Journal articles: 'Distance-based similarity measure'

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Tang, Hui-Chin, and Shen-Tai Yang. "Counterintuitive Test Problems for Distance-Based Similarity Measures Between Intuitionistic Fuzzy Sets." Mathematics 7, no. 5 (2019): 437. http://dx.doi.org/10.3390/math7050437.

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This paper analyzes the counterintuitive behaviors of adopted twelve distance-based similarity measures between intuitionistic fuzzy sets. Among these distance-based similarity measures, the largest number of components of the distance in the similarity measure is four. We propose six general counterintuitive test problems to analyze their counterintuitive behaviors. The results indicate that all the distance-based similarity measures have some counterintuitive test problems. Furthermore, for the largest number of components of the distance-based similarity measure, four types of counterintuitive examples exist. Therefore, the counterintuitive behaviors are inevitable for the distance-based similarity measures between intuitionistic fuzzy sets.

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Sulaiman, Nor Hashimah, Daud Mohamad, Jamilah Mohd Shariff, Sharifah Aniza Sayed Ahmad, and Kamilah Abdullah. "Extended FTOPSIS with Distance and Set Theoretic-Based Similarity Measure." Indonesian Journal of Electrical Engineering and Computer Science 9, no. 2 (2018): 387. http://dx.doi.org/10.11591/ijeecs.v9.i2.pp387-394.

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Comparing fuzzy numbers is an essential process in deducing the output of many fuzzy decision making methods. One of the comparison methods commonly used is by using similarity measure. The main advantage of the similarity measure over other approaches is its ability to minimize the loss of information in the computational process. Several similarity measures have been applied effectively in fuzzy decision making methods. In this paper, a new similarity measure based on the geometric distance, the center of gravity, Hausdorf distance and the set theoretic similarity formula known as the Dice similarity index are incorporated into the Extended Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) method particularly in calculating the closeness coefficients. This similarity measure is in favor of others as it is able to discriminate two similar shape fuzzy numbers effectively with two different locations. A validation process is carried out by implementing the proposed procedure of the Extended FTOPSIS with the new similarity measure in solving a supplier selection problem and the ranking outcome is then compared with the Extended FTOPSIS with other existing similarity measure. The result shows that the Extended FTOPSIS with the proposed similarity measure gives a consistent result without reducing any information in the computational process.

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Extended, FTOPSIS with Distance and Set Theoretic-Based Similarity Measure, Mohamad Daud, Mohd Shariff Jamilah, Aniza Sayed Ahmad Sharifah, and Abdullah Kamilah. "Extended FTOPSIS with Distance and Set Theoretic-Based Similarity Measure." Indonesian Journal of Electrical Engineering and Computer Science 9, no. 2 (2018): 387–94. https://doi.org/10.11591/ijeecs.v9.i2.pp387-394.

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Comparing fuzzy numbers is an essential process in deducing the output of many fuzzy decision making methods. One of the comparison methods commonly used is by using similarity measure. The main advantage of the similarity measure over other approaches is its ability to minimize the loss of information in the computational process. Several similarity measures have been applied effectively in fuzzy decision making methods. In this paper, a new similarity measure based on the geometric distance, the center of gravity, Hausdorf distance and the set theoretic similarity formula known as the Dice similarity index are incorporated into the Extended Fuzzy Technique for Order Preference by Similarity to Ideal Solution (FTOPSIS) method particularly in calculating the closeness coefficients. This similarity measure is in favor of others as it is able to discriminate two similar shape fuzzy numbers effectively with two different locations. A validation process is carried out by implementing the proposed procedure of the Extended FTOPSIS with the new similarity measure in solving a supplier selection problem and the ranking outcome is then compared with the Extended FTOPSIS with other existing similarity measure. The result shows that the Extended FTOPSIS with the proposed similarity measure gives a consistent result without reducing any information in the computational process.

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Ren, Haiping, Shixiao Xiao, and Hui Zhou. "A Chi-square Distance-based Similarity Measure of Single-valued Neutrosophic Set and Applications." International Journal of Computers Communications & Control 14, no. 1 (2019): 78–89. http://dx.doi.org/10.15837/ijccc.2019.1.3430.

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The aim of this paper is to propose a new similarity measure of singlevalued neutrosophic sets (SVNSs). The idea of the construction of the new similarity measure comes from Chi-square distance measure, which is an important measure in the applications of image analysis and statistical inference. Numerical examples are provided to show the superiority of the proposed similarity measure comparing with the existing similarity measures of SVNSs. A weighted similarity is also put forward based on the proposed similarity. Some examples are given to show the effectiveness and practicality of the proposed similarity in pattern recognition, medical diagnosis and multi-attribute decision making problems under single-valued neutrosophic environment.

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Liu, Donghai, Guangyan Liu, and Zaiming Liu. "Some Similarity Measures of Neutrosophic Sets Based on the Euclidean Distance and Their Application in Medical Diagnosis." Computational and Mathematical Methods in Medicine 2018 (November 28, 2018): 1–9. http://dx.doi.org/10.1155/2018/7325938.

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Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of single-valued neutrosophic sets (SVNSs) and interval-valued neutrosophic sets (IVNSs) are defined based on the Euclidean distance measure, respectively, and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SVNSs and IVNSs, which are then compared to other existing similarity measures.

