Pseudo Metrics Research Articles

Düğümlerle Eşlenen Bitopolojiler Üzerine Bir Çalışma

The bitopologies have been associated with some knots in the literature with the help of a method called the knot digraph notation. The knot graphs and quasi pseudo metric spaces were used to obtain these bitopologies. With the help of quasi pseudo metrics, two topologies were obtained on a set. In this way, an association between some knots and bitopologies was established. The authors sought an answer to the question “Given the bitopologies associated with knots, can the knot itself be obtained ?” and they gave a method. This mentioned method consists of 6 steps.. In this work, it is shown in detail that according to the Alexander-Briggs notation, the reverse of the knot digraph notation is provided for the knots 3(1), 5(1), 5(2), 6(1), 6(2), 7(1), 7(2), 7(3), 8(1), 8(2), 8(3), 9(1), 9(2), 9(3), 10(1), 10(2), 10(3).

Road networks reliability estimations and optimizations: A Bi-directional bottom-up, top-down approach

In this paper, we present a novel three-stage reduction-based estimation and optimization heuristics to evaluate and improve large-scale road networks’ reliability efficiently. Some necessary rules and tools are developed, in the 1st stage, to translate a large-scale physical road network into a mathematical graph. Then, in the 2nd stage, a bottom-up reduction algorithm is formulated to estimate network reliability. Finally, in the 3rd stage, a top-down method is proposed to improve the road network reliability by employing mathematical optimization models. Hence, this is a bidirectional bottom-up top-down (BUTD) method that (1) is genuinely based on the mathematical theory of reliability, (2) is computationally efficient by avoiding NP-hardness, and (3) by relaxing the need to employ pseudo metrics of reliability, e.g., vulnerability, resilience, etc. from the complex network theory in analyzing the large-scale road networks. The approach is explained using an illustrative example and a case study.

A new definition of fuzzy k-pseudo metric and its induced fuzzifying structures

In this paper, a new definition of a fuzzy $k$-pseudo metric is introduced and its induced fuzzifying structures are constructed, such as a fuzzifying neighborhood system, a fuzzifying topology, a fuzzifying closure operator, a fuzzifying uniformity.Besides, it is shown that there is a one-to-one correspondence between fuzzy $k$-pseudo metrics and nests of crisp $k$-pseudo metrics.

Aggregation of partial T-indistinguishability operators and partial pseudo–metrics

In this contribution we address our attention on the aggregation of partial T-indistinguishability operators (relations) and partial pseudo-metrics. A characterization of those functions that allow to merge a collection of partial T–indistinguishability operators into a new one was provided by Calvo et al. in [10] by means of (T,TM)-tuples, but here we present another characterization in terms of (+,max⁡)-tuples. Also, we analyze the aggregation of a collection (Ei)i=1n of partial Ti-indistinguishability operators. Moreover, we provide that a generalized inter–exchange composition functions condition is a sufficient condition to guarantee that a function merges partial Ti-indistinguishability operators into a single one. In addition, we give different expressions of those aggregation functions that are object of our study, most of them are defined by means of the additive generators of the corresponding t-norms and another particular function. We see that the functions, that merge partial S-pseudo-metrics into a new one, are related to the functions that aggregate partial pseudo-metrics. Finally, we show the relation between the functions, that merge partial T-indistinguishability operators and the functions that preserve the partial T⁎-pseudo-metrics in the aggregation process.

Quantitative Stability Analysis of Two-Stage Stochastic Linear Programs with Full Random Recourse

In this paper, we apply the parametric linear programing technique and pseudo metrics to study the quantitative stability of the two-stage stochastic linear programing problem with full random recourse. Under the simultaneous perturbation of the cost vector, coefficient matrix, and right-hand side vector, we first establish the locally Lipschitz continuity of the optimal value function and the boundedness of optimal solutions of parametric linear programs. On the basis of these results, we deduce the locally Lipschitz continuity and the upper bound estimation of the objective function of the two-stage stochastic linear programing problem with full random recourse. Then by adopting different pseudo metrics, we obtain the quantitative stability results of two-stage stochastic linear programs with full random recourse which improve the current results under the partial randomness in the second stage problem. Finally, we apply these stability results to the empirical approximation of the two-stage stochastic programing model, and the rate of convergence is presented.

