In this paper an approach to information quantitative measuring is offered. This information is given as a fuzzy number. It is a particular case of the fuzzy set which is defined by a membership function. It should be noted that this function is determined on the basis of some segment on the set of real numbers. Therefore, a problem changes into construction of the fuzzy number membership function. Quasiconcave membership functions of fuzzy numbers are most frequently used in economic and social problems. For this type of fuzzy numbers this paper provides an algorithm of the fuzzy numbers' membership function construction according to the expert's opinion. The algorithm is based on a segment sequential localization procedure. The fuzzy number membership function is defined by means of this segment using the expert opinion. This procedure is similar to the procedure of extremum seeking of the quasiconcave function through the instrumentality of the sequential measurements of its values. Two ways of such localization have been examined.
Countering cyber threats, especially attack detection, is a challenging area of research in the field of information assurance. Intruders use polymorphic mechanisms to masquerade the attack payload and evade the detection techniques. Many supervised and unsupervised learning approaches from the field of machine learning and pattern recognition have been used to increase the efficacy of intrusion detection systems (IDSs). Supervised learning approaches use only labeled samples to train a classifier, but obtaining sufficient labeled samples is cumbersome, and requires the efforts of domain experts. However, unlabeled samples can easily be obtained in many real world problems. Compared to supervised learning approaches, semi-supervised learning (SSL) addresses this issue by considering large amount of unlabeled samples together with the labeled samples to build a better classifier. This paper proposes a novel fuzziness based semi-supervised learning approach by utilizing unlabeled samples assisted with supervised learning algorithm to improve the classifier’s performance for the IDSs. A single hidden layer feed-forward neural network (SLFN) is trained to output a fuzzy membership vector, and the sample categorization (low, mid, and high fuzziness categories) on unlabeled samples is performed using the fuzzy quantity. The classifier is retrained after incorporating each category separately into the original training set. The experimental results using this technique of intrusion detection on the NSL-KDD dataset show that unlabeled samples belonging to low and high fuzziness groups make major contributions to improve the classifier’s performance compared to existing classifiers e.g., naive bayes, support vector machine, random forests, etc.
The paper describes the relation between fuzzy and non-fuzzy description logics. It gives an overview about current research in these areas and describes the difference between tasks for description logics and fuzzy logics. The paper also deals with the transformation properties of description logics to fuzzy logics and backwards. While the process of transformation from a description logic to a fuzzy logic is a trivial inclusion, the other way of reducing information from fuzzy logic to description logic is a difficult task, that will be topic of future work.
Giant planets are thought to have cores in their deep interiors, and the division into a heavy-element core and hydrogen-helium envelope is applied in both formation and structure models. We show that the primordial internal structure depends on the planetary growth rate, in particular, the ratio of heavy elements accretion to gas accretion. For a wide range of likely conditions, this ratio is in one-to-one correspondence with the resulting post-accretion profile of heavy elements within the planet. This flux ratio depends sensitively on the assumed solid-surface density in the surrounding nebula. We suggest that giant planets' cores might not be distinct from the envelope and includes some hydrogen and helium, and the deep interior can have a gradual heavy-element structure. Accordingly, Jupiter's core may not be well defined. Accurate measurements of Jupiter's gravitational field by Juno could put constraints on Jupiter's core mass. However, as we suggest here, the definition of Jupiter's core is complex, and the core's physical properties (mass, density) depend on the actual definition of the core and on the planet's growth history.
In contemporary health science sophisticated apparatus delivers a lot of data on vital processes in patients. All of them are processed as a bulk of numbers not suitable directly for diagnosing or research purposes. Moreover, which is common in biomedical sciences, measured data are intrinsically inaccurate, i.e., fuzzy. In order to overcome these deficiencies a set of visualization methods has been developed as well as dedicated file formats. In the paper authors discuss selected formats and imaging techniques useful for cardiologists. Problems of medical data processing is outlined. Strengthens and weaknesses of raw STL file format are analyzed. Visualization styles of data fuzziness using experimental package ScPovPlot3D based on POVRay are proposed and discussed.
To improve the generalization performance of random vector functional link networks (RVFL), we propose a novel fuzziness based RVFL algorithm (F-RVFL) from the perspective of fuzzy theory for semi-supervised learning. Compared with the RVFL algorithm, the proposed F-RVFL algorithm shows better generalization performance on classification problems. In addition, we studied the relationship between the samples' output fuzziness and the classifier performance and obtained some useful conclusions, which gives a new direction for RVFL performance optimization.
Some decision making applications require to encode statistics and fuzziness. In this work two frameworks are considered: coherent conditional probabilities and possibilities, which allow to give a rigorous interpretation of membership function. A comparison of the two interpretations is given to employ a general Bayesian inferential approach able to embed fuzzy information.
In this study, Fuzzy Cognitive Maps (FCMs), which are powerful tools for graphical representation of knowledge, are analyzed from an ambiguity and fuzziness perspective. In conventional FCMs the causal strengths are represented with singleton (crisp) fuzzy numbers, but recently, other researchers proposed different FCM structures where uniform (interval) or triangular fuzzy numbers are used in causal strength representation. Here, FCMs are analyzed by means of fuzziness and ambiguity measures that are proposed in literature to investigate the capability of models to represent uncertainties. In addition, two new measures, called the average ambiguity measure (AAM) and the average fuzziness measure (AFM), are proposed to indicate uncertainty representation of an FCM. A well-known FCM model of a public health system is used as a case study to show how the fuzzy weights determine the uncertainty representation of FCMs, and then the outcomes are discussed.
We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein’s field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.