American Institute of Mathematical Sciences

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Mathematical Foundations of Computing

August 2019 , Volume 2 , Issue 3

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2019, 2(3): 183-201 doi: 10.3934/mfc.2019013 +[Abstract](1856) +[HTML](704) +[PDF](395.03KB)
Abstract:

The primary goal of this paper is to solve the investment problem based on linguistic picture decision making method under the linguistic triangular picture linguistic fuzzy environment. First to define the triangular picture linguistic fuzzy numbers. Further, we define operations on triangular picture linguistic fuzzy numbers and their aggregation operator namely, triangular picture fuzzy linguistic induce OWA (TPFLIOWA) and triangular picture fuzzy linguistic induce OWG (TPFLIOWG) operators. Multi-criteria group decision making method is developed based on TPFLIOWA and TPFLIOWG operators and solve the uncertainty in the investment problem. We study the applicability of the proposed decision making method under triangular picture linguistic fuzzy environment and construct a descriptive example of investment problem. We conclude from the comparison and sensitive analysis that the proposed decision making method is more effective and reliable than other existing models.

2019, 2(3): 203-213 doi: 10.3934/mfc.2019014 +[Abstract](1499) +[HTML](567) +[PDF](1204.64KB)
Abstract:

Chromium and its compounds are widely used in many industries in China and play a very important role in the national economy. At the same time, heavy metal chromium pollution poses a great threat to the ecological environment and human health. Therefore, it's necessary to safely and effectively remove the chromium from pollutants. In practice, there are many factors which influence the removal efficiency of the chromium. However, few studies have investigated the relationship between multiple factors and the removal efficiency of the chromium till now. To this end, this paper uses the green synthetic iron nanoparticles to remove the chromium and investigates the impacts of multiple factors on the removal efficiency of the chromium. A novel model that maps multiple given factors to the removal efficiency of the chromium is proposed through the advanced machine learning methods, i.e., XGBoost and random forest (RF). Experiments demonstrate that the proposed method can predict the removal efficiency of the chromium precisely with given influencing factors, which is very helpful for finding the optimal conditions for removing the chromium from pollutants.

2019, 2(3): 215-250 doi: 10.3934/mfc.2019015 +[Abstract](1673) +[HTML](817) +[PDF](1663.77KB)
Abstract:

One of the most significant challenges in data clustering is the evolution of the data distributions over time. Many clustering algorithms have been introduced to deal specifically with streaming data, but common amongst them is that they require users to set input parameters. These inform the algorithm about the criteria under which data points may be clustered together. Setting the initial parameters for a clustering algorithm is itself a non-trivial task, but the evolution of the data distribution over time could mean even optimally set parameters could become non-optimal as the stream evolves. In this paper we extend the RepStream algorithm, a combination graph and density-based clustering algorithm, in a way which allows the primary input parameter, the \begin{document}$K$\end{document} value, to be automatically adjusted over time. We introduce a feature called the edge distribution score which we compute for data in memory, as well as introducing an incremental method for adjusting the \begin{document}$K$\end{document} parameter over time based on this score. We evaluate our methods against RepStream itself, and other contemporary stream clustering algorithms, and show how our method of automatically adjusting the \begin{document}$K$\end{document} value over time leads to higher quality clustering output even when the initial parameters are set poorly.

2019, 2(3): 251-266 doi: 10.3934/mfc.2019016 +[Abstract](1272) +[HTML](528) +[PDF](403.16KB)
Abstract:

In this paper, eigenstructure assignment problems for polynomial matrix systems ensuring normalization and impulse elimination are considered. By using linearization method, a polynomial matrix system is transformed into a descriptor linear system without changing the eigenstructure of original system. By analyzing the characteristic polynomial of the desired system, the normalizable condition under feedback is given, and moreover, the parametric expressions of controller gains for eigenstructure ensuring normalization are derived by singular value decomposition. Impulse elimination in polynomial matrix systems is investigated when the normalizable condition is not satisfied. The parametric expressions of controller gains for impulse elimination ensuring finite eigenstructure assignment are formulated. The solving algorithms of corresponding controller gains for eigenstructure assignment ensuring normalization and impulse elimination are also presented. Numerical examples show the effectiveness of proposed method.

2019, 2(3): 267-277 doi: 10.3934/mfc.2019017 +[Abstract](1571) +[HTML](718) +[PDF](342.98KB)
Abstract:

This paper discusses admissibility problem of singular fractional order systems with order \begin{document}$1<\alpha<2$\end{document}. The alternative necessary and sufficient admissibility conditions are proposed, in which include linear matrix inequalities (LMIs) with equality constraints and LMIs without equality constraints. Moreover, these criteria are brand-new and different from the existing results. The state feedback control to stabilize singular fractional order systems is derived. Two numerical examples are presented to shown the effectiveness of our results.