On vector valued pseudo metrics and applications

In this article, we will introduce a new concept of gauge spaces induced by a family of vector valued pseudo metrics. After this, we will also prove some results to ensure the existence of fixed points of self mappings. As an application of our result, we will give an existence theorem to ensure the existence of solutions of n different integral equations.

Case-based reasoning classifier based on learning pseudo metric retrieval

A learning pseudo metric case-based reasoning classification method is proposed.A new classifier is redesigned on the basis of the traditional CBR classifier.The algorithm of LPM-CBR has some anti-interference ability and good robustness.The LPM-based retrieval method can improve the quality and learning ability of CBR. In case-based reasoning (CBR) classification systems, the similarity metrics play a key role and directly affect the system's performance. Based on our previous work on the learning pseudo metrics (LPM), we propose a case-based reasoning method for pattern classification, where the widely used Euclidean distance is replaced by the LPM to measure the closeness between the target case and each source case. The same type of case as the target case can be retrieved and the category of the target case can be defined by using the majority of reuse principle. Experimental results over some benchmark datasets and a fault diagnosis of the Tennessee-Eastman (TE) process demonstrate that the proposed reasoning techniques in this paper can effectively improve the classification accuracy, and the LPM-based retrieval method can substantially improve the quality and learning ability of CBR classifiers.

Convergence of intuitionistic fuzzy sets

We define pointwise convergence, uniform convergence, Γ-convergence and convergence in supremum metric for the intuitionistic fuzzy sets. The uniform convergence is in the topology induced by lower and upper pseudo metrics. The Γ-convergence is the Kuratowski–Painlevé convergence of the endographs of the intuitionistic fuzzy sets. The supremum metric is the supremum of Hausdroff distance among the ζ-cuts of the intuitionistic fuzzy sets. We discuss the mutual relationship of these convergences. Topological structures are also discussed in detail. Adequate number of examples are given to illustrate the relationship among these convergences.

Using Artificial Intelligence Techniques to Implement a Multifactor Authentication System

The recent years have seen a rise in the number of cases of cyber-crime committed through identity theft and fraud. To address this problem, this paper uses adaptive neural-fuzzy inference system, fuzzy logic and artificial neural network to implement a multifactor authentication system through a technique of information fusion. To begin with, the identity attributes are mined using the three corpora from three major sources namely the social networks, a set of questionnaires and application forms from the various services offered both in the real and cyberspace. The statistical information generated by the corpora is then used to compose an identity attribute metric model. The composed identity attributes metrics values classified as biometrics, device metrics and pseudo metrics are then fused at the score level through a technique of information fusion in a multifactor authentication system by using each of the above artificial intelligence technologies and the results compared.

Identity Attributes Mining, Metrics Composition and Information Fusion Implementation Using Fuzzy Inference System

Term weight a technique in text mining and entropy from Shannon’s information theory are both used to quantify information. In this paper they are used to develop an identity attribute metrics model. Using term weight and entropy metrics values, Sugeno-style fuzzy inference system is envisaged in the implementation of information fusion in a multimode authentication system. This is in an effort to provide a solution to the cases of identity theft and fraud. Three corpora are used to mine the identity attributes and generate the statistical information required to compose a metric model from a set of questionnaires and the application forms for the various services. Triangular and sigmoidally shaped membership functions are used in the fuzzification of the three inputs categorised as biometrics, pseudo metrics and device metrics.

Learning Pseudo Metric for Intelligent Multimedia Data Classification and Retrieval

While people compare images using semantic concepts, computers compare images using low-level visual features that sometimes have little to do with these semantics. To reduce the gap between the high-level semantics of visual objects and the low-level features extracted from them, in this paper we develop a framework of learning pseudo metrics (LPM) using neural networks for semantic image classification and retrieval. Performance analysis and comparative studies, by experimenting on an image database, show that the LPM has potential application to multimedia information processing.