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Qiang, He Qun, Chun Hua Qian, and Sheng Rong Gong. "Similarity Measure for Image Retrieval Based on Hausdorff Distance." Applied Mechanics and Materials 635-637 (September 2014): 1039–44. http://dx.doi.org/10.4028/www.scientific.net/amm.635-637.1039.

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In general, it is difficult to segment accurately image regions or boundary contours and represent them by feature vectors for shape-based image query. Therefore, the object similarity is often computed by their boundaries. Hausdorff distance is nonlinear for computing distance, it can be used to measure the similarity between two patterns of points of edge images. Classical Hausdorff measure need to express image as a feature matrix firstly, then calculate feature values or feature vectors, so it is time-consuming. Otherwise, it is difficult for part pattern matching when shadow and noise existed. In this paper, an algorithm that use Hausdorff distance on the image boundaries to measure similarity is proposed. Experimental result has showed that the proposed algorithm is robust.

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Zeng, Yanqiu, Haiping Ren, Tonghua Yang, Shixiao Xiao, and Neal Xiong. "A Novel Similarity Measure of Single-Valued Neutrosophic Sets Based on Modified Manhattan Distance and Its Applications." Electronics 11, no. 6 (2022): 941. http://dx.doi.org/10.3390/electronics11060941.

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A single-valued neutrosophic (SVN) set contains three parameters, which can well describe three aspects of an objective thing. However, most previous similarity measures of SVN sets often encounter some counter-intuitive examples. Manhattan distance is a well-known distance, which has been applied in pattern recognition, image analysis, ad-hoc wireless sensor networks, etc. In order to develop suitable distance measures, a new distance measure of SVN sets based on modified Manhattan distance is constructed, and a new distance-based similarity measure also is put forward. Then some applications of the proposed similarity measure are introduced. First, we introduce a pattern recognition algorithm. Then a multi-attribute decision-making method is proposed, in which a weighting method is developed by building an optimal model based on the proposed similarity measure. Furthermore, a clustering algorithm is also put forward. Some examples are also used to illustrate these methods.

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Zhang, Hailong, and Yongbin Zhou. "Mahalanobis Distance Similarity Measure Based Higher Order Optimal Distinguisher." Computer Journal 60, no. 8 (2017): 1131–44. http://dx.doi.org/10.1093/comjnl/bxw093.

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Zhang, Hailong, Yongbin Zhou, and Dengguo Feng. "Mahalanobis distance similarity measure based distinguisher for template attack." Security and Communication Networks 8, no. 5 (2014): 769–77. http://dx.doi.org/10.1002/sec.1033.

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Rakhmawati, Nur Aini, and Miftahul Jannah. "Food Ingredients Similarity Based on Conceptual and Textual Similarity." Halal Research Journal 1, no. 2 (2021): 87–95. http://dx.doi.org/10.12962/j22759970.v1i2.107.

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Open Food Facts provides a database of food products such as product names, compositions, and additives, where everyone can contribute to add the data or reuse the existing data. The open food facts data are dirty and needs to be processed before storing the data to our system. To reduce redundancy in food ingredients data, we measure the similarity of ingredient food using two similarities: the conceptual similarity and textual similarity. The conceptual similarity measures the similarity between the two datasets by its word meaning (synonym), while the textual similarity is based on fuzzy string matching, namely Levenshtein distance, Jaro-Winkler distance, and Jaccard distance. Based on our evaluation, the combination of similarity measurements using textual and Wordnet similarity (conceptual) was the most optimal similarity method in food ingredients.

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Liu, Donghai, Yuanyuan Liu, and Xiaohong Chen. "The New Similarity Measure and Distance Measure of a Hesitant Fuzzy Linguistic Term Set Based on a Linguistic Scale Function." Symmetry 10, no. 9 (2018): 367. http://dx.doi.org/10.3390/sym10090367.

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The existing cosine similarity measure for hesitant fuzzy linguistic term sets (HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure. Due to this disadvantage, a new similarity measure combining the existing cosine similarity measure and the Euclidean distance measure of HFLTSs is proposed, which is constructed based on a linguistic scale function; the related properties are also given. According to the relationship between the distance measure and the similarity measure, a corresponding distance measure between HFLTSs is obtained. Furthermore, we generalize the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained distance measure of the HFLTSs. The principal advantages of the proposed method are that it cannot only effectively transform linguistic information in different semantic environments, but it can also avoid the shortcomings of existing the cosine similarity measure. Finally, a case study is conducted to illustrate the feasibility and effectiveness of the proposed method, which is compared to the existing methods.

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Li, Mu, Qilong Wang, David Zhang, Peihua Li, and Wangmeng Zuo. "Joint distance and similarity measure learning based on triplet-based constraints." Information Sciences 406-407 (September 2017): 119–32. http://dx.doi.org/10.1016/j.ins.2017.04.027.

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Shao, Songtao, and Xiaohong Zhang. "Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes." Mathematics 7, no. 7 (2019): 649. http://dx.doi.org/10.3390/math7070649.

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Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes.

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G, Poornalatha, and Prakash Raghavendra. "Alignment Based Similarity distance Measure for Better Web Sessions Clustering." Procedia Computer Science 5 (2011): 450–57. http://dx.doi.org/10.1016/j.procs.2011.07.058.

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15

Wan, Xiaojun. "A novel document similarity measure based on earth mover’s distance." Information Sciences 177, no. 18 (2007): 3718–30. http://dx.doi.org/10.1016/j.ins.2007.02.045.

