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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 measure, 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.

The most straightforward approaches to checking the degrees of similarity and differentiation between two sets are to use distance and cosine similarity metrics. The cosine of the angle between two n-dimensional vectors in n-dimensional space is called cosine similarity. Even though the two sides are dissimilar in size, cosine similarity may readily find commonalities since it deals with the angle in between. Cosine similarity is widely used because it is simple, ideal for usage with sparse data, and deals with the angle between two vectors rather than their magnitude. The distance function is an elegant and canonical quantitative tool to measure the similarity or difference between two sets. This work presents new metrics of distance and cosine similarity amongst Fermatean fuzzy sets. Initially, the definitions of the new measures based on Fermatean fuzzy sets were presented, and their properties were explored. Considering that the cosine measure does not satisfy the axiom of similarity measure, then we propose a method to construct other similarity measures between Fermatean fuzzy sets based on the proposed cosine similarity and Euclidean distance measures and it satisfies the axiom of the similarity measure. Furthermore, we obtain a cosine distance measure between Fermatean fuzzy sets by using the relationship between the similarity and distance measures, then we extend the technique for order of preference by similarity to the ideal solution method to the proposed cosine distance measure, which can deal with the related decision-making problems not only from the point of view of geometry but also from the point of view of algebra. Finally, we give a practical example to illustrate the reasonableness and effectiveness of the proposed method, which is also compared with other existing methods.

Set pair analysis (SPA) is an updated theory for dealing with the uncertainty, which overlaps with the other existing theories such as vague, fuzzy, intuitionistic fuzzy set (IFS). Keeping the advantages of it, in this paper, we propose some novel similarity measures to measure the relative strength of the different intuitionistic fuzzy sets (IFSs) after pointing out the weakness of the existing measures. For it, a connection number, the main component of SPA theory is formulated in the form of the degrees of identity, discrepancy, and contrary. Then, based on it some new similarity and weighted similarity measures between the connection number sets are defined. A comparative analysis of the proposed and existing measures are formulated in terms of the counter-intuitive cases for showing the validity of it. Finally, an illustrative example is provided to demonstrate it.

The intuitionistic fuzzy set (IFS), as a generation of Zadeh’s fuzzy set, can express and process uncertainty much better. Similarity measures between IFSs are used to indicate the similarity degree between the information carried by IFSs. Although several similarity measures for IFSs have been proposed in previous studies, some of them cannot satisfy the axioms of similarity, or provide counterintuitive cases. In this paper, we first review several widely used similarity measures and then propose a new similarity measures. As the consistency of two IFSs, the proposed similarity measure is defined based on the direct operation on the membership function, non-membership function, hesitation function and the upper bound of membership function of two IFS, rather than based on the distance measure or the relationship of membership and non-membership functions. It proves that the proposed similarity measure satisfies the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns. Experiments on medical diagnosis and cluster analysis are carried out to illustrate the applicability of the proposed similarity measure in practice.

This study mainly focuses on developing a new flexible technique for interval-valued intuitionistic fuzzy cosine similarity measures, which significantly analyzes the strength of the relationship between two objects. Based on the notion of a cosine similarity measure between IVIFSs, the proposed measure is formulated. Then, the measure is demonstrated to satisfy some essential properties, which prepare the ground for applications in different areas. Finally, the study uses the proposed measure to solve real-world decision problems such as pattern recognition, medical diagnosis, and multi-criteria decision-making problems with interval-valued intuitionistic fuzzy information. The numerical examples of the mentioned applications are delivered to validate the effectiveness of the developed approach in solving real-life problems.

Handling unreliable detections and avoiding identity switches are crucial for the success of multiple object tracking (MOT). Ideally, MOT algorithm should use true positive detections only, work in real-time and produce no identity switches. To approach the described ideal solution, we present the BoostTrack, a simple yet effective tracing-by-detection MOT method that utilizes several lightweight plug and play additions to improve MOT performance. We design a detection-tracklet confidence score and use it to scale the similarity measure and implicitly favour high detection confidence and high tracklet confidence pairs in one-stage association. To reduce the ambiguity arising from using intersection over union (IoU), we propose a novel Mahalanobis distance and shape similarity additions to boost the overall similarity measure. To utilize low-detection score bounding boxes in one-stage association, we propose to boost the confidence scores of two groups of detections: the detections we assume to correspond to the existing tracked object, and the detections we assume to correspond to a previously undetected object. The proposed additions are orthogonal to the existing approaches, and we combine them with interpolation and camera motion compensation to achieve results comparable to the standard benchmark solutions while retaining real-time execution speed. When combined with appearance similarity, our method outperforms all standard benchmark solutions on MOT17 and MOT20 datasets. It ranks first among online methods in HOTA metric in the MOT Challenge on MOT17 and MOT20 test sets. We make our code available at https://github.com/vukasin-stanojevic/BoostTrack .

