Existing Similarity Measures Research Articles

Similarity Measures of Probabilistic Interval Preference Ordering Sets and Their Applications in Decision-Making

The concept of probabilistic interval preference ordering sets (PIPOSs) provides a scientific and intuitive framework for solving real-life multi-criteria group decision-making problems. In some areas such as investment decision-making and supplier selection, PIPOSs have a wider application space, and the development of similarity and distance measures based on PIPOSs holds great significance. Similarity measure is a basic and prominent tool for dealing with imperfect and ambiguous information in fuzzy sets, but it can also be used to deal with uncertain information in preference ordering. These metrics play an important role in the actual decision-making process, as they effectively quantify the degree of similarity between two PIPOSs, and further allow for the prioritization of different scenarios. In this article, we sort out the definitions and arithmetic rules of PIPOSs, and creatively propose several new similarity measures based on PIPOSs. Then, we propose a group decision-making method based on similarity measures and conduct a comparative study with three existing similarity measures to illustrate its advantages over existing metrics. Finally, we confirm its validity through numerical illustrations in the case study, and also conduct a comparative assessment to verify the scientific validity and effectiveness of the newly introduced measure against the existing metrics.

Some novel Dice similarity measures for picture fuzzy sets and their applications

The similarity measures, as an important tool for assessing the similarity between picture fuzzy sets, have attracted the attention of numerous scholars and achieved rich achievements. Although existing similarity measures have exhibited their unique research contributions, they still fail to distinguish between highly similar but different picture fuzzy sets. This phenomenon poses a major challenge in applications, limiting our ability to make accurate judgments in scenarios that necessitate meticulous differentiation of picture fuzzy sets. Furthermore, the current research focuses on proposing individual and specific calculation formulas, particularly in the realm of Dice similarity measures. However, the systematic, uniform construction of Dice similarity measures remains mostly untapped. The main objective of this article is to propose a method for constructing Dice similarity measures. Through this approach, we can not only integrate existing Dice similarity measures into a unified framework, but also generate novel similarity measures. Firstly, we introduce a function that satisfies specific conditions as the basis for constructing Dice similarity measures. Secondly, by selecting different functions, we obtain various similarity measures. Finally, we propose the pattern recognition algorithm, the face recognition algorithm and the cluster analysis algorithm, all based on the proposed similarity measures. These algorithms are then applied to various fields, including pattern recognition, face recognition, and clustering analysis. Experimental results demonstrate that the proposed similarity measures not only compensate for the shortcomings of existing similarity measures but also exhibit high reliability and practicality, offering a powerful new tool for research and applications in related fields.

Similarity measure on intuitionistic fuzzy sets based on Benchmark Line and it’s diverse applications

An intuitionistic fuzzy set (IFS) is an extension of fuzzy sets that can deal with inconsistent and uncertain information more accurately. In this paper, a novel similarity measure is presented that might be applied to several application issues in decision-making, pattern recognition, and medical diagnostics. IFSs are sources of information that contain both the membership and non-membership degrees of the elements in the set. As such, similarity measures based on geometric concepts might occasionally be misleading. Hence, five parameters are specified to develop the similarity measure. These parameters are membership information similarity, non-membership information similarity, maximum cross-information similarity, minimum cross-information similarity, and product cross-information similarity. Most of the existing similarity measures cannot reasonably determine the appropriate similarity degree when the IFS points lie on the benchmark line. On the other hand, product cross-information similarity is a new parameter introduced in this study that has a significant role in handling benchmark problems more effectively and reasonably. The proposed similarity measure compensates for several counterintuitive problems related to decision-making and pattern recognition. Complexity analysis illustrates the complexity level of the proposed measure, which is reliable. Finally, various challenges with applications in decision-making, pattern recognition, and medical diagnosis difficulties are used to validate the suggested similarity measure.

