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The ever-increasing demand for high-quality solutions drives research toward more sophisticated decision-making solutions. In the field of decision making, the ability to solve complex real-world problems is of paramount importance. To this end, fuzzy sets are used, which offer the possibility of incorporating uncertainty into the values describing decision options. This study focuses on Pythagorean fuzzy sets, an extension of classical fuzzy sets, providing even more tools for modeling real-world problems by presenting a distance measure for these specific sets. A verification of the characteristics of the proposed distance measure has been carried out, proving its validity. The proposed measure is characterized by a more straightforward formula and thus simplifies the calculations. Furthermore, to confirm its usability, a multi-criteria decision-making methodology is presented, the results of which are compared with two multi-criteria decision-making methods, namely, PF-TOPSIS and PF-VIKOR, and another distance measure previously presented in the literature. The comparative analysis highlights lower variability in terms of preference values calculated using the proposed distance measure, which confirms the stability and reliability of the newly proposed distance measure while maintaining low computational complexity. Moreover, a high correlation with rankings calculated using PF-TOPSIS ensures its utility in terms of decision making. [ABSTRACT FROM AUTHOR]

In this study we propose a measure of the entropy of the norm (R, S) for q-row orthopair fuzzy sets (qROFS). The proposed entropy measure is validated both theoretically and practically to ensure validity. We also propose a simple methodology for the purpose of solving a multi-criteria decision-analysis problems using the introduced entropy measure. This method takes into account different circumstances of criteria weights, such as unknown weights, as well as other cases when the weights are not fully known. Finally, a demonstration with numerical examples for the proposed entropy has been provided to show how to apply the novel methodologies. [ABSTRACT FROM AUTHOR]

A graph is a tool for designing a system's required interconnection network. The topology of such networks determines their compatibility. For the first time, in this work we construct subdivided η ζ network S (η ζ Γ) and discussed their topology. In graph theory, there are a variety of invariants to study the topology of a network, but topological indices are designed in such a way that these may transform the graph into a numeric value. In this work, we study S (η ζ Γ) via Zagreb connection indices. Due to their predictive potential for enthalpy, entropy, and acentric factor, these indices gain value in the field of chemical graph theory in a very short time. η ζ Γ formed by ζ time repeated process which consists η ζ copies of graph Γ along with η 2 | V (Γ) | ζ η ζ − 1 edges which used to join these η ζ copies of Γ. The free hand to choose the initial graph Γ for desired network S (η ζ Γ) and its relation with chemical networks along with the repute of Zagreb connection indices enhance the worth of this study. These computations are theoretically innovative and aid topological characterization of S (η ζ Γ) . [ABSTRACT FROM AUTHOR]

Background and objectives: Machine learning approaches using random forest have been effectively used to provide decision support in health and medical informatics. This is especially true when predicting variables associated with Medicare reimbursements. However, more work is needed to analyze and predict data associated with reimbursements through Medicare and Medicaid services for physical therapy practices in the United States. The key objective of this study is to analyze different machine learning models to predict key variables associated with Medicare standardized payments for physical therapy practices in the United States. Materials and Methods: This study employs five methods, namely, multiple linear regression, decision tree regression, random forest regression, K-nearest neighbors, and linear generalized additive model, (GAM) to predict key variables associated with Medicare payments for physical therapy practices in the United States. Results: The study described in this article adds to the body of knowledge on the effective use of random forest regression and linear generalized additive model in predicting Medicare Standardized payment. It turns out that random forest regression may have any edge over other methods employed for this purpose. Conclusions: The study provides a useful insight into comparing the performance of the aforementioned methods, while identifying a few intricate details associated with predicting Medicare costs while also ascertaining that linear generalized additive model and random forest regression as the most suitable machine learning models for predicting key variables associated with standardized Medicare payments. [ABSTRACT FROM AUTHOR]