Cosine Distance Measure Research Articles

Cosine similarity and distance measures for [formula omitted] quasirung orthopair fuzzy sets: Applications in investment decision-making

Similarity measures and distance measures are used in a variety of domains, such as data clustering, image processing, retrieval of information, and recognizing patterns, in order to measure the degree of similarity or divergence between elements or datasets. p,q− quasirung orthopair fuzzy (p,q− QOF) sets are a novel improvement in fuzzy set theory that aims to properly manage data uncertainties. Unfortunately, there is a lack of research on similarity and distance measure between p,q− QOF sets. In this paper, we investigate different cosine similarity and distance measures between to p,q− quasirung orthopair fuzzy sets (p,q− ROFSs). Firstly, the cosine similarity measure and the Euclidean distance measure for p,q− QOFSs are defined, followed by an exploration of their respective properties. Given that the cosine measure does not satisfy the similarity measure axiom, a method is presented for constructing alternative similarity measures for p,q− QOFSs. The structure is based on the suggested cosine similarity and Euclidean distance measures, which ensure adherence to the similarity measure axiom. Furthermore, we develop a cosine distance measure for p,q− QOFSs that connects similarity and distance measurements. We then apply this technique to decision-making, taking into account both geometric and algebraic perspectives. Finally, we present a practical example that demonstrates the proposed justification and efficacy of the proposed method, and we conclude with a comparison to existing approaches.

Modified TODIM method based on cumulative prospect theory with Type-2 neutrosophic number for green supplier selection

Today’s consumers’ awareness of environmental protection and social morality is forcing companies to implement sustainable supply chains. Choosing a green supplier can not only determine the sustainable development of the supply chain, but also protect the environment and enhance the company’s reputation, in line with the background of green development. Green supplier selection is a multi-attribute decision-making (MADM) problem. Type-2 neutrosophic number (T2NN) can be compatible with more fuzzy information, and the green supplier selection problem also has a lot of fuzzy information, which makes T2NN very suitable for supplier selection. In this paper, a new method named CPT-TODIM-CDMT is proposed for green supplier selection of T2NN set based on TODIM. A new distance measure named cosine distance measure is proposed for T2NN set, and is applied in TODIM method. In this new method, attribute weight is determined by entropy method and optimized by CPT. The gains and losses preference in the CPT is also applied to the step of calculating the dominance degree in the TODIM method. A case study is used to verify the method. Through the comparison of the results of different decision-making models and the sensitivity research of the coefficients in the model, the correctness, validity and stability of the model are verified.

Comment on “New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach”

Comment on “New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach”

Big data cluster tendency techniques with spectral features for efficient data partitions assessment

Cluster tendency assessment in big data poses a challenge, particularly for non-compact separated (non-CS) datasets with irregular boundaries. This paper introduces a novel Spectral-Based Visual Technique (SVT) to address this limitation. Determining the similarity features for the data objects is a crucial computation in data clustering. Distance measures such as Euclidean and cosine are widely employed in clustering applications. By pre-determining cluster tendency, the quality of clusters is obtained using the algorithms of Visual Assessment of Cluster Tendency (VAT) and cosine-based VAT (cVAT). Both VAT and cVAT utilize Euclidean and cosine distance measures to identify the similarity features of objects. For extensive data cluster tendency assessment, an extended concept of VAT, Clustering using Improved Visual Assessment of Tendency (ClusiVAT), is employed to derive clusters with scalable amounts of time and memory loads. However, it operates efficiently for Compactly Separated (CS) datasets. The research gap lies in the need to deliver the quality of big data partitions (or clusters) for non-compact separated (non-CS) datasets. Thus, this paper proposes a spectral-based visual cluster tendency technique to address the challenge of significant data clustering for non-CS datasets. Experimental analysis employs benchmarked datasets to illustrate the performance of the proposed work compared to other techniques.

New cosine similarity and distance measures for Fermatean fuzzy sets and TOPSIS approach.

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.

