Similarity Measure Of Sets Research Articles

Research on the Synergistic Development of China’s Pension Industry and Pension Career

To adapt to the new demographic trends and foster high-quality and sustainable population growth, this study analyzes the synergistic development of the pension industry and pension career based on the data of 31 provinces in China from 2016 to 2022, using a distance coordination model, the latest Vague set similarity measure method, new grey relational analysis, kernel density estimation, and Markov chain. The findings indicate that (1) the development levels of China’s pension industry and pension career have shown a steady upward trend, with the gap between them gradually narrowing, though the overall development of the pension career remains higher than that of the pension industry. (2) The synergistic degree of China’s pension industry and pension career is high, with the degree of synergy fluctuating but generally increasing. (3) The synergistic development degree of the pension industry and pension career has continued to rise. The increase in the synergistic development degree shows a spatial distribution pattern of “Central > East > West”. (4) The spatial distribution of synergistic development of China’s pension industry and pension career is uneven, and in the long term, regions with higher synergistic development levels tend to positively influence less developed regions.

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.

Selection of healthcare waste disposal strategies with Lq* q-rung orthopair multi-fuzzy soft set similarity measures

The global challenges associated with urbanization and the escalating waste production have been magnified in recent times, particularly in the context of the COVID-19 pandemic. In response to these challenges, municipal authorities, especially in developing nations, are confronted with the imperative task of discerning the most suitable healthcare waste (HCW) disposal methods. These methods are crucial for the effective management of medical waste, both during and after the COVID-19 era. This study introduces a novel similarity measure designed for lattice ordered q-rung orthopair multi-fuzzy soft sets (Lq* q-ROMnFSSs) and exploring some of their essential characteristics. Currently, no established methods are available for gauging the similarity of Lq* q-ROMnFSSs sets. Therefore, this paper takes a pioneering step by presenting similarity measures tailored for Lq* q-ROMnFSSs sets. Moreover, we propose an evaluation methodology that leverages the lattice ordered q-rung orthopair multi-fuzzy soft information to determine the optimal health care waste (HCW) disposal approach. This approach seeks to enhance decision-making within the realm of waste management, facilitating more informed and effective choices in handling healthcare waste.

Similarity measure between generalized intuitionistic fuzzy sets with three kinds of negation

The similarity measure of intuitionistic fuzzy sets is a primary method for dealing with uncertainty and fuzzy problems and is commonly used in fuzzy decision-making and pattern recognition. The current mainstream similarity measure is based on the classical fuzzy set with only one negation, which often violates the intuitionistic problem in applications because the actual semantics of multiple negations are not considered. To solve the inconsistency and irrationality problems in the classical similarity methods, we introduce three negations (contradiction negation, opposition negation, and mediation negation) in the intuitionistic fuzzy set to obtain the generalized intuitionistic fuzzy set and prove its related property theorem. On this basis, our similarity measure adopts a mediational negation to represent non-membership, which fully utilizes the multiple negation information of non-membership and hesitancy and avoids the loss of fuzzy information. We verify the method’s rationality, validity, and originality through pattern recognition experiments and numerical examples, which improves the performance of intuitionistic fuzzy set similarity in practical applications and provides a new approach for future research on intuitionistic fuzzy inference.

Exponential similarity measure of confidence consistency fuzzy cubic sets in fuzzy multiset scenarios and its application in piano performance evaluation

A consistency fuzzy set is composed of mean values and consistency degrees of fuzzy sequences in the transformation process of a fuzzy multiset (FM), but lacks confidence intervals in relation to a confidence level of fuzzy sequences, which shows its deficiency. To solve this deficiency, this paper aims to propose an improved transformation approach from FM to a confidence consistency fuzzy cubic set (CCFCS) and to develop an exponential similarity measure of CCFCSs for modeling piano performance evaluation (PPE) in a FM scenario. Consequently, this study includes the following context. First, a transformation approach from FM to CCFCS is proposed in terms of mean values, consistency degrees (the complement of standard deviation), and confidence intervals of fuzzy sequences subject to a confidence level and normal distribution. Second, the exponential similarity measure of CCFCSs is proposed in the scenario of FMs. Third, a PPE model is developed based on the proposed similarity measure of CCFCSs in the FM scenario. Finally, the developed model is applied to a piano performance competition organized by Shaoxing University in China as an actual evaluation example, and then the rationality and validity of the proposed model in the scenario of FMs are verified through sensitivity and comparison analysis.

