• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.581-600
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• 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.719-732
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• 2018

In this manuscript, hybrid fixed point results for four maps using (E.A) and tangential properties in the setting of metric space are studied. Application to system of functional equations is also studied.

• ETRI Journal
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• v.36 no.3
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• pp.333-342
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• 2014

Most hyper-ellipsoidal clustering (HEC) approaches use the Mahalanobis distance as a distance metric. It has been proven that HEC, under this condition, cannot be realized since the cost function of partitional clustering is a constant. We demonstrate that HEC with a modified Gaussian kernel metric can be interpreted as a problem of finding condensed ellipsoidal clusters (with respect to the volumes and densities of the clusters) and propose a practical HEC algorithm that is able to efficiently handle clusters that are ellipsoidal in shape and that are of different size and density. We then try to refine the HEC algorithm by utilizing ellipsoids defined on the kernel feature space to deal with more complex-shaped clusters. The proposed methods lead to a significant improvement in the clustering results over K-means algorithm, fuzzy C-means algorithm, GMM-EM algorithm, and HEC algorithm based on minimum-volume ellipsoids using Mahalanobis distance.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.10 no.5
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• pp.193-199
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• 2010

In this paper, we propose a new metric to measure the dynamic connection states of Ad Hoc network. The new metric measures the total path break up time $\sum_{i}T_i$, where $T_i$ is the time period during which maximum cluster distance exceeds the radio range. $T_i$ can be calculated from the maximum cluster distance function of time, which can be computed from the node position samples of mobility model. The proposed metric can be used as a total system metric as well as an individual connection metric.

• Journal of KIISE:Databases
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• v.34 no.5
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• pp.437-447
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• 2007

A variety of similarity metrics have been used to measure the degree of web page changes. In this paper, we first define criteria for web page changes to evaluate the effectiveness of the similarity metrics in terms of six important types of web page changes. Second, we propose a new similarity metric appropriate for measuring the degree of web page changes. Using real web pages and synthesized pages, we analyze the five existing metrics (i.e., the byte-wise comparison, the TF IDF cosine distance, the word distance, the edit distance, and the shingling) and ours under the proposed criteria. The analysis result shows that our metric represents the changes more effectively than other metrics. We expect that our study can help users select an appropriate metric for particular web applications.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.517-526
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• 2013

We give a fixed point theorem for complete fuzzy metric space which generalizes fuzzy Banach contraction theorems established by V. Gregori and A. Spena [Fuzzy Sets and Systems 125 (2002), 245-252] using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9] in metric spaces.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.485-500
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• 2014

In this paper, we establish coupled fixed point theorems for mixed monotone mappings satisfying nonlinear contraction involving a pair of altering distance functions in ordered G-metric spaces. Via presented theorems we extend and generalize the results of Harjani et al. [J. Harjani, B. L$\acute{o}$pez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011) 1749-1760] and Choudhury and Maity [B.S. Choudhury and P. Maity, Coupled fixed point results in generalized metric spaces. Math. Comput. Model. 54 (2011), 73-79].

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.203-210
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• 2007

Let X be a hyperbolic region in the complex plane C such that the hyperbolic metrix ${\lambda}_X(w){\mid}dw{\mid}$ exists. Let $R(X)=sup\{{\delta}_X(w):w{\in}X\}$ where ${\delta}_X(w)$ is the euclidean distance from w to ${\partial}X$. Here ${\partial}X$ is the boundary of X. A hyperbolic region X is called a Bloch region if R(X) < ${\infty}$. In this paper, we obtain lower bounds for the hyperbolic metric on Bloch regions in terms of the distance to the boundary.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.1
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• pp.41-52
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• 1994

Imprecision of evaluation or lack of prior information about preference can be an obstacle for decision maker in representing his strict preference. Therefore, fuzziness of preference can take place, and in addition, intransitivity or incomparability of preference becomes the critical difficulty in making complete preorder of alternatives. In order to get better solution and to improve practical usufulness, MCDM should be established as a pseudo-criterion model that include fuzzy preference. In this paper, we suggest a pseudo-criterion model that can make complete preorder of alternatives by metric distance measure.

• Journal of Navigation and Port Research
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• v.47 no.6
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• pp.367-375
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• 2023

This study developed a new distance metric for vessel trajectories, applicable to marine traffic control services in the Korean coastal waters. The proposed metric is designed through the weighted summation of the traditional Hausdorff distance, which measures the similarity between spatiotemporal data and incorporates the differences in the average Speed Over Ground (SOG) and the variance in Course Over Ground (COG) between two trajectories. To validate the effectiveness of this new metric, a comparative analysis was conducted using the actual Automatic Identification System (AIS) trajectory data, in conjunction with an agglomerative clustering algorithm. Data visualizations were used to confirm that the results of trajectory clustering, with the new metric, reflect geographical distances and the distribution of vessel behavioral characteristics more accurately, than conventional metrics such as the Hausdorff distance and Dynamic Time Warping distance. Quantitatively, based on the Davies-Bouldin index, the clustering results were found to be superior or comparable and demonstrated exceptional efficiency in computational distance calculation.