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Baudrier, E., G. Millon, F. Nicolier, R. Seulin, and S. Ruan. "Hausdorff distance-based multiresolution maps applied to image similarity measure." Imaging Science Journal 55, no. 3 (2007): 164–74. http://dx.doi.org/10.1179/174313107x166884.

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KHARAL, ATHAR. "DISTANCE AND SIMILARITY MEASURES FOR SOFT SETS." New Mathematics and Natural Computation 06, no. 03 (2010): 321–34. http://dx.doi.org/10.1142/s1793005710001724.

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In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.

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Ye, Jun, Shigui Du, and Rui Yong. "Similarity Measures between Intuitionistic Fuzzy Credibility Sets and Their Multicriteria Decision-Making Method for the Performance Evaluation of Industrial Robots." Mathematical Problems in Engineering 2021 (January 19, 2021): 1–10. http://dx.doi.org/10.1155/2021/6630898.

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To enhance the credibility level/measure of an intuitionistic fuzzy set (IFS), this study proposes the notion of an intuitionistic fuzzy credibility set (IFCS) to express the hybrid information of a pair of a membership degree and a credibility degree and a pair of a nonmembership degree and a credibility degree. Next, we propose generalized distance and similarity measures between IFCSs and then further generalize the weighted generalized distance measure of IFCSs to the trigonometric function-based similarity measures of IFCSs, including the cosine, sine, tangent, and cotangent similarity measures based on the weighted generalized distance measure of IFCSs. Then, a multicriteria decision making (MCDM) method using the proposed similarity measures is developed in the environment of IFCSs. An illustrative example about the performance evaluation of industrial robots and comparative analysis are presented to indicate the applicability and efficiency of the developed method in the setting of IFCSs.

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Devi, M. Varshana. "Cluster Tree Based Hybrid Document Similarity Measure." COMPUSOFT: An International Journal of Advanced Computer Technology 03, no. 01 (2014): 494–98. https://doi.org/10.5281/zenodo.14620743.

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Cluster tree based hybrid similarity measure is established to measure the hybrid similarity. In cluster tree, the hybrid similarity measure can be calculated for the random data even it may not be the co -occurred and generate different views. Different views of tree can be combined and choose the one which is significant in cost. A method is proposed to combine the multiple views. Multiple views are represented by different distance measures into a single cluster. Comparing the cluster tree based hybrid similarity with the traditional statistical methods it gives the better feasibility for intelligent based search. It helps in improving the dimensionality reduction and semantic analysis. 

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Uddin, Sharif, Md Rashedul Islam, Sheraz Ali Khan, et al. "Distance and Density Similarity Based Enhancedk-NN Classifier for Improving Fault Diagnosis Performance of Bearings." Shock and Vibration 2016 (2016): 1–11. http://dx.doi.org/10.1155/2016/3843192.

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An enhancedk-nearest neighbor (k-NN) classification algorithm is presented, which uses a density based similarity measure in addition to a distance based similarity measure to improve the diagnostic performance in bearing fault diagnosis. Due to its use of distance based similarity measure alone, the classification accuracy of traditionalk-NN deteriorates in case of overlapping samples and outliers and is highly susceptible to the neighborhood size,k. This study addresses these limitations by proposing the use of both distance and density based measures of similarity between training and test samples. The proposedk-NN classifier is used to enhance the diagnostic performance of a bearing fault diagnosis scheme, which classifies different fault conditions based upon hybrid feature vectors extracted from acoustic emission (AE) signals. Experimental results demonstrate that the proposed scheme, which uses the enhancedk-NN classifier, yields better diagnostic performance and is more robust to variations in the neighborhood size,k.

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Sirbiladze, Gia, Bidzina Midodashvili, and Teimuraz Manjafarashvili. "Divergence and Similarity Characteristics for Two Fuzzy Measures Based on Associated Probabilities." Axioms 13, no. 11 (2024): 776. http://dx.doi.org/10.3390/axioms13110776.

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The article deals with the definitions of the distance, divergence, and similarity characteristics between two finite fuzzy measures, which are generalizations of the same definitions between two finite probability distributions. As is known, a fuzzy measure can be uniquely represented by the so-called its associated probability class (APC). The idea of generalization is that new definitions of distance, divergence, and similarity between fuzzy measures are reduced to the definitions of distance, divergence, and similarity between the APCs of fuzzy measures. These definitions are based on the concept of distance generator. The proof of the correctness of generalizations is provided. Constructed distance, similarity, and divergence relations can be used in such applied problems as: determining the difference between Dempster-Shafer belief structures; Constructions of collaborative filtering similarity relations; non-additive and interactive parameters of machine learning in phase space metrics definition, object clustering, classification and other tasks. In this work, a new concept is used in the fuzzy measure identification problem for a certain multi-attribute decision-making (MADM) environment. For this, a conditional optimization problem with one objective function representing the distance, divergence or similarity index is formulated. Numerical examples are discussed and a comparative analysis of the obtained results is presented.

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Labriji, Amine, Salma Charkaoui, Issam Abdelbaki, Abdelouhaed Namir, and El Houssine Labriji. "Similarity Measure of Graphs." International Journal of Recent Contributions from Engineering, Science & IT (iJES) 5, no. 2 (2017): 42. http://dx.doi.org/10.3991/ijes.v5i2.7251.