A Study of Multi-criterion Fuzzy Decision-making Methods: Recent Trends and Directions

A plausible soft computing model for addressing ambiguity and vagueness in decision-making circumstances is the concept of intuitionistic fuzzy sets (IFSs). Utilizing similarity-distance metrics, cases like diagnostic analysis, Finance and Investment, pattern recognition, Risk Analysis and Assessment, etc. have been investigated. Numerous methods of distance and similarity have been suggested and utilized to solve deciding circumstances. Although the existing similarity measures and their distance counterparts are fairly significant, they have certain accuracy and conceptual alignment issues that need to be addressed in order to improve output reliability. As a result, a unique similarity-distance technique is introduced in this paper. To demonstrate the benefits of the innovative similarity-distance strategy over related current approaches, a comparative analysis is presented. The theoretical and philosophical aspects of the approach are set aside, and the analysis is solely focused on the algorithmic (technical) point of view. Applying the ranking algorithm yields a solution. A comparative study is presented to illustrate the advantages of the suggested measures. The outcomes of applying the suggested similarity metrics are confirmed by a technique known as Topsis. The outcomes are more logical, consistent, and productive in a skeptical setting.

Time-Aware Similarity Integration for User-Based Collaborative Filtering

A time-aware collaborative filtering-based recommender system provides item recommendations for the current user by prioritizing recent items preferred by similar neighbors over past preferred items. The similarity measure critically affects the performance of the system, and this study focuses on measuring the similarity between users that changes over time. After dividing the users’ rating time into intervals and computing similarity for each time interval, the final similarity is generated as a weighted sum by assigning lower weights to past similarity values and higher weights to more recent similarity values. Additionally, to ensure continuity of similarity measurement, consecutive time intervals are set to overlap. As a result of experiments applying the proposed method to the existing similarity measures, significant performance improvement was achieved in terms of some of the major performance metrics. In particular, the degree of coverage improvement was the highest, and the performance improvement effect was higher when the overlap size between time intervals was large rather than when it was small.

Selecting an optimal approach to reduce energy crises under interval-valued intuitionistic fuzzy environment

The concept of interval-valued intuitionistic fuzzy sets is intellectually stimulating and holds significant utility in the representation and analysis of real-world problems. The development of similarity measures within the class of interval-valued intuitionistic fuzzy sets possesses significant importance across various academic disciplines, particularly in the fields of decision-making and pattern recognition. The utilization of similarity measures is of utmost importance in the decision-making process when implementing interval-valued intuitionistic fuzzy sets. This is due to its inherent capability to quantitatively assess the level of resemblance or similarity between two interval-valued intuitionistic fuzzy sets. In this article, the drawbacks of the existing similarity measures in the context of an interval-valued intuitionistic fuzzy environment are addressed, and a novel similarity measure is presented. Many fundamental properties of this new interval-valued intuitionistic fuzzy similarity measure are also established, and the effectiveness of this similarity measure is illustrated by presenting a useful example. Moreover, a comparison is given to demonstrate the validity of the newly proposed similarity measure within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment. In addition, an algorithm is designed to solve multi-criteria decision making problems by means of the proposed measure in the interval-valued intuitionistic fuzzy setting. Furthermore, this newly defined similarity measure is successfully applied to select an optimal renewable energy source to reduce energy crises. Finally, we conduct a comparative study to showcase the authenticity of the recently defined technique within the existing knowledge of similarity measures in the interval-valued intuitionistic fuzzy environment.

Utilizing Generative Adversarial Networks Using a Category of Fuzzy-Based Structural Similarity Indices for Constructing Datasets in Meteorology

Machine learning and image processing are closely related fields that have undergone major development and application in recent years. Machine learning algorithms are being used to develop sophisticated techniques for analyzing and interpreting images, such as object detection, image classification, and image segmentation. One important aspect of image processing is the ability to compare and measure the similarity between different images by providing a way to quantify the similarity between images using various features such as contrast, luminance, and structure. Generally, the flexibility of similarity measures enables fine-tuning the comparison process to achieve the desired outcomes. This is while the existing similarity measures are not flexible enough to address diverse and comprehensive practical aspects. To this end, we utilize triangular norms (t-norms) to construct an inclusive class of similarity measures in this article. As is well-known, each t-norm possesses distinctive attributes that allow for novel interpretations of image similarities. The proposed class of t-norm-based structural similarity measures offers numerous options for decisionmakers to consider various issues and interpret results more broadly in line with their objectives. For more details, in the Experiments section, the proposed method is applied to grayscale and binarized images and a specific experiment related to meteorology. Eventually, the presented diverse case studies confirm the efficiency and key features of the t-norm-based structural similarity.

