Yazar "Ozkaya, Murat" seçeneğine göre listele

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    Axioms of Decision Criteria for 3D Matrix Games and Their Applications
    (Mdpi, 2022) Ozkaya, Murat; Izgi, Burhaneddin; Perc, Matjaz
    In this paper, we define characteristic axioms for 3D matrix games and extend the definitions of the decision criteria under uncertainty to three dimensions in order to investigate the simultaneous effect of two different states on the decision process. We first redefine the Laplace, Wald, Hurwicz, and Savage criteria in 3D. We present a new definition depending on only the infinity-norm of the 3D payoff matrix for the Laplace criterion in 3D. Then, we demonstrate that the Laplace criterion in 3D explicitly satisfies all the proposed axioms, as well as the other three criteria. Moreover, we illustrate a fundamental example for a three-dimensional matrix with 3D figures and show the usage of each criterion in detail. In the second example, we model a decision process during the COVID-19 pandemic for South Korea to show the applicability of the 3D decision criteria using real data with two different states of nature for individuals' actions for the quarantine. Additionally, we present an agricultural insurance problem and analyze the effects of the hailstorm and different speeds of wind on the harvest by the 3D criteria. To the best of our knowledge, this is the first study that brings 3D matrices in decision and game theories together.
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    Öğe
    Machine learning tree trimming for faster Markov reward game solutions
    (Elsevier, 2025) Izgi, Burhaneddin; Ozkaya, Murat; Ure, Nazim Kemal; Perc, Matjaz
    Existing methodologies for solving Markov reward games mostly rely on state-action frameworks and iterative algorithms to address these challenges. However, these approaches often impose significant computational burdens, particularly when applied to large-scale games, due to their inherent complexity and the need for extensive iterative calculations. In this paper, we propose a new neural network architecture for solving Markov reward games in the form of a decision tree with relatively large state and action sets, such as 2-actions-3-stages, 3-actions-3-stages, and 4-actions-3-stages, by trimming the decision tree. In this context, we generate datasets of Markov reward games with sizes ranging from 103 to 105 using the holistic matrix norm-based solution method and obtain the necessary components, such as the payoff matrices and the corresponding solutions of the games, for training the neural network. We then propose a vectorization process to prepare the outcomes of the matrix norm-based solution method and adapt them for training the proposed neural network. The neural network is trained using both the vectorized payoff and transition matrices as input, and the prediction system generates the optimal strategy set as output. In the model, we approach the problem as a classification task by labeling the optimal and non-optimal branches of the decision tree with ones and zeros, respectively, to identify the most rewarding paths of each game. As a result, we propose a novel neural network architecture for solving Markov reward games in real time, enhancing its practicality for real-world applications. The results reveal that the system efficiently predicts the optimal paths for each decision tree, with f1-scores slightly greater than 0.99, 0.99, and 0.97 for Markov reward games with 2-actions-3-stages, 3-actions-3-stages, and 4-actions-3-stages, respectively.