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<p class="0abstract">The topic of identifying the similarity of graphs was considered as highly recommended research field in the Web semantic, artificial intelligence, the shape recognition and information research. One of the fundamental problems of graph databases is finding similar graphs to a graph query. Existing approaches dealing with this problem are usually based on the nodes and arcs of the two graphs, regardless of parental semantic links. For instance, a common connection is not identified as being part of the similarity of two graphs in cases like two graphs without common concepts, the measure of similarity based on the union of two graphs, or the one based on the notion of maximum common sub-graph (SCM), or the distance of edition of graphs. This leads to an inadequate situation in the context of information research. To overcome this problem, we suggest a new measure of similarity between graphs, based on the similarity measure of Wu and Palmer. We have shown that this new measure satisfies the properties of a measure of similarities and we applied this new measure on examples. The results show that our measure provides a run time with a gain of time compared to existing approaches. In addition, we compared the relevance of the similarity values obtained, it appears that this new graphs measure is advantageous and offers a contribution to solving the problem mentioned above.</p>

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Chen, Wen Can, and Xiao Dong Liu. "New Fuzzy Similarity Measure for Restricted Mobile Networks." Advanced Engineering Forum 6-7 (September 2012): 1093–97. http://dx.doi.org/10.4028/www.scientific.net/aef.6-7.1093.

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Similarity-based search has been a hot research topic for a long history, which is widely used in many applications. The large scale Restricted Floating Sensor (RFS) network is an important mod-el in offshore data collection [1]. Due to the mobility and the large number of sensors, improved techniques are needed to deal with uncertainty and mass queries. As a theoretical basis, this paper constructs a new fuzzy similarity measure based on distance. With examples we illustrate that many common similarity functions can be constructed from these measures. From [2] we know our work over distance and similarity is a reasonable generalization and extension of other Fuzzy Sets. This work provides a theoretical guidance for constructing a fuzzy query processing strategy for our RFS networks.

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Elfakir, Youssef, Ghizlane Khaissidi, Mostafa Mrabti, Driss Chenouni, and Manal Boualam. "Combined cosine-linear regression model similarity with application to handwritten word spotting." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 3 (2020): 2367. http://dx.doi.org/10.11591/ijece.v10i3.pp2367-2374.

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The similarity or the distance measure have been used widely to calculate the similarity or dissimilarity between vector sequences, where the document images similarity is known as the domain that dealing with image information and both similarity/distance has been an important role for matching and pattern recognition. There are several types of similarity measure, we cover in this paper the survey of various distance measures used in the images matching and we explain the limitations associated with the existing distances. Then, we introduce the concept of the floating distance which describes the variation of the threshold’s selection for each word in decision making process, based on a combination of Linear Regression and cosine distance. Experiments are carried out on a handwritten Arabic image documents of Gallica library. These experiments show that the proposed floating distance outperforms the traditional distance in word spotting system.

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Youssef, Elfakir, Khaissidi Ghizlane, Mrabti Mostafa, and Chenouni Manal Boualam Driss. "Combined cosine-linear regression model similarity with application to handwritten word spotting." International Journal of Electrical and Computer Engineering (IJECE) 10, no. 3 (2020): 2367–74. https://doi.org/10.11591/ijece.v10i3.pp2367-2374.

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The similarity or the distance measure have been used widely to calculate the similarity or dissimilarity between vector sequences, where the document images similarity is known as the domain that dealing with image information and both similarity/distance has been an important role for matching and pattern recognition. There are several types of similarity measure, we cover in this paper the survey of various distance measures used in the images matching and we explain the limitations associated with the existing distances. Then, we introduce the concept of the floating distance which describes the variation of the threshold’s selection for each word in decision making process, based on a combination of Linear Regression and cosine distance. Experiments are carried out on a handwritten Arabic image documents of Gallica library. These experiments show that the proposed floating distance outperforms the traditional distance in word spotting system.

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Ye, Jun. "Clustering Methods Using Distance-Based Similarity Measures of Single-Valued Neutrosophic Sets." Journal of Intelligent Systems 23, no. 4 (2014): 379–89. http://dx.doi.org/10.1515/jisys-2013-0091.

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AbstractClustering plays an important role in data mining, pattern recognition, and machine learning. Single-valued neutrosophic sets (SVNSs) are useful means to describe and handle indeterminate and inconsistent information that fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-valued neutrosophic information, this article proposes single-valued neutrosophic clustering methods based on similarity measures between SVNSs. First, we define a generalized distance measure between SVNSs and propose two distance-based similarity measures of SVNSs. Then, we present a clustering algorithm based on the similarity measures of SVNSs to cluster single-valued neutrosophic data. Finally, an illustrative example is given to demonstrate the application and effectiveness of the developed clustering methods.

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Gurukar, Saket, Deepak Ajwani, Sourav Dutta, Juho Lauri, Srinivasan Parthasarathy, and Alessandra Sala. "Towards Quantifying the Distance between Opinions." Proceedings of the International AAAI Conference on Web and Social Media 14 (May 26, 2020): 229–39. http://dx.doi.org/10.1609/icwsm.v14i1.7294.

