Weighted Cosine Similarity Measure Research Articles

Elastic deep autoencoder for text embedding clustering by an improved graph regularization

Text clustering is a task for grouping extracted information of the text in different clusters, which has many applications in recommender systems, sentiment analysis, and more. Deep learning-based methods have become increasingly popular due to their high accuracy in identifying nonlinear structures. They usually consist of two major parts: dimensionality reduction and clustering. Autoencoders are simple unsupervised neural networks used for better representation of low-dimensional data and have shown good performance in dealing with non-linear features. However, while they utilize the Frobenius norm to deal well with Gaussian noise, they are sensitive to outlier data and Laplacian noise. In this paper, a deep autoencoder with an adapted elastic loss for text embedding clustering (EDA-TEC) is proposed. The elastic loss is a combination of the Frobenius norm and L2,1-norm to consider both types of noises. Additionally, to maintain the high-dimensional data geometric structure, a modified graph regularization term based on the weighted cosine similarity measure is used. EDA-TEC also improves clustering results by considering the sparsity regularization of the manifold representation data. In this jointly end-to-end deep learning model, better representation and text clustering results are achieved with high accuracy on common datasets compared to existing methods.11https://github.com/safinal/text-embedding-clustering.

Multicriteria Decision-Making Problem via Weighted Cosine Similarity Measure and Several Characterizations of Hypergroup and (Weak) Polygroups under the Triplet Single-Valued Neutrosophic Structure

Polygroups are an extended form of groups and a subclass of hypergroups that follow group-type axioms. In this paper, we define a triplet single-valued neutrosophic set, which is a generalization of fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets, and we combine this novel concept with hypergroups and polygroups. Firstly, the main goal of this paper is to introduce hypergroups, polygroups, and anti-polygroups under a triplet single-valued neutrosophic structure and then present various profound results. We also examine the interaction and properties of level sets of triplet single-valued neutrosophic polygroups and (normal) subpolygroups. Secondly, we rank the alternatives and select the best ones in a single-valued neutrosophic environment using the weighted cosine similarity measure between each alternative and the ideal alternative. Finally, we provide an example that clearly shows how the proposed decision-making method is applied.

Unsupervised authorship attribution using feature selection and weighted cosine similarity

This paper presents a computational model for the unsupervised authorship attribution task based on a traditional machine learning scheme. An improvement over the state of the art is achieved by comparing different feature selection methods on the PAN17 author clustering dataset. To achieve this improvement, specific pre-processing and features extraction methods were proposed, such as a method to separate tokens by type to assign them to only one category. Similarly, special characters are used as part of the punctuation marks to improve the result obtained when applying typed character n-grams. The Weighted cosine similarity measure is applied to improve the B3 F-score by reducing the vector values where attributes are exclusive. This measure is used to define distances between documents, which later are occupied by the clustering algorithm to perform authorship attribution.

Spherical Fuzzy Sets-Based Cosine Similarity and Information Measures for Pattern Recognition and Medical Diagnosis

Spherical fuzzy set (SFS) is a modified version of fuzzy set (FS) to cope with uncertainty and complicated data in real-decision theory. In this article, some similarity measures, called cosine similarity measure (CSM), weighted cosine similarity measure (WCSM), set-theoretic similarity measure (STSM), weighted set-theoretic similarity measure (WSTSM), gray similarity measure (GSM), and weighted gray similarity measure (WGSM) are utilized in the setting of SFSs. Further, the information energy, correlation co-efficient (CC) and weighted correlation co-efficient (WCC) of SFSs are also introduced in this manuscript. The established measures based on SFSs are utilized in the setting of pattern recognition and medical diagnosis to express the validity and reliability of the explored measures with the help of some numerical examples. The projected measures based on SFSs are compared with existing measures, to show that the established measures for SFSs are more generalized than existing measures. The advantages and sensitive analysis of the investigated measures are also discussed in detail.

SOME SIMILARITY MEASURES FOR PICTURE FUZZY SETS AND THEIR APPLICATIONS

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 Intuitionistic Fuzzy Linguistic Cosine Similarity Measure and Its Application in Pattern Recognition

We propose the cosine similarity measures for intuitionistic fuzzy linguistic sets (IFLSs) and interval-valued intuitionistic fuzzy linguistic sets (IVIFLSs), which are expressed by the linguistic scale function based on the cosine function. Then, the weighted cosine similarity measure and the ordered weighted cosine similarity measure for IFLSs and IVIFLSs are introduced by taking into account the importance of each element, and the properties of the cosine similarity measures are also given. The main advantage of the proposed cosine similarity measures is that the decision-makers can flexibly select the linguistic scale function depending on the actual semantic situation. Finally, we present the application of the cosine similarity measures for intuitionistic fuzzy linguistic term sets and interval-valued intuitionistic fuzzy linguistic term sets to pattern recognition and medical diagnosis, and the existing cosine similarity measures are compared with the proposed cosine similarity measures by the illustrative example.

An improved cosine similarity measure for intuitionistic fuzzy sets and their applications to decision-making process

In the present study, improved cosine similarity measure for an intuitionistic fuzzy sets (IFSs) has been proposed by considering the interaction between the pairs of the membership degrees. Pairs of membership, non-membership are to be considered as vector representation during the formulation. The shortcomings of the existing measures have been highlighted and overcome by using the proposed measure. Also, in order to deal with the situation where the elements in a set are correlative, weighted cosine similarity measure has been defined. Finally, multi-criteria decision making (MCDM) method, based on the proposed similarity measure, has been presented under intuitionistic fuzzy environment. Numerical examples, one from the investment the money and others from the pattern recognition and medical diagnosis, have been taken to demonstrate the efficiency of the proposed approach and compared their results with the existing approaches results.