Strict intuitionistic fuzzy distance/similarity measures based on Jensen-Shannon divergence

Being a pair of dual concepts, the normalized distance and similarity measures are important tools for decision-making and pattern recognition under the intuitionistic fuzzy set framework. In this paper, we first construct some counterexamples to illustrate that two existing similarity measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values (IFVs); (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance “1” can be achieved under these two distances, leading to counter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Moreover, we prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is superior to the existing ones. In particular, our proposed distance measure can better distinguish and rank intuitionistic fuzzy sets.

Similarity metrics vs human judgment of similarity for binary data: Which is best to predict typicality?

Similarity measures for binary data have been subject to a number of comparative studies. In contrast to these studies, we provide a comparison of similarity measures with human judgment of similarity. For this purpose, we utilize the phenomenon of typicality, whose definition is based on similarity. We observe how well the similarity of objects – either computed by a similarity measure or provided by human judgment – enables the prediction of typicality of these objects in various human categories. In doing so, we examine a large variety of existing similarity measures, and utilize recently available extensive data involving binary data as well as data on human judgment of similarity and typicality.

CWEmd: A Lightweight Similarity Measurement for Resource-Constrained Vehicular Networks

Generating an accurate machine learning (ML) model is of great importance for the Internet of Vehicles (IoV). However, obtaining such a model is challenging due to the fact that sub-groups of in-network vehicles receive data from different resources. A worthwhile investment then would be identifying those groups before inferring models. Similarity metrics are widely used to distinguish different groups. However, the efficiency of most existing similarity measurements is at the cost of increased computational complexity and decreased accuracy, making them unsuitable for IoV’s stringent conditions. To address this issue, we propose a computationally efficient method to measure the similarity of different vehicles, where a simplified version of Earth Mover’s Distance (EMD) is adopted. This distance metric is then embedded into a distributed clustering algorithm to learn the global pattern for vehicular systems. Our algorithm’s overall performance is measured using an Asynchronous Message Delay Simulator. Compared to the best algorithm of the state-of-the-art, our proposed algorithm converges slightly slower (by less than 1%) but improves the clustering accuracy by as much as 20% with synthetic data. Additionally, real-world data collected from Vehicles validates the efficiency of our proposed algorithm.

An improved method to estimate the similarity between LR-type fuzzy numbers

This paper presents an improved method for estimating the similarity between LR-type fuzzy numbers. By considering different left and right shape functions, we can conveniently compute the similarity between trapezoidal fuzzy numbers, Gaussian fuzzy numbers and normal fuzzy numbers. An algorithm for computing the proposed similarity measure between LR-type fuzzy numbers and a numerical method for approximating it are provided. Some of its properties are also examined. The performance of the proposed method is compared with some existing similarity measures through using different sets of LR-type fuzzy numbers. It is shown that the similarity between LR-type fuzzy numbers with parameters from any real number belonged to the real number set R is considered in the proposed method. The given similarity measure is scale-invariant and takes into account the shape of LR-type fuzzy numbers, which can overcome the shortcomings of existing methods.

A novel multi-parameter similarity measure of interval neutrosophic sets for medical diagnosis

The use of similarity measures in interval-valued neutrosophic sets (IVNSs) theory is essential for comparing and assessing the degree of IVNSs difference. However, existing similarity measures for IVNSs suffer from several issues such as lacking precise axiomatic definitions, counterintuitive results, division by zero errors, inability to distinguish between positive and negative differences, and failure to satisfy the ranking definition. To address these limitations, we propose a novel multi-parameter similarity measure for IVNSs based on the tangent function. We demonstrate that our measure satisfies the axiomatic definition and apply it to medical diagnosis, achieving accurate diagnostic results. Additionally, we consider the interactions between symptoms, adjust the proposed similarity measure using Choquet integrals, and provide analytical comparisons to demonstrate the advantages of our improved similarity measure, highlighting its stability and high confidence in the field of medical diagnosis.This study contributes to the advancement of similarity measures in IVNSs theory and provides valuable insights for the field of medical diagnosis.