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Increasingly, critical decisions in public policy, governance, and business strategy rely on a deeper understanding of the needs and opinions of constituent members (e.g. citizens, shareholders). While it has become easier to collect a large number of opinions on a topic, there is a necessity for automated tools to help navigate the space of opinions. In such contexts understanding and quantifying the similarity between opinions is key. We find that measures based solely on text similarity or on overall sentiment often fail to effectively capture the distance between opinions. Thus, we propose a new distance measure for capturing the similarity between opinions that leverages the nuanced observation – similar opinions express similar sentiment polarity on specific relevant entities-of-interest. Specifically, in an unsupervised setting, our distance measure achieves significantly better Adjusted Rand Index scores (up to 56x) and Silhouette coefficients (up to 21x) compared to existing approaches. Similarly, in a supervised setting, our opinion distance measure achieves considerably better accuracy (up to 20% increase) compared to extant approaches that rely on text similarity, stance similarity, and sentiment similarity.

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Jiang, Yong, Xinmin Wang, and Hai-Tao Zheng. "A semantic similarity measure based on information distance for ontology alignment." Information Sciences 278 (September 2014): 76–87. http://dx.doi.org/10.1016/j.ins.2014.03.021.

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Adabitabar Firozja, M., G. H. Fath-Tabar, and Z. Eslampia. "The similarity measure of generalized fuzzy numbers based on interval distance." Applied Mathematics Letters 25, no. 10 (2012): 1528–34. http://dx.doi.org/10.1016/j.aml.2012.01.009.

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Tasaddi Maalak Hanoun and Kadhim M. Hashim. "Modify Manhattan Distance for Image Similarity." Open Journal of Science and Technology 2, no. 4 (2020): 12–16. http://dx.doi.org/10.31580/ojst.v2i4.984.

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A New measure is proposed for assessing the similarity among gray-scale images. The well-known Structural Similarity Index Measure (SSIM) has been designed using a statistical approach that fails under significant noise (lowPSNR). The proposed measure, denoted by Manhattan distance and STD, uses a combination of two parts: the first part is the Geometric method, while the second part is based on the statistical feature. The concept of manhattan distance is used in the geometric part. The new measure shows the advantages of statistical approaches and geometric approaches. The proposed similarity method is an outcome for the human face. The novel measure outperforms the classical SSIM in detecting image similarity at low PSNR, with a significant difference in performance. AMS subject classification:

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Wang, Wei, and Jin Ye Peng. "A New Similarity Measure between Vague Sets Based on Information Similarity Coefficient and its Application." Applied Mechanics and Materials 401-403 (September 2013): 959–63. http://dx.doi.org/10.4028/www.scientific.net/amm.401-403.959.

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According to the facts that similar measure between vague set is based on the distance measure mostly, A new similarity measure between vague sets based on information similarity coefficient is presented ,which can satisfy the axiom definition of similarity measure between vague sets. Finally ,an application in the field of content-based recommendation system of electric commerce is given .The example shows that the methods is practical and effective and can improve the quality and accuracy of the recommendation．

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Ashraf, Shahzaib, Attaullah, Muhammad Naeem, Asghar Khan, Noor Rehman, and M. K. Pandit. "Novel Information Measures for Fermatean Fuzzy Sets and Their Applications to Pattern Recognition and Medical Diagnosis." Computational Intelligence and Neuroscience 2023 (March 8, 2023): 1–19. http://dx.doi.org/10.1155/2023/9273239.

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Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in decision-making, data mining, medical diagnosis, and pattern recognition. This paper aims to expand the literature on FFSs by proposing many innovative Fermatean fuzzy sets-based information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for FFSs. Another achievement of this research is to establish a systematic transformation of information measures (distance measure, similarity measure, entropy measure, and inclusion measure) for the FFSs. To accomplish this aim, new formulae for information measures of FFSs have been presented. To demonstrate the validity of the measures, we employ them in pattern recognition, building materials, and medical diagnosis. Additionally, a comparison between traditional and novel similarity measures is described in terms of counter-intuitive cases. The findings demonstrate that the innovative information measures do not include any absurd cases.

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Liu, Shihu, Yingjie Liu, Chunsheng Yang, and Li Deng. "Relative Entropy of Distance Distribution Based Similarity Measure of Nodes in Weighted Graph Data." Entropy 24, no. 8 (2022): 1154. http://dx.doi.org/10.3390/e24081154.

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Many similarity measure algorithms of nodes in weighted graph data have been proposed by employing the degree of nodes in recent years. Despite these algorithms obtaining great results, there may be still some limitations. For instance, the strength of nodes is ignored. Aiming at this issue, the relative entropy of the distance distribution based similarity measure of nodes is proposed in this paper. At first, the structural weights of nodes are given by integrating their degree and strength. Next, the distance between any two nodes is calculated with the help of their structural weights and the Euclidean distance formula to further obtain the distance distribution of each node. After that, the probability distribution of nodes is constructed by normalizing their distance distributions. Thus, the relative entropy can be applied to measure the difference between the probability distributions of the top d important nodes and all nodes in graph data. Finally, the similarity of two nodes can be measured in terms of this above-mentioned difference calculated by relative entropy. Experimental results demonstrate that the algorithm proposed by considering the strength of node in the relative entropy has great advantages in the most similar node mining and link prediction.

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Aljanabi, Mohammed Abdulameer, Zahir M. Hussain, and Song Feng Lu. "An Entropy-Histogram Approach for Image Similarity and Face Recognition." Mathematical Problems in Engineering 2018 (July 9, 2018): 1–18. http://dx.doi.org/10.1155/2018/9801308.