Interval-Valued Intuitionistic Fuzzy Ordered Weighted Cosine Similarity Measure and Its Application in Investment Decision-Making

We present the interval-valued intuitionistic fuzzy ordered weighted cosine similarity (IVIFOWCS) measure in this paper, which combines the interval-valued intuitionistic fuzzy cosine similarity measure with the generalized ordered weighted averaging operator. The main advantage of the IVIFOWCS measure provides a parameterized family of similarity measures, and the decision maker can use the IVIFOWCS measure to consider a lot of possibilities and select the aggregation operator in accordance with his interests. We have studied some of its main properties and particular cases such as the interval-valued intuitionistic fuzzy ordered weighted arithmetic cosine similarity (IVIFOWACS) measure and the interval-valued intuitionistic fuzzy maximum cosine similarity (IVIFMAXCS) measure. The IVIFOWCS measure not only is a generalization of some similarity measure, but also it can deal with the correlation of different decision matrices for interval-valued intuitionistic fuzzy values. Furthermore, we present an application of IVIFOWCS measure to the group decision-making problem. Finally the existing similarity measures are compared with the IVIFOWCS measure by an illustrative example.

Cosine Similarity Measure Based Multi-attribute Decision-making with Trapezoidal Fuzzy Neutrosophic Numbers

The objective of the study is to present cosine similarity measure based multi-attribute decision making under neutrosophic environment. The assesments of alternatives over the attributes are expressed with trapezoidal fuzzy neutrosophic numbers in which the three independent components namely, truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F) are expressed by trapezoidal fuzzy numbers. Cosine similarity measure between two trapezoidal fuzzy neutrosophic numbers and its properties are introduced. Expected value of trapezoidal fuzzy neutrosophic number is defined to determine the attribute weight. With these attribute weights, weighted cosine similarity measure between relative positive ideal alternative and each alternative is determined to find out the best alternative in multi-attribute decision-making problem. Finally, a numerical example is provided to illustrate the proposed approach

Interval-valued intuitionistic fuzzy cosine similarity measures for multiple attribute decision-making

In this work, considering all information carried by the membership degrees, nonmembership degree, and hesitancy degree in interval-valued intuitionistic fuzzy sets (IVIFSs) as 3-D vector representations, we propose a cosine similarity measure and a weighted cosine similarity measure for IVIFSs based on the extension of the cosine similarity measure (angular coefficient) between intuitionistic fuzzy sets in 2-D vector space. Then, the weighted cosine similarity measure for IVIFSs is applied to multiple attribute decision-making problems under the interval-valued intuitionistic fuzzy environment. Through the similarity measure between the ideal alternative and each alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. Finally, two illustrative examples are given to demonstrate the applications and efficiency of the proposed decision-making method.

Multicriteria decision-making method using the correlation coefficient under single-valued neutrosophic environment

The paper presents the correlation and correlation coefficient of single-valued neutrosophic sets (SVNSs) based on the extension of the correlation of intuitionistic fuzzy sets and demonstrates that the cosine similarity measure is a special case of the correlation coefficient in SVNS. Then a decision-making method is proposed by the use of the weighted correlation coefficient or the weighted cosine similarity measure of SVNSs, in which the evaluation information for alternatives with respect to criteria is carried out by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree under single-valued neutrosophic environment. We utilize the weighted correlation coefficient or the weighted cosine similarity measure between each alternative and the ideal alternative to rank the alternatives and to determine the best one(s). Finally, an illustrative example demonstrates the application of the proposed decision-making method.

Multicriteria decision-making method based on a cosine similarity measure between trapezoidal fuzzy numbers

The degree of similarity or dissimilarity between the objects under study plays an important role. In vector space, especially, the cosine similarity measure is often used in information retrieval, citation analysis, and automatic classification. However, it scarcely deals with trapezoidal fuzzy information and multicriteria decision-making problems. For this purpose, a cosine similarity measure between trapezoidal fuzzy numbers is proposed based on an extension of the cosine similarity between fuzzy sets and is applied to fuzzy multicriteria decision-making problems under the conditions that the criteria weights and the evaluated values in the decision matrix are expressed by the form of trapezoidal fuzzy numbers. Through the expected weight and the weighted cosine similarity measure between each alternative and the ideal alternative, the ranking order of all alternatives can be determined and the best alternative can be easily identified as well. The proposed method is simple and effective. Finally, an illustrative example demonstrates the implementation process of the technique.

Cosine similarity measures for intuitionistic fuzzy sets and their applications

In this work, considering the information carried by the membership degree and the non-membership degree in Atanassov’s intuitionistic fuzzy sets (IFSs) as a vector representation with the two elements, a cosine similarity measure and a weighted cosine similarity measure between IFSs are proposed based on the concept of the cosine similarity measure for fuzzy sets. To demonstrate the efficiency of the proposed cosine similarity measures, the existing similarity measures between IFSs are compared with the cosine similarity measure between IFSs by numerical examples. Finally, the cosine similarity measures are applied to pattern recognition and medical diagnosis.