Spherical-dynamic time warping – A new method for similarity-based remaining useful life prediction

Machinery prognostics and health management (PHM) plays a key role in the reliable and efficient operation of industrial processes. With the emerging big data era, data-driven prognostic methods which avoid considering complicated system models have attracted growing research interest. Among many data-driven models, similarity-based prediction methods have been popular due to their strong interpretability and relatively simple implementation process. Nevertheless, when quantifying the similarity between two trajectories, most existing similarity measures neglect the nonlinearity of the distance measurement at different degradation stages and degradation alignments with timing difference, which may not be sufficient to retrieve the most suitable trajectories for remaining useful life (RUL) prediction. To overcome these limitations, a spherical-Dynamic Time Warping (spherical-DTW) algorithm is put forward to find an optimal match between the test and training trajectories at the retrieval step. Dynamic Time Warping allows degradation alignments with timing difference through stretching or compressing the trajectories with regard to time, thereby the data in similar degradation levels can be well aligned across different units. Moreover, a newly defined nonlinear spherical distance method is introduced and incorporated into the retrieval process to account for the nonlinearity of the damage propagation process. The significance of this study is that the newly proposed spherical-DTW algorithm goes one step further to consider the nonlinearity of fault evolutions and allow degradation pattern alignments with timing difference when performing similarity-based prognostics. Two run-to-failure cases, involving a real-world industrial compressor failure case and a gas turbine engine failure dataset, are investigated to demonstrate the effectiveness and superiority of the proposed algorithm.

Interval-valued functional clustering based on the improved Euclidean distance with application to air quality index

Interval function clustering is a statistical method used to classify functional data based on interval number similarity measurements. However, existing similarity measurements focus on measuring the similarity of the curves in terms of numerical distance. This ignores the changing characteristics of the curve shape, which may lead to unreasonable clustering results when clustering interval-valued functional data. To address this issue, an improved Euclidean-distance-based interval-valued functional clustering method is proposed in this study. By deducing a specific calculation formula for the Euclidean distance of the interval function under the basis function and derivative information, the absolute difference in the numerical value was reflected based on the distance of the basis function, and the curve shape difference was reflected based on the distance of the derivative function information. Furthermore, a similarity measurement method combining numerical distance and curve shape was constructed to reflect the change characteristics of the functional data more completely and improve the K-means clustering process. Finally, the air quality index of different cities is taken as an example to cluster, and the differences and variation characteristics of different types of air quality are analyzed, which verifies the effectiveness of the proposed method.

Extend Tversky’s Ratio Model to an Asymmetric Similarity Measurement Model with Three Conditional Parameters: 3p-ASM Model

Generally, the similarity between objects is often measured by symmetric operators, such as Cosine, Dice, and Jaccard similarity. However, the ratio model originally proposed by Tversky pointed out that the similarity using the feature matching method tends to be asymmetric. Furthermore, in many practical situations, the existing similarity measures using the feature matching method have some limitations: the calculation formulas are symmetrical, it is not intuitive based on binary features, and it is not easy to calculate based on fuzzy sets. To overcome such limitations, some other asymmetries have proposed to directly combine Tversky’s ratio model with the classical symmetric similarity metric, which in turn leads to the inability to identify different features between the compared objects and affects their similarity accuracy. Therefore, aiming to avoid these, this paper will focus on extending Tversky’s ratio model to a series of 3-parameter asymmetric similarity metrics (3p-ASM), using three conditional parameters to describe both common and different features. First, the set-based 3p-ASM is achieved due to the general and fuzzy set-theoretic operations, when estimating features in left{ 0,1right} and left[ 0,1right] , respectively. Then, considering that the estimated values of features can also be expressed as vectors, it will be extended to the vector-based 3p-ASM. Finally, a vector form of 3p-ASM is compared with existing classical methods and a comparative analysis is performed to demonstrate its effectiveness and validity. It is then applied to the KNN model in order to select the most similar items.

Tinba: Incremental partitioning for efficient trajectory analytics

Applications with mobile and sensing devices have already become ubiquitous. In most of these applications, trajectory data is continuously growing to huge volumes. Existing systems for big trajectory data organize trajectories at distributed block storage systems. Systems like DITA that use block storage (e.g., 128 MB each) are more efficient for analytical queries, but they cannot incrementally maintain the partitioned data and do not support delete operations, resulting in difficulties in trajectory analytics. In this paper, we propose an incremental trajectory partitioning framework Tinba that enables distributed block storage systems to efficiently maintain optimized partitions under incremental updates of trajectories. We employ a data flushing technique to bulk ingest trajectory data for random writing in distributed file system (DFS). We recast the incremental partitioning problem as an optimal partitioning problem and prove its NP-hardness. A cost–benefit model is proposed to address the optimal partitioning problem. Moreover, Tinba supports most of the existing similarity measures to quantify the similarity between trajectories. A heuristic is developed to instantiate the Tinba framework. Comprehensive experiments on real-world and synthetic datasets demonstrate the advancements in ingestion performance and partition quality, as opposed to other trajectory partition methods.