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Image similarity and image recognition are modern and rapidly growing technologies because of their wide use in the field of digital image processing. It is possible to recognize the face image of a specific person by finding the similarity between the images of the same person face and this is what we will address in detail in this paper. In this paper, we designed two new measures for image similarity and image recognition simultaneously. The proposed measures are based mainly on a combination of information theory and joint histogram. Information theory has a high capability to predict the relationship between image intensity values. The joint histogram is based mainly on selecting a set of local pixel features to construct a multidimensional histogram. The proposed approach incorporates the concepts of entropy and a modified 1D version of the 2D joint histogram of the two images under test. Two entropy measures were considered, Shannon and Renyi, giving a rise to two joint histogram-based, information-theoretic similarity measures: SHS and RSM. The proposed methods have been tested against powerful Zernike-moments approach with Euclidean and Minkowski distance metrics for image recognition and well-known statistical approaches for image similarity such as structural similarity index measure (SSIM), feature similarity index measure (FSIM) and feature-based structural measure (FSM). A comparison with a recent information-theoretic measure (ISSIM) has also been considered. A measure of recognition confidence is introduced in this work based on similarity distance between the best match and the second-best match in the face database during the face recognition process. Simulation results using AT&T and FEI face databases show that the proposed approaches outperform existing image recognition methods in terms of recognition confidence. TID2008 and IVC image databases show that SHS and RSM outperform existing similarity methods in terms of similarity confidence.

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Veerammal, P., and A. Maheswari. "A Distance Measure Between Intuitionistic Fuzzy Multisets Sets in Pattern Recognition." Shanlax International Journal of Arts, Science and Humanities 9, S1-May (2022): 134–38. http://dx.doi.org/10.34293/sijash.v9is1-may.5950.

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In this paper, we propose new method to calculate the distance between intuitionistic fuzzy sets (IFSs) based on the three dimensional representation of IFSs and analyze the relations of similarity measure and distance measure of IFSs. Finally, we apply the proposed measures to pattern recognitions.

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Suo, Chunfeng, Xuanchen Li, and Yongming Li. "Distance-Based Knowledge Measure and Entropy for Interval-Valued Intuitionistic Fuzzy Sets." Mathematics 11, no. 16 (2023): 3468. http://dx.doi.org/10.3390/math11163468.

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The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this paper, we not only extend the axiomatic definition of the knowledge measure of the interval-valued intuitionistic fuzzy set to a more general level but also establish a new knowledge measure function complying with the distance function combined with the technique for order preference by similarity to ideal solution (TOPSIS). Further, we investigate the properties of the proposed knowledge measure based on mathematical analysis and numerical examples. In addition, we create the entropy function by calculating the distance from the interval-valued fuzzy set to the most fuzzy point and prove that it satisfies the axiomatic definition. Finally, the proposed entropy is applied to the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy information. Experimental results demonstrate the effectiveness and practicability of the proposed entropy measure.

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MUSTAPHA, NORZIEHA, Fatin Fadhlina Ahmad Riza, Nor Athirah Mansor, Nur Akmal Shafira Mazlan, Suriana Alias, and Roliza Md Yasin. "Utilizing the Clustering Techniques using Distance-Based Similarity Measures of SVNS in Medical Diagnosis." Applied Mathematics and Computational Intelligence (AMCI) 12, no. 4 (2023): 52–65. http://dx.doi.org/10.58915/amci.v12i4.251.

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The clustering techniques, combined with distance-based similarity measures of Single Valued Neutrosophic Sets (SVNS) are studied and applied in medical diagnosis. The study starts with reviewing SVNS' theoretical foundations, emphasising its ability to capture and handle ambiguous data. This study focuses on integrating distance-based similarity measurements to improve the clustering process, which has seen limited implementation thus far. The set of data includes three patients with five symptoms and three diagnoses. To deal with the data in medical diagnosis, each patient is diagnosed with a disease based on distance-based similarity measures. The disease with the highest similarity measure value indicates the recognized disease for that patient. Then, the diseases are clustered into different categories depend on the values of confidence level. The obtained results show that the suggested method enhances the precision of medical diagnosis significantly, especially in cases with ambiguity and uncertainty.

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Zhao, Chun Jiang. "A Modified Method to Measure Similarity of Generalized Fuzzy Numbers." Advanced Materials Research 159 (December 2010): 393–98. http://dx.doi.org/10.4028/www.scientific.net/amr.159.393.

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A modified method to measure the similarity between the generalized fuzzy numbers based on Wasserstein distance is proposed. The method is more fully considered the difference of the generalized fuzzy numbers, especially the shape difference, by Wasserstein distance. The results of comparing the eighteen sets of generalized fuzzy numbers show that the method can overcome the drawbacks of the existing methods, and calculate the similarity measure excellently.

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Mrs., A. Sumathi*1 &. Dr. N. Sengottaiyan2. "PERFORMANCE ENHANCEMENT OF DISTANCED BASED ALGORITHMS FOR CLASSIFICATION PROCESS." INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & RESEARCH TECHNOLOGY 6, no. 8 (2017): 104–8. https://doi.org/10.5281/zenodo.839133.

