In this paper, we determine the fuzzy SIMILARITY MEASURES of the U. S. state rankings with respect to domestic violence, female homicide, and sexual violence against teens. We find that the fuzzy SIMILARITY MEASURES are low. We then consider the best state rankings and determine the fuzzy SIMILARITY MEASURES of this ranking a with the previous three rankings. We also develop some theoretical results concerning fuzzy SIMILARITY MEASURES.

Image matching is a critical process in various photogrammetry, computer vision and remote sensing applications such as image registration, 3D model reconstruction, change detection, image fusion, pattern recognition, autonomous navigation, and digital elevation model (DEM) generation and orientation. The primary goal of the image matching process is to establish the correspondence between two images of the same scene (i. e., the reference and input images). Image matching methods are generally classified as feature-based matching and template matching. Feature-based methods extract image features (points, lines, regions) and attempt to establish the correspondence between these features. Template matching methods, also known as area-based methods, are generally defined as the process of finding a template in an image, based on a SIMILARITY measure such as cross-correlation and mutual information. Identical image windows of predefined size are applied for the computation of correspondence. SIMILARITY MEASURES play an essential role in the quality of template matching in photogrammetry, remote sensing, and computer vision. Various SIMILARITY MEASURES have been proposed in the literature. Each SIMILARITY measure has its strengths and weaknesses. In this paper, the capability of some well-known SIMILARITY MEASURES for matching of various close range and satellite images with diverse geometric and radiometric differences are evaluated. Also, to increase the template matching stability against geometric and radiometric variations, a novel weighting approach for computing of SIMILARITY MEASURES has been introduced. The proposed approach is based on three weight factor that are computed using gradient and Gaussian functions. By applying this weighting approach for cross correlation SIMILARITY measure, a novel measure named Weighted Cross-Correlation (WCC) has been presented. Ten algorithms, including SSD (Sum of Squared Differences), LSSSD (Locally Scaled Sum of Squared Differences), NSSD (Normalized Sum of Squared Differences), JF (Jeffrey Divergence), Tanimoto, ISD (Incremental Sign Distance), IRV (Intensity-Ratio Variance), CC (Cross-Correlation), MI (Mutual Information) and WCC are considered for evaluation. To evaluate the capability of various SIMILARITY MEASURES, a number of template-matching experiments were applied. Several synthetic and real images for different geometric and radiometric variations including, scale, rotation, viewpoint, blur, and illumination changes are used as data set. The SIMILARITY MEASURES are evaluated using three evaluation criteria, including success rate, positional accuracy, and computation time. The experimental results indicate that the proposed WCC method outperforms the other SIMILARITY MEASURES for all images and all types of transformations. Based on the evaluation results, the WCC method can be applied to the reliable template matching for a variety of photogrammetric and remote sensing applications. Generally, after the WCC, better results, on average, were obtained by the NSSD, LSSSD, and CC MEASURES in most cases. For illumination variations, MI and ISD methods provide the best results. The fastest method is the IRV and the slowest method is MI. Evaluation of the performance of the various SIMILARITY MEASURES for other applications such as dense matching process is suggested as future work.

In this paper, we discuss the importance of nuclear power for the future of the world with respect to climate change. In  particular, we examine the involvement of nuclear power by countries in several different ways. We consider first the   involvement of countries with respect to the amount of nuclear power produced, global energy transition, and capacity  factor. Countries are ranked with respect to these three involvement areas. The fuzzy SIMILARITY MEASURES of these  rankings are found to be low in most cases. We next place countries in their respective regions. We rank the countries  with respect to their carbon dioxide emissions and their greenhouse gas emissions. We then determine the fuzzy  SIMILARITY MEASURES of the countries with respect to the rankings. We found that one of the fuzzy SIMILARITY MEASURES  involving green house gas emissions is high.

The main objective of data mining is to acquire information from a set of data for prospect applications using a measure. The concerning issue is that one often has to deal with large scale data. Several dimensionality reduction techniques like various feature extraction methods have been developed to resolve the issue. However, the geometric view of the applied measure, as an additional consideration, is generally neglected. Since each measure has its own perspective to the data, different interpretations may achieved on data depending on the used measure. While efforts are often focused on adjusting the feature extraction techniques for mining the data, choosing a suitable measure regarding to the nature or general characteristics of the data or application is more appropriate. Given a couple of sequences, a specific measure may consider them as similar while another one may quantify them as dissimilar. The goal of this research is twofold: evincing the role of feature extraction in data mining and revealing the significance of SIMILARITY MEASURES geometric attributes in detecting the relationships between data. Differrent SIMILARITY MEASURES are also applied to three synthetic datasets and a real set of ECG time series to examine their performance.

In this paper, we expose cosine, jaccard and dice SIMILARITY MEASURES and rough interval Pythagorean mean operator. Some of the important properties of the defined SIMILARITY MEASURES have been established. Then the proposed methods are applied for solving multi attribute decision making problems. Finally, a numerical example is solved to show the feasibility, applicability and effectiveness of the proposed strategies.

The hesitant fuzzy soft set (HFSS), as a combination of hesitant fuzzy and soft sets, is regarded as a useful tool for dealing with the uncertainty and ambiguity of real-world problems. In HFSSs, each element is defined in terms of several parameters with arbitrary membership degrees. In addition, distance and SIMILARITY MEASURES are considered as the important tools in different areas such as pattern recognition, clustering, medical diagnosis, and the like. For this purpose, the present study aimed to evaluate the distance and SIMILARITY MEASURES for HFSSs by using well-known Hamming, Euclidean, and Minkowski distance MEASURES. Further, some examples were used to demonstrate that these MEASURES fail to perform well in some applications. Accordingly, new distance and SIMILARITY MEASURES were proposed by considering a hesitance index for HFSSs and the effect of considering hesitance index was shown by using an example of pattern recognition. Finally, the application of the proposed MEASURES and hesitance index was investigated in the clustering and decision-making problem, respectively. In conclusion, the use of the proposed MEASURES in clustering and hesitance index in decision-making can provide better and more reasonable results.

In this work, we shall present some novel process to measure the SIMILARITY between picture fuzzy sets. Firstly, we adopt the concept of intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets and picture fuzzy sets. Secondly, we develop some SIMILARITY MEASURES between picture fuzzy sets, such as, cosine SIMILARITY measure, weighted cosine SIMILARITY measure, set-theoretic SIMILARITY measure, weighted set-theoretic cosine SIMILARITY mea-sure, grey SIMILARITY measure and weighted grey SIMILARITY measure. Then, we apply these SIMILARITY MEASURES between picture fuzzy sets to building material recognition and minerals field recognition. Finally, two illustrative examples are given to demonstrate the efficiency of the SIMILARITY MEASURES for building material recognition and minerals field recognition.

Co-citation forms a relational document network. Co-citation-based MEASURES are found to be effective in retrieving relevant documents. However, they are far from ideal and need further enhancements. Co-opinion concept was proposed and tested in previous research and found to be effective in retrieving relevant documents. The present study endeavors to explore the correlation between opinion (dis)SIMILARITY MEASURES and the traditional co-citation-based ones including Citation Proximity Index (CPI), co-citedness and co-citation context SIMILARITY. The results show significant, though weak to medium, correlations between the variables. The correlations are direct for co-opinion measure, while being inverse for the opinion distance. Accordingly, the two groups of MEASURES are revealed to represent some similar aspects of the document relation. Moreover, the weakness of the correlations implies that there are different dimensions represented by the two groups.