A novel parameter similarity measure between interval-valued picture fuzzy sets with its app-lication in pattern recognition

As an extension of picture fuzzy sets (PFSs), interval-valued picture fuzzy sets (IVPFSs) can better model and handle incomplete, indeterminate and inconsistent information in some practical applications. One of the important topics in IVPFSs is the similarity measure of IVPFSs, for which few studies have been proposed within the literature. Moreover, some existing similarity measures cannot adequately meet the conditions of similarity measure with some counterintuitive cases. In this work, we devise a novel similarity measure between IVPFSs based on the effect of the margin of the degree of refusal membership. First, the interval-valued picture fuzzy numbers will be transformed into two right-angled triangular-based pyramids in a spatial rectangular coordinate system. Then, a new parameter distance measure for IVPFSs is defined to assess the similarity between IVPFNs according to the centers of gravity of their corresponding right-angled triangular-based pyramids. Meanwhile, a comparison between different similarity measures is performed to illustrate that the proposed similarity measure can overcome the deficiencies of other extant measures. Finally, we apply it to handle pattern recognition problems. The comparison results indicate that the proposed algorithm can adequately meet the conditions of similarity measure, produce more reasonable and creditable results and perform well in complex contexts.

An Advanced Entropy Measure of IFSs via Similarity Measure

The Entropy measure of an intuitionistic fuzzy set (IFS) plays a significant role in decision making sciences, for instance, medical diagnosis, pattern recognition, criminal investigation, etc. The inadequate nature of an entropy measure may lead to some invalid results. Therefore, it is significant to use an efficient entropy measure for studying various decision-making problems under IFS environment. This paper first proposes a novel similarity measure for IFS. Based on the proposed similarity measure, an advanced entropy measure is defined with a different axiomatic approach. This axiomatic approach allows us to measure an IFS's entropy with the help of a similarity measure. To show the efficiency of the proposed similarity measure, a comparative study is performed with the existing similarity measures. Some structural linguistic variables are taken as examples to show the validity and consistency of the proposed entropy measure along with the existing entropy measures. Finally, based on the proposed entropy measure, a multi-criteria decision-making problem is performed.

Extended Belief Rule-Based System With Accurate Rule Weights and Efficient Rule Activation for Diagnosis of Thyroid Nodules

Extended belief-rule-based (EBRB) system is a representative rule-based system and has attracted much attention due to its capability of solving the problems of combinatorial explosion and time-consuming optimization incurred by belief-rule-based system. Despite their advantages, the development of EBRB suffers from some shortcomings, such as the unreasonable calculation of similarity between input and antecedent belief distributions (BDs), inaccurate calculation of individual matching degrees and rule weights, and inefficient determination of activation rules. To address these shortcomings, this article proposes a new EBRB system, in which an existing similarity measure between two BDs is adopted to accurately calculate the individual matching degrees and rule weights. Furthermore, the activation weight of a rule is efficiently calculated within an activation group generated using the affinity propagation algorithm, which is utilized to determine whether the rule is activated. The activation rules are then integrated using their weights and the evidential reasoning algorithm to generate the inference result. To demonstrate its accuracy and efficiency, the proposed EBRB system is employed to help diagnose thyroid nodules based on the historical examination reports collected from a tertiary hospital located in Hefei, Anhui, China. The findings are highlighted by the comparison of the proposed EBRB system with existing EBRB systems based on the historical reports and datasets derived from the University of California at Irvine.

Intuitionistic Fuzzy Modulus Similarity Measure

The concept of intuitionistic fuzzy sets (IFSs) is an expected explanation for finding the appropriate information. It originated from concept of fuzzy set (FS) theory, which extends the classical conception of a fuzzy set. This paper examines a number of widely employed similarity measures then proposes an IFSs modulus similarity measure and a weight similarity measure. Initially, the authors have discussed numerous existing similarity measures, some of which are unable to justify the axioms of being a similarity measure. Furthermore, some numerical examples are presented to compare the existing similarity measures with the proposed similarity measure. The proposed similarity measure is a practical and effective method for determining the qualitative similarity between IFSs, which do not have any paradoxical nature. In addition, the proposed similarity measure has been demonstrated practically in pattern recognition and medical diagnosis problem. Suggestions for future research comprise the conclusions of the paper.