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Nowadays there is vast amount of data being collected and stored in databases and without automatic methods for extracting this information it is practically impossible to mine for them. In Data Mining, the Classification processes perchance the most recognizable and most popular concepts. Actually Classification maps data into predefined groups or classes. Classification normally uses prediction rules to express knowledge. This Prediction rules are expressed in the form of IF - THEN rules. Sometimes this classification referred to as supervised learning by reason of the classes is determined before examining the data. Classification consists of predicting a certain outcome based on a given input. In order to predict the outcome, the algorithm processes a training set containing a set of attributes and the respective outcome, usually called goal or prediction attribute. Classification problems handled by using some known type of classification algorithms such that Statistical-Based Algorithms, Distance Based Algorithms etc,. All approaches to performing classification assume some knowledge of the data. This paper will focus on Distance Based Algorithms in classification. In Distance Based Algorithms each item is mapped to the same class may be thought of as more similar to the other items in that class than items found in other classes. Therefore, similarity or distance measures may be used to identify the "alikeness" of different items in the database. Using a similarity measure for classification where the classes are predefined is somewhat simpler than using a similarity measure for clustering where the classes are not known in advance. So the classification problem then becomes one of determining similarity not among all tuples in the database but between each tuple and the query

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Tiwari, Sunita, and Saroj Kaushik. "EMD-Based Semantic User Similarity Using Past Travel Histories." Journal of Cases on Information Technology 24, no. 3 (2022): 1–17. http://dx.doi.org/10.4018/jcit.20220701.oa2.

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The cost-effective and easy availability of handheld mobile devices and ubiquity of location acquisition services such as GPS and GSM networks has helped expedient logging and sharing of location histories of mobile users. This work aims to find semantic user similarity using their past travel histories. Application of the semantic similarity measure can be found in tourism-related recommender systems and information retrieval. The paper presents Earth Mover’s Distance (EMD) based semantic user similarity measure using users' GPS logs. The similarity measure is applied and evaluated on the GPS dataset of 182 users collected from April 2007 to August 2012 by Microsoft's GeoLife project. The proposed similarity measure is compared with conventional similarity measures used in literature such as Jaccard, Dice, and Pearsons’ Correlation. The percentage improvement of EMD based approach over existing approaches in terms of average RMSE is 10.70%, and average MAE is 5.73%.

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Shen, Xingchen, Shixu Fang, and Wenwen Qiang. "Dimensionality Reduction by Similarity Distance-Based Hypergraph Embedding." Atmosphere 13, no. 9 (2022): 1449. http://dx.doi.org/10.3390/atmos13091449.

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Dimensionality reduction (DR) is an essential pre-processing step for hyperspectral image processing and analysis. However, the complex relationship among several sample clusters, which reveals more intrinsic information about samples but cannot be reflected through a simple graph or Euclidean distance, is worth paying attention to. For this purpose, we propose a novel similarity distance-based hypergraph embedding method (SDHE) for hyperspectral images DR. Unlike conventional graph embedding-based methods that only consider the affinity between two samples, SDHE takes advantage of hypergraph embedding to describe the complex sample relationships in high order. Besides, we propose a novel similarity distance instead of Euclidean distance to measure the affinity between samples for the reason that the similarity distance not only discovers the complicated geometrical structure information but also makes use of the local distribution information. Finally, based on the similarity distance, SDHE aims to find the optimal projection that can preserve the local distribution information of sample sets in a low-dimensional subspace. The experimental results in three hyperspectral image data sets demonstrate that our SDHE acquires more efficient performance than other state-of-the-art DR methods, which improve by at least 2% on average.

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Nikolic, Bojan, and Boris Sobot. "Measures of string similarities based on the Hamming distance." Publications de l'Institut Mathematique 116, no. 130 (2024): 13–33. http://dx.doi.org/10.2298/pim2430013n.

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We consider measures of similarity between two sets of strings built up using the Hamming distance and tools of persistence homology as a basis. First we describe the construction of the Cech filtration adjoined to the set of strings, the persistence module corresponding to this filtration and its barcode structure. Using these means, we introduce a novel similarity measure for two sets of strings, based on a comparison of bars within their barcodes of the same dimension. Our idea is to look for a comparison that will take under consideration not only the overlap of bars, but also ensure that observed bars are qualitatively matched, in the sense that they represent similar homological features. To make this idea happen, we developed a method called the separation of simplex radii technique.

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Dhanalakshmi, Dr P. Rajarajeswari, P. "An Application of Similarity Measure of Fuzzy Soft Set Based on Distance." IOSR Journal of Mathematics 4, no. 4 (2012): 27–30. http://dx.doi.org/10.9790/5728-0442730.

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Garcia-Hernandez, Carlos, Alberto Fernández, and Francesc Serratosa. "Ligand-Based Virtual Screening Using Graph Edit Distance as Molecular Similarity Measure." Journal of Chemical Information and Modeling 59, no. 4 (2019): 1410–21. http://dx.doi.org/10.1021/acs.jcim.8b00820.

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Gao, Zhi, Yuwei Wu, Mehrtash Harandi, and Yunde Jia. "A Robust Distance Measure for Similarity-Based Classification on the SPD Manifold." IEEE Transactions on Neural Networks and Learning Systems 31, no. 9 (2020): 3230–44. http://dx.doi.org/10.1109/tnnls.2019.2939177.

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Bui, Hong-Nhung, Quang-Thuy Ha, and Tri-Thanh Nguyen. "A NOVEL SIMILARITY MEASURE FOR TRACE CLUSTERING BASED ON NORMALIZED GOOGLE DISTANCE." JP Journal of Heat and Mass Transfer, Special Issue 3 (August 9, 2018): 341–46. http://dx.doi.org/10.17654/hmsi318341.