In this paper, we initiate a new axiomatic definition of single-valued neutrosophic distance measure and similarity measure, which is expressed by single-valued neutrosophic number that will reduce the information loss and remain more original information. Meanwhile, a novel score function is proposed. Then, the objective weights of various attributes are determined via gray system theory. Moreover, we present the combined weights, which can show both the subjective information and the objective information. Later, we present three algorithms to deal with multi-attribute decision-making problem based on revised Technique for Order Preference by Similarity to an Ideal Solution, Multi-Attributive Border Approximation area Comparison and similarity measure. Finally, the effectiveness and feasibility of approaches are demonstrated by two numerical examples.

Mass spectrometry data is one of the key sources of information in many workflows in medicine and across the life sciences. Mass fragmentation spectra are generally considered to be characteristic signatures of the chemical compound they originate from, yet the chemical structure itself usually cannot be easily deduced from the spectrum. Often, spectral similarity measures are used as a proxy for structural similarity but this approach is strongly limited by a generally poor correlation between both metrics. Here, we propose MS2DeepScore: a novel Siamese neural network to predict the structural similarity between two chemical structures solely based on their MS/MS fragmentation spectra. Using a cleaned dataset of > 100,000 mass spectra of about 15,000 unique known compounds, we trained MS2DeepScore to predict structural similarity scores for spectrum pairs with high accuracy. In addition, sampling different model varieties through Monte-Carlo Dropout is used to further improve the predictions and assess the model’s prediction uncertainty. On 3600 spectra of 500 unseen compounds, MS2DeepScore is able to identify highly-reliable structural matches and to predict Tanimoto scores for pairs of molecules based on their fragment spectra with a root mean squared error of about 0.15. Furthermore, the prediction uncertainty estimate can be used to select a subset of predictions with a root mean squared error of about 0.1. Furthermore, we demonstrate that MS2DeepScore outperforms classical spectral similarity measures in retrieving chemically related compound pairs from large mass spectral datasets, thereby illustrating its potential for spectral library matching. Finally, MS2DeepScore can also be used to create chemically meaningful mass spectral embeddings that could be used to cluster large numbers of spectra. Added to the recently introduced unsupervised Spec2Vec metric, we believe that machine learning-supported mass spectral similarity measures have great potential for a range of metabolomics data processing pipelines.

In this paper, we propose new vector similarity measures of single-valued and interval neutrosophic sets by hybridizing the concepts of Dice and cosine similarity measures. We present their applications in multi-attribute decision making under neutrosophic environment. We use these similarity measures to find out the best alternative by determining the similarity measure values between the ideal alternative and each alternative. The results of the proposed similarity measures have been validated by comparing with other existing similarity measures reported in the literature for multi-attribute decision making. The main thrust of the proposed similarity measures will be in the field of practical decision making, medical diagnosis, pattern recognition, data mining, clustering analysis, etc.

Plenty of researches have been carried out, focusing on the measures of distance, similarity, and correlation between intuitionistic fuzzy sets (IFSs). However, most of them are single-valued measures and lack of potential for efficiency validation. In this paper, a new vector valued similarity measure for IFSs is proposed based on OWA operators. The vector is defined as a two-tuple consisting of the similarity measure and uncertainty measure, in which the latter is the uncertainty of the former. OWA operators have the ability to aggregate all values in the universe of discourse of IFSs, and to determine the weights according to specific applications. A framework is built to measure similarity between IFSs. A series of definitions and theorems are given and proved to satisfy the corresponding axioms defined for IFSs. In order to illustrate the effectiveness of the proposed vector valued similarity measure, a classification problem is used as an application.