Search Results (9)

In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers ${\mathbb{R}}_0^{+}$. More precisely, we prove several new results concerning these theories. We introduce to the literature the concept of eigenvalues and eigenvectors of a semi-linear operator, describing how to compute them. The topological properties of semi-vector spaces, such as completeness and separability, are also investigated here. New families of semi-vector spaces derived from the semi-metric, semi-norm and semi-inner product, among others, are exhibited. Furthermore, we show several new results concerning semi-algebras. After this theoretical approach, we apply such a theory in fuzzy automata. More precisely, we describe the semi-algebra of A-fuzzy regular languages and we apply the theory of fuzzy automata for counting patterns in DNA sequences. Full article

The current damage is the most stubborn and difficult fault of high-power motor bearings because its vibration characteristics are easily confused with those of ordinary bearing mechanical faults. If it is discriminated as an ordinary mechanical fault without electrical insulation protection, the current damage of bearing shafts will still repeatedly appear. Aiming at the problem that it is difficult to identify the bearing current damage fault under variable working conditions, a bearing shaft current damage identification method based on multiscale feature label propagation and manifold metric transfer (MFLP-MMT) is proposed. Firstly, the multiscale sub-band signal is obtained by wavelet packet decomposition, and the multiscale sub-band fuzzy entropy is obtained by calculating its fuzzy entropy. Then, according to the extracted features, a neighbor graph is constructed on the source domain of the known fault label to obtain the pseudo label of the target domain sample, and the source domain label information is gradually diffused by way of the graph label propagation. The multiscale sub-band fuzzy entropy of the sample is mapped to the low-dimensional manifold space by locality preserving projections (LPP), and the source domain samples close to the target domain are given higher weights by cross-domain density ratio estimation to solve the problem of domain offset. Combined with the label samples of the target domain in label propagation, the manifold distance metric is learned to minimize the intra-class distance and maximize the inter-class distance in the domain and eliminate the overlapping phenomenon in the domain. By increasing the range of label propagation after each iteration, the label propagation error of the leading graph is gradually reduced, and unsupervised metric transfer learning is realized. The experimental results show that the new method is superior to the semi-supervised transfer learning method in fault identification ability; the highest fault identification accuracy can reach 100% and it has a good robustness. Full article

In this paper, we provide several Arzelà–Ascoli-type results on the space of all continuous functions from a Tychonoff space X into the fuzzy sets of ${\mathbb{R}}^n$, $(F_{USCB}\left({\mathbb{R}}^n\right),H_{end})$, which are upper semi-continuous and have bounded support endowed with the endograph metric. Namely, we obtain positive results when X is considered to be a $k_r$-space and $C(X,(F_{USCB}\left({\mathbb{R}}^n\right),H_{end}))$ is endowed with the compact open topology, as well as when we assume that X is pseudocompact and $C(X,(F_{USCB}\left({\mathbb{R}}^n\right),H_{end}))$ is equipped with the uniform topology. Full article

Asymptotically coupled coincidence points and asymptotically coupled fixed points in fuzzy semi-metric spaces are studied in this paper. The fuzzy semi-metric space is taken into account, which lacks symmetric conditions. In this case, the desired results are separately investigated based on four different types of triangle inequalities. The uniqueness of asymptotically coupled coincidence points cannot be guaranteed, and it can only be addressed in a weak sense of uniqueness. However, the uniqueness of asymptotically coupled fixed points can be guaranteed using different arguments. Full article

This paper investigates the common coupled coincidence points and common coupled fixed points in fuzzy semi-metric spaces. The symmetric condition is not necessarily satisfied in fuzzy semi-metric space. Therefore, four kinds of triangle inequalities are taken into account in order to study the Cauchy sequences. Inspired by the intuitive observations, the concepts of rational condition and distance condition are proposed for the purpose of simplifying the discussions. Full article

Convergence using dual double fuzzy semi-metric is studied in this paper. Two types of dual double fuzzy semi-metric are proposed in this paper, which are called the infimum type of dual double fuzzy semi-metric and the supremum type of dual double fuzzy semi-metric. Under these settings, we also propose different types of triangle inequalities that are used to investigate the convergence using dual double fuzzy semi-metric. Full article

The convergence using the fuzzy semi-metric and dual fuzzy semi-metric is studied in this paper. The infimum type of dual fuzzy semi-metric and the supremum type of dual fuzzy semi-metric are proposed in this paper. Based on these two types of dual fuzzy semi-metrics, the different types of triangle inequalities can be obtained. We also study the convergence of these two types of dual fuzzy semi-metrics. Full article

We propose the so-called fuzzy semi-metric space in which the symmetric condition is not assumed to be satisfied. In this case, there are four kinds of triangle inequalities that should be considered. The purpose of this paper is to study the common coincidence points and common fixed points in the newly proposed fuzzy semi-metric spaces endowed with the so-called ⋈-triangle inequality. The other three different kinds of triangle inequalities will be the future research, since they cannot be similarly investigated as the case of ⋈-triangle inequality. Full article