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Ramli, Nazirah, Siti Musleha Ab Mutalib, Daud Mohamad, Mahmod Othman, and Asyura Abd Nassir. "Fuzzy Time Series Forecasting Accuracy Based on Hybrid Similarity Measure." Journal of Science and Mathematics Letters 11, no. 2 (2023): 93–103. http://dx.doi.org/10.37134/jsml.vol11.2.11.2023.

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The majority of fuzzy time series forecasting (FTSF) algorithms assess forecasting accuracy using an error-based distance. The predicted value is defuzzified to a crisp number and the error-based distance will be computed. Defuzzification causes some information to be lost, which leads to its inability to comprehend the level of uncertainty that has been preserved during the forecasting process. This paper proposes an enhanced FTSF model with forecasting accuracy developed based on a new hybrid similarity measure combining the centre of gravity and area and height. Three properties of the hybrid similarity measure are presented. The FTSF model is implemented in the case of the Malaysian unemployment rate. The findings indicate that, on average more than 94% of the predicted value was identical to historical data. The forecasting accuracy is produced directly from the forecasting value without undergoing the defuzzification process, which can preserve some information from being lost.

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Kondruk, N. E. "METHODS FOR DETERMINING SIMILARITY OF CATEGORICAL ORDERED DATA." Radio Electronics, Computer Science, Control, no. 2 (June 29, 2023): 31. http://dx.doi.org/10.15588/1607-3274-2023-2-4.

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Context. The development of effective distance metrics and similarity measures for categorical features is an important task in data analysis, machine learning, and decision theory since a significant portion of object properties is described by non-numerical values. Typically, the dependence between categorical features may be more complex than simply comparing them for equality or inequality. Such attributes can be relatively similar, and to construct an effective model, it is necessary to consider this similarity when calculating distance or similarity measures. Objective. The aim of the study is to improve the efficiency of solving practical data analysis problems by developing mathematical tools for determining the similarity of objects based on categorical ordered features. Method. A distance based on weighted Manhattan distance and a similarity measure for determining the similarity of objects based on categorical ordinal features (i.e. a linear order with scales of preference considering the problem domain can be specified on the attribute value set) are proposed. It is proven that the distance formula satisfies the axioms of non-negativity, symmetry, triangle inequality, and upper bound, and therefore is a distance metric in the space of ranked categorical features. It is also proven that the similarity measure presented in the study satisfies the axioms of boundedness, symmetry, maximum and minimum similarity, and is described by a decreasing function. Results. The developed approach has been implemented in an applied problem of determining the degree of similarity between objects described by ordered categorical features. Conclusions. In this study, mathematical tools were developed to determine similarity between structured data described by categorical attributes that can be ordered based on a specific priority in the form of a ranking system with preferences. Their properties were analyzed. Experimental studies have shown the convenience and “intuitive understanding” of the logic of data processing in solving practical problems. The proposed approach can provide the opportunity to conduct new meaningful research in data analysis. Prospects for further research lie in the experimental use of the proposed tools in practical tasks and in studying their effectiveness.

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Wang, Bing, Jia Zhu, and Daijun Wei. "The self-similarity of complex networks: From the view of degree–degree distance." Modern Physics Letters B 35, no. 18 (2021): 2150331. http://dx.doi.org/10.1142/s0217984921503310.

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Self-similarity of complex networks has been discovered and attracted much attention. However, the self-similarity of complex networks was measured by the classical distance of nodes. Recently, a new feature, which is named as degree–degree distance, is used to measure the distance of nodes. In the definition of degree–degree distance, the relationship between two nodes is dependent on degree of nodes. In this paper, we explore the self-similarity of complex networks from the perspective of degree–degree distance. A box-covering algorithm based on degree–degree distance is proposed to calculate the value of dimension of complex networks. Some complex networks are studied, and the results show that these networks have self-similarity from the perspective of degree–degree distance. The proposed method for measuring self-similarity of complex networks is reasonable.

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Ke, Di, Yafei Song, and Wen Quan. "New Distance Measure for Atanassov’s Intuitionistic Fuzzy Sets and Its Application in Decision Making." Symmetry 10, no. 10 (2018): 429. http://dx.doi.org/10.3390/sym10100429.

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The intuitionistic fuzzy set introduced by Atanassov has greater ability in depicting and handling uncertainty. Intuitionistic fuzzy measure is an important research area of intuitionistic fuzzy set theory. Distance measure and similarity measure are two complementary concepts quantifying the difference and closeness of intuitionistic fuzzy sets. This paper addresses the definition of an effective distance measure with concise form and specific meaning for Atanassov’s intuitionistic fuzzy sets (AIFSs). A new distance measure for AIFSs is defined based on a distance measure of interval values and the transformation from AIFSs to interval valued fuzzy sets. The axiomatic properties of the new distance measure are mathematically investigated. Comparative analysis based in numerical examples indicates that the new distance measure is competent to quantify the difference between AIFSs. The application of the new distance measure is also discussed. A new method for multi-attribute decision making (MADM) is developed based on the technique for order preference by similarity to an ideal solution method and the new distance measure. Numerical applications indicate that the developed MADM method can obtain reasonable preference orders. This shows that the new distance measure is effective and rational from both mathematical and practical points of view.

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Journal articles on the topic 'Distance-based similarity measure'

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