Analysis of the structure of web resources using the object model

The methodology for analyzing the structure of a web resource using an object model, which is based on the description of the page in HTML and using style sheets, has been proposed. The object of research is a web resource page, the model of which is depicted as a DOM tree. Data on the structural elements of the tree are supplemented with information about the styles of the design of the pages. To determine the similarity of pages, it is proposed to apply a criterion that takes into account the structural and stylistic similarity of pages with the corresponding coefficients. To compare page models with each other, the method of aligning trees will be used. Editing distance is used as a metric, and renaming operations, deleting, and adding a tree node is used as editing operations. To determine the similarity in styles, the Jaccard metric is used. To cluster web pages, the k-means method with a cosine distance measure is applied. Intracluster analysis is carried out using a modification of the Zhang-Shasha algorithm. The proposed approach is implemented in the form of an algorithm and software using Python programming language and related libraries. The computational experiment was performed to analyze the structure of individual websites existing on the Internet, as well as to group pages from different web resources. The structure of the formed clusters was analyzed, the RMS similarity of elements in the middle of the clusters was calculated. To assess the quality of the developed approach for the tasks under consideration, expert partitioning was built, the values of accuracy and completeness metrics were calculated. The results of the analysis of the structure of the web resource can be used to improve the structure of the components of the web resource, to understand the navigation of users on the site, to reengineer the web resource

Probabilistic Linguistic Matrix Game Based on Fuzzy Envelope and Prospect Theory with Its Application

Game theory is a powerful tool in modeling strategic interaction among rational players. However, as practical problems become more complex, uncertainty inevitably appears in the game. Due to the advantages of probabilistic linguistic term sets (PLTSs) in comprehensively and flexibly portraying uncertainty, fuzziness and hesitancy, this paper uses PLTSs to express players’ payoff values, and aims to develop an integrated method based on fuzzy envelope and prospect theory (PT) under a probabilistic linguistic environment for solving matrix games. In this method, an improved probabilistic ordered weighted averaging (POWA) operator is defined. Then, a novel trapezoidal fuzzy envelope for PLTSs is proposed and some related theorems are analyzed. Next, based on the defined cosine distance measure for PLTSs, the players’ psychological behavior in the game is considered by establishing the prospect value function. Besides, the applicability and practicability of the proposed method is verified with an example from the development strategy of Sanjiangyuan National Nature Reserve (SNNR) in China. Finally, some comparative analyses are carried out to illustrate the superiority of the proposed method. In order to improve the application of this proposed method, a decision support system (DSS) based on it is designed.

Cosine similarity, distance and entropy measures for fuzzy soft matrices

Cosine similarity, distance and entropy measures for fuzzy soft matrices

Complex linear Diophantine fuzzy sets and their cosine similarity measures with applications

In this paper, the concept of complex linear Diophantine fuzzy set (CLDFS), which is obtained by integrating the phase term into the structure of the linear Diophantine fuzzy set (LDFS) and thus is an extension of LDFS, is introduced. In other words, the ranges of grades of membership, non-membership, and reference parameters in the structure of LDFS are extended from the interval [0, 1] to unit circle in the complex plane. Besides, this set approach is proposed to remove the conditions associated with the grades of complex-valued membership and complex-valued non-membership in the framework of complex intuitionistic fuzzy set (CIFS), complex Pythagorean fuzzy set (CPyFS), and complex q-rung orthopair fuzzy set (Cq-ROFS). It is proved that each of CIFS, CPyFS, and Cq-ROFS is a CLDFS, but not vice versa. In addition, some operations and relations on CLDFSs are derived and their fundamental properties are investigated. The intuitive definitions of cosine similarity measure (CSM) and cosine distance measure (CDM) between two CLDFSs are introduced and their characteristic principles are examined. An approach based on CSM is proposed to tackle medical diagnosis issues and its performance is tested by dealing with numerical examples. Finally, a comparative study of the proposed approach with several existing approaches is created and its advantages are discussed.

Score-based likelihood ratios for linguistic text evidence with a bag-of-words model

The likelihood ratio paradigm for quantifying the strength of evidence has been researched in many fields of forensic science. Within this paradigm, score-based approaches for estimating likelihood ratios are becoming more prevalent in the forensic science literature. In this study, a score-based approach for estimating likelihood ratios is implemented for linguistic text evidence. Text data are represented via a bag-of-words model with the Z-score normalised relative frequencies of selected most-frequent words (the number of the most-frequent words = N), and the Euclidean, Manhattan and Cosine distance measures are trialled as the score-generating functions for comparing paired text samples. The score-to-likelihood-ratio conversion model was built using a common source method, and the best fitting model was selected from the parametric models of the Normal, Log-normal, Gamma and Weibull distributions. With the Amazon Product Data Authorship Verification Corpus, two groups of documents (each group including documents of approximately 700, 1400 and 2100 words) were synthesised for each author, allowing 720 same-author comparisons and 517,680 different-author comparisons to test the validity of the system. A series of experiments was conducted using combinations of the following conditions: the three score functions, the different values of N for the feature vector and the different document lengths. The validity of the system was assessed using the log-likelihood-ratio cost (Cllr), and the strength of the derived likelihood ratios was charted in the form of Tippett plots. It was demonstrated that 1) the Cosine measure consistently outperforms the other measures—the best performance is achieved with N = 260, regardless of the document length (e.g., Cllr values of 0.70640, 0.45314 and 0.30692, respectively, for 700, 1400 and 2100 words)—and 2) the derived likelihood ratios are very well calibrated irrespective of the distance measures and document lengths. A follow-up experiment showed that the described score-based approach is relatively robust and stable for a limited quantity of background data. The derived likelihood ratios that were estimated separately to the three distance measures were logistic regression fused; and the fusion achieved a further improvement in performance—for example, a Cllr of 0.23494 for 2100 words. This study demonstrates the possibility of designing likelihood ratio–based systems that discriminate between same-author and different-author documents.