Cosine and cotangent similarity measures for intuitionistic fuzzy hypersoft sets with application in MADM problem

Intuitionistic fuzzy hypersoft sets (IFHSSs) are a novel model that is projected to address the limitations of Intuitionistic fuzzy soft sets (IFSSs) regarding the entitlement of a multi-argument domain for the approximation of parameters under consideration. It is more flexible and reliable as it considers the further classification of parameters into their relevant parametric valued sets. In this paper, we proposed some trigonometric (cosine and cotangent) similarity measures and their weighted trigonometric similarity measures (SMs). Trigonometric Similarity measures (SMs) for intuitionistic fuzzy hypersoft sets (IFHSSs) are significantly implied to check the similarity measures and help to determine the similarity between different factors. Also, in order to evaluate the validity of the significant study and apply the results to a daily life problem. We use them to solve problems involving the selection of renewable energy sources. According to several technical contributing factors, the analysis identifies the ideal location for the implementation of the energy production units. Future case studies with many features and additional bifurcation along with multiple decision-makers can use the suggested methodologies. Also, several existing structures, such as fuzzy, Pythagorean fuzzy, Neutrosophic theories, etc., can be utilized with the suggested method.

Similarity measures of picture fuzzy sets and their applications to pattern recognition1

As the theory of picture fuzzy sets has been developed, more information in life can be expressed in mathematical terms. Similarity measure is a special tool for quantifying the similarity between two sets, so studying similarity measure on picture fuzzy sets has become a trending topic. This new research direction has drawn a great deal of attention from experts and has led to a number of important results which have led to significant results in a number of practical applications. By examining these new findings, we discovered that there are many studies on similarity measure of picture fuzzy sets, some of them are deficient in solving certain problems, and such similarity measures can lead to the calculation of unreasonable data in practical applications, affecting the final results. Secondly, there is still room for research similarity measures on exponential functions. Considering these two aspects, we propose two new similarity measures based on exponential function, which not only satisfy the axiomatic definition of similarity measures, but also show reasonable computational results in practical applications.

Impact of trigonometric similarity measures for pythagorean fuzzy sets and their applications

In fuzzy set theory, the similarity measure is a significant device that measures the degree of correlation between two objects. An extension to intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS) have been widely employed in numerous disciplines. It is critical to investigate the similarity measure of PFS. The study proposes the trigonometric function to suggest new similarity measures of PFS to handle the uncertainty that the existing similarity measures are unable to differentiate. Firstly, axiomatic descriptions of similarity measures for the proposed measures are proved. Then, an example is used to validate the proposed measures. Application to pattern recognition and medical diagnosis is also discussed in real-life scenarios. The validity of the suggested similarity measures is proved by comparing the results to the effectiveness of current equivalent similarity measures. Finally, a comparative study of these real-life examples reveals that the novel similarity measures are more flexible and dependable than the current similarity measures in dealing with various real application difficulties.

Similarity and entropy measures for circular intuitionistic fuzzy sets

A recent extension of intuitionistic fuzzy sets (IFSs) is the circular intuitionistic fuzzy set (C-IFS), where the performance of each alternative is described by a circle with a fixed radius rather than a specific orthopair. This article presents the similarity and dissimilarity measures for C-IFSs. Their basic axioms are proven, and some of their characteristics are brought to light. The axiomatic definition of entropy measures for C-IFSs is given. Several mathematical expressions are provided to measure the entropy of C-IFSs. The conversions of entropy into similarity measures and from similarity into entropy are given. The inferior ratio method, which relies on similarity measures, is extended for the C-IFS framework. The method is illustrated through a case study of site selection for an epidemic hospital. The solutions of the given approach are compared with the existing decision-making techniques.

