, as the main body of decision-making, the incomplete rational behaviour characteristics of experts cannot be ignored. These factors will greatly reduce the satisfaction of decision-making experts with the results of intelligent group decision-making.

Therefore, it is important to utilize probability theory and advanced mathematics methods to study intelligent decision-making and its applications, which would be a quite promising research line representing a high-quality breakthrough in this topic.

You are cordially invited to submit papers related to all aspects of intelligent decision-making, both theoretical and applicational. This involves (but is not limited to) probability theory-based linguistic decision making, large-scale fuzzy group decision-making, advanced mathematics-based linguistic decision making, data envelopment analysis, data aggregation theory, stochastic  decision-making, graph theory-driven decision-making, mathematic game theory, and their applications in environment, renewable energy, emergency response, medicine, manufacturing, etc.

Dr. Feifei Jin
Guest Editor

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Keywords

  • probability theory-based linguistic decision making
  • probability distribution linguistic decision making
  • large-scale fuzzy group decision-making
  • advanced mathematics-based linguistic decision making
  • data envelopment analysis
  • stochastic decision-making
  • graph theory-driven decision-making
  • mathematic game theory
  • data-driven intelligent decision making
  • information aggregation operators in intelligent fuzzy decision-making
  • consistency adjustment algorithms
  • stochastic preference information

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Published Papers (1 paper)

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Research

18 pages, 572 KB  
Article
Comparative Analysis of the Existence and Uniqueness Conditions of Parameter Estimation in Paired Comparison Models
by László Gyarmati, Éva Orbán-Mihálykó and Csaba Mihálykó
Axioms 2023, 12(6), 575; https://doi.org/10.3390/axioms12060575 - 9 Jun 2023
Cited by 5 | Viewed by 1389
Abstract
In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice and the parameters are estimated by maximum likelihood method. The existence and uniqueness of the estimator are key issues of the [...] Read more.
In this paper, paired comparison models with stochastic background are investigated. We focus on the models that allow three options for choice and the parameters are estimated by maximum likelihood method. The existence and uniqueness of the estimator are key issues of the evaluation. In the case of two options, a necessary and sufficient condition is given by Ford in the Bradley–Terry model. We generalize this statement for the set of strictly log-concave distribution. Although in the case of three options the necessary and sufficient condition is not known, there are two different sufficient conditions that are formulated in the literature. In this paper, we generalize them; moreover, we compare these conditions. Their capacities to indicate the existence of the maximum were analyzed using a large number of computer simulations. These simulations support that the new condition indicates the existence of the maximum much more frequently than the previously known ones. Full article
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