Some Similarity and Distance Measures between Complex Interval-Valued q-Rung Orthopair Fuzzy Sets Based on Cosine Function and their Applications

The purpose of this paper is to present a new method to solve the decision-making algorithm based on the cosine similarity and distance measures by utilizing the uncertain and vague information. A complex interval-valued q-rung orthopair fuzzy set (CIVQROFS) is a reliable and competent technique for handling the uncertain information with the help of the complex-valued membership grades. To address the degree of discrimination between the pairs of the sets, cosine similarity measures (CSMs) and distance measures (DMs) are an accomplished technique. Driven by these, in this manuscript, we defined some CSMs and DMs for the pairs of CIVQROFSs and investigated their several properties. Choosing that the CSMs do not justify the axiom of the similarity measure (SM), then we investigate a technique to developing other CIVQROFSs-based SMs using the explored CSMs and Euclidean DMs, and it fulfills the axiom of the SMs. In addition, we find the cosine DMs (CDMs) by considering the inter-relationship between the SM and DMs; then, we have modified the procedure for the rank of partiality by similarity to the ideal solution method for the CDMs under investigation, which can deal with the associated decision-making problems not only individually from the argument of the opinion of geometry but also the fact of the opinion of algebra. Finally, we provide a numerical example to demonstrate the practicality and effectiveness of the proposed procedure, which is also in line with existing procedures. Graphical representations of the measures developed are also used in this manuscript.

Some Cosine Similarity Measures and Distance Measures between Complex q-Rung Orthopair Fuzzy Sets and Their Applications

Some Cosine Similarity Measures and Distance Measures between Complex q-Rung Orthopair Fuzzy Sets and Their Applications

Optimized multimodal biometric system based fusion technique for human identification

This paper presents three novelty aspects in developing biometric system-based face recognition software for human identification applications. First, the computations cost is greatly reduced by eliminating the feature extraction phase and considering only the detected face features from the phase congruency. Secondly, a motivation towards applying a new technique, named mean-based training (MBT) is applied urgently to overcome the matching delay caused by the long feature vector. The last novelty aspect is utilizing the one-to-one mapping relationship for fusing the edge-to-angle unimodal classification results into a multimodal system using the logical-OR rule. Despite some dataset difficulties like Unconstrained Facial Images(UFI) which includes varying illuminations, expressions, occlusions, and poses, the multimodal system has highly improved the accuracy rate and achieved a promising recognition result, where the decision fusion is classified correctly (84, 92, and 72%) with only one training vector per MBT in contrast to (80, 62, and 68%) with five training vectors for Normal matching. These results are measured by Eucledian, Manhattan, and Cosine distance measure respectively.

Delaunay triangulation based text detection from multi-view images of natural scene

Text detection in the wild is still considered as a challenging issue to the researchers because of its several real time applications like forensic application, where CCTV camera captures images at different angles of the same scene. Unlike the existing methods that consider a single view captured orthogonally for text detection, this paper considers multi-view (view-1 and view-2 of the same spot) of the same scene captured at different angles or different height distances for text detection. For each pair of the same scene, the proposed method extracts features that describe characteristics of text components based on Delaunay Triangulation (DT), namely corner points, area and cavity of the DT. The features of corresponding DT in view-1 and view-2 are compared through cosine distance measure to estimate the similarity between two components of respective view-1 and view-2. If the pair satisfies the similarity condition, the components are considered as Candidate Text Components (CTC). In other words, these are the common components for view-1 and view-2 that satisfy the similarity condition. From each CTC of view-1 and view-2, the proposed method finds nearest neighbor components to restore the components of the same text line based on estimating degree of similarly between CTC and neighbor components using Chi-square and cosine distance measures. Furthermore, the proposed method uses a recognition step to detect correct texts by comparing recognition results of view-1 and view-2. The same recognition step is used for removing false positives to improve the performance of the proposed method. Experimental results on our own dataset, which contains pair of images of different situations, and the standard datasets, namely, ICDAR 2013, MSRATD-500, CTW1500, Total-text, ICDAR 2017 MLT and COCO-text, show that the proposed method outperforms the existing methods.

Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

Some cosine similarity measures and distance measures between q -rung orthopair fuzzy sets

Some cosine similarity measures and distance measures between <i>q</i> -rung orthopair fuzzy sets

Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic distance measure and the cosine function is given. A corresponding cosine distance measure between NHFLTSs is proposed according to the relationship between the similarity measure and the distance measure, and we develop the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained cosine distance measure. The main advantages of the proposed NHFLTS is defined on linguistic scale function, the decision makers can flexibly convert the linguistic information to semantic values, and the proposed cosine distance measure between NHFLTSs with TOPSIS method can deal with the related decision information not only from the point of view of algebra, but also from the point of view of geometry. Finally, the reasonableness and effectiveness of the proposed method is demonstrated by the illustrative example, which is also compared to the other existing methods.

A leakage-free resonance sparse decomposition technique for bearing fault detection in gearboxes

Most of rotating machinery deficiencies are related to defects in rolling element bearings. Reliable bearing fault detection still remains a challenging task, especially for bearings in gearboxes as bearing-defect-related features are nonstationary and modulated by gear mesh vibration. A new leakage-free resonance sparse decomposition (LRSD) technique is proposed in this paper for early bearing fault detection of gearboxes. In the proposed LRSD technique, a leakage-free filter is suggested to remove strong gear mesh and shaft running signatures. A kurtosis and cosine distance measure is suggested to select appropriate redundancy r and quality factor Q. The signal residual is processed by signal sparse decomposition for highpass and lowpass resonance analysis to extract representative features for bearing fault detection. The effectiveness of the proposed technique is verified by a succession of experimental tests corresponding to different gearbox and bearing conditions.

Structural damage detection using transmissibility together with hierarchical clustering analysis and similarity measure

Maintenance and repairing in actual engineering for long-term used structures, such as pipelines and bridges, make structural damage detection indispensable, as an unanticipated damage may give rise to a disaster, leading to huge economic loss. A new approach for detecting structural damage using transmissibility together with hierarchical clustering and similarity analysis is proposed in this study. Transmissibility is derived from the structural dynamic responses characterizing the structural state. First, for damage detection analysis, hierarchical clustering analysis is adopted to discriminate the damaged scenarios from an unsupervised perspective, taking transmissibility as feature for discriminating damaged patterns from undamaged ones. This is unlike directly predicting the structural damage from the indicators manifestation, as sometimes this can be vague due to the small difference between damaged scenarios and the intact baseline. For comparison reasons, cosine similarity measure and distance measure are also adopted to draw out sensitive indicators, and correspondingly, these indicators will manifest in recognizing damaged patterns from the intact baseline. Finally, for verification purposes, simulated results on a 10-floor structure and experimental tests on a free-free beam are undertaken to check the suitability of the raised approach. The results of both studies are indicative of a good performance in detecting damage that might suggest potential application in actual engineering real life.

Building a dynamic correlation network for fat-tailed financial asset returns.

In this paper, a novel approach to building a dynamic correlation network of highly volatile financial asset returns is presented. Our method avoids the spurious correlation problem when estimating the dynamic correlation matrix of financial asset returns by using a filtering approach. A multivariate volatility model, DCC–GARCH, is employed to filter the fat-tailed returns. The method is proven to be more reliable for detecting dynamic changes in the correlation matrix compared with the widely used method of calculating time-dependent correlation matrices over a fixed size moving window, which can have fundamental problems when applied to fat-tailed returns. We apply the method to selected Japanese stock returns to observe the dynamic network changes as a case study. The estimated time-dependent correlation matrices are then compared with those calculated by using the traditional method to highlight the advantages of the proposed method. Two types of indicators, namely the largest eigenvalue and cosine distance measures, are introduced to identify significant changes in the correlation matrix for an initial screening of remarkable stress events. A more detailed network-based analysis is then conducted by examining topological measures calculated from the network adjacency matrices. The higher density and lower heterogeneity of the correlation network during stress periods are clearly observed, while the correlation network of stock returns is shown to be robust with regard to time. The method discussed in this paper is not limited to stock returns; it can also be applied to build a dynamic correlation network of other financial and non-financial time series with high volatility.