In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It is proved that a pairwise weakly Lindelof property is not a hereditary property.

In this article, we have introduced the notion of pairwise compactness in bi-isotonic spaces via finite intersection property and pairwise open cover. Moreover, we have given pairwise compactness of bi-isotonic subspaces with both reduced closure and interior functions. We have characterized pairwise compactness by the neighborhood concept; however, the axioms of bi-isotonic spaces are insufficient to prove the theorem, and we have studied this in bi-closure spaces. For similar reasons, occasionally, bi-closure spaces have been considered with additional explanations, even if some concepts related to compactness have been naturally extended to bi-isotonic spaces. Additionally, interesting results have been obtained considering the pairwise Hausdorffness and compactness relationship. It has also been observed that resembling cross-relationships exist for closed subsets of pairwise compact spaces. Finally, it has been observed that the pairwise compactness of bi-closure spaces is preserved under bi-continuity.

Analytical Hierarchy Process is a method of solving a Multiple Attribute Decision Mak-ing. This method is based on the pairwise comparisons between the alternatives. These comparisons form a matrix named pairwise comparison matrix or judgment matrix. The weights of mentioned alternatives will be determined from this mentioned above matrix. In the case of consistency of the judgments, the cited weights are reliable and trusty. On the other hand, if the consistency of the judgment matrix is not acceptable, the result sufficient level of trust. In this case it is requested that the decision maker revise the judg-ment. In this paper we propose a method to approximate a consistent judgment matrix from an inconsistent one without the revision of the judgments. This method is based on decreasing the effects of the mistakes made by the decision maker.

Introduction: This study aimed to investigate the reliability and agreement of the Beta-band Intermuscular Coherence (Bb-IMC) as a clinical assessment tool for Non-Specific Chronic Low Back Pain (NS-CLBP) patients and healthy subjects by studying four phases of the Flexion-Extension Task (F-ET): standing, flexion, relaxation, and extension phases. Materials and Methods: Twenty-four men with NS-CLBP and 20 healthy subjects voluntarily participated in this study. All subjects performed three trials of F-ET while the surface electromyography was recorded from the lumbar erector spinal, gluteus maximus, and hamstring muscles of both sides. Beta-band intermuscular coherence analysis was used to calculate the pool coherence and the pairwise coherence for all mentioned muscles. Afterward, the Intra-class Correlation Coefficient (ICC), Standard Error of Measurement (SEM), and Minimal Detectable Change (MDC) for four phases of F-ET were used to analyze the intrarater reliability and agreement of the measurements. Results: The investigation of ICC, SEM, and MDC showed that the reliability was moderate to a high level for pool and pairwise coherence of Bb-IMC in all mentioned muscles for four phases of the flexion-extension task in NS-CLBP patients and healthy subjects. Yet, the agreement was low because the measurement error was relatively large. Conclusion: So far, no studies have used the Bb-IMC method to study low back pain, which is carried out in our research to check the reliability of this new method. Our findings revealed that pool and pairwise coherence obtained during F-ET have moderate to a high level of reliability for using Bb-IMC and could be considered a tool for the NS-CLBP patients’ assessment. Despite the small sample size investigated, in clinical practice the using Bb-IMC measure can help to study the interaction of corticospinal in NS-CLBP and also in healthy subjects. This measure requires larger sample sizes in addition to studying other circumstances and functional movements such as lifting weight. Further, more research appears to be warranted by the observed effectiveness of a particular intervention in modulation mechanisms of corticospinal tract function by Bb-IMC in NS-CLBP.

Semi-supervised clustering, utilizing the supervision information to guide the clustering process, could improve the clustering effect of the models. Most of existing semi-supervised clustering models only consider pairwise constraints or pointwise constraints. In this paper, the semi-supervised method is applied to the fuzzy clustering algorithm, and a robust semi-supervised fuzzy clustering algorithm is proposed. Firstly, fully considering prior knowledge, our models integrate pointwise constraints and pairwise constraints into a unified framework to improve the clustering performance of the fuzzy clustering algorithm. Secondly, in order to alleviate the impact of outliers, the robust performance of the models is considered by introducing an adaptive loss function into the models. Thirdly, our models can capture the global structures and the local manifold structures of data sets. Finally, a simple and efficient algorithm is proposed to solve the models, which ensures that the obtained solution is sparse and satisfies the constraint conditions in our models. Compared with five representative methods, experimental results on public datasets, such as text dataset (dbworld), voice dataset (Isolet), image datasets (YALE, Umist), chemical dataset (wine) and biological datasets (colon, TOX-171), show the effectiveness of the proposed models.