Intelligent Medical Diagnosis Reasoning Using Composite Fuzzy Relation, Aggregation Operators and Similarity Measure of q-Rung Orthopair Fuzzy Sets

Medical diagnosis is the process of finding out what is the disease a person may be suffering from. From the symptoms and their gradation, the doctor can decide which the dominant disease is. Nevertheless, in the process of medical diagnosis, there is ambiguity, uncertainty, and a lack of medical knowledge that can adversely affect the doctor’s judgment. Thus, a tool of artificial intelligence, fuzzy logic, has come to enhance the decision-making of diagnosis in a medical environment. Fuzzy set theory uses the membership degree to characterize the uncertainty and, therefore, fuzzy sets are integrated into imperfect data in order to make a reliable diagnosis. The patient’s medical status is represented as q-rung orthopair fuzzy values. In this paper, many versions and methodologies were applied such as the composite fuzzy relation, fuzzy sets extensions (q-ROFS) with aggregation operators, and similarity measures, which were proposed as decision-making intelligent methods. The aim of this procedure was to find out which of the diseases (viral fever, malaria fever, typhoid fever, stomach problems, and chest problems), was the most influential for each patient. The work emphasizes the contribution of aggregation operators in medical data in order to contain more than one expert’s aspect. The performance of the methodology was quite good and interesting as most of the results were in agreement with previous works.

Uncertainty and decision-making with multi-polar interval-valued neutrosophic hypersoft set: A distance, similarity measure and machine learning approach

The issue of decision-making (DM) is intricate due to the environment's ambiguous, imprecise, and uncertain nature, particularly when multiple attributes are involved and further subdivided. To address such complex problems, the concept of the hypersoft set has been employed. This article shows how to combine the multi-polar interval-valued neutrosophic set with the hypersoft set. This can help you solve DM problems that have more than one attribute. Additionally, we define similarity measures for multipolar interval-valued neutrosophic hypersoft sets (mPIVNHSs). We discuss the proposed extensions' definitions and mathematical operations and present an algorithm to solve DM problems related to everyday life using the proposed operators under mPIVNHSs. A machine learning method called K-Nearest Neighbor (KNN) is also employed to calculate ranking in the selection of sites for a new store. By utilizing the potential of data point similarity, K-Nearest Neighbors (KNN) and similarity measurements have practical value in daily life. KNN mimics the human propensity to draw from related experiences, resulting in applications like customized suggestions. Parallel to this, similarity metrics statistically evaluate resemblance to support tasks like personalized advice across fields like biology and social networks. Finally, we conclude the present study by comparing it with the existing studies, and future directions are also given.

Similarity Measure of Plithogenic Cubic Vague Sets: Examples and Possibilities

The crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets are the extension of the plithogenic set, in which elements are characterized by the number of attributes and each attribute can assume many values. To achieve more accuracy and precise exclusion, a contradiction or dissimilarity degree is specified between each attribute and the values of the dominating attribute. A plithogenic cubic vague set is a combination of a plithogenic cubic set and a vague set. The key tool for resolving problems with pattern recognition and clustering analysis is the similarity measure. In this research, we characterize and investigate the similarities between two Plithogenic Cubic Vague sets (PCVSs) for (z≡F), (z≡IF) and (z≡N). Also, examples are given to examine similarities in the pattern recognition application problems.

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.

Exponential Function-Based Similarity Measures for q-Rung Linear Diophantine Fuzzy Sets and Their Application to Clustering Problem

The q-rung linear Diophantine fuzzy set is a recently developed tool to handle with uncertain and vague information in real-life issues and can be applied for reference parameter-based opinions. Similarity measures determine distance with dimensions that represent features of the objects. Despite the importance of exponential function-based similarity measures, there is no satisfactory formulation for q-rung linear Diophantine fuzzy sets in the literature. This paper proposes similarity measures based on exponential function for q-rung linear Diophantine fuzzy sets and thus presents the first formulas for calculating the similarity coefficient between two q-rung linear Diophantine fuzzy sets. The salient features of the new similarity measures are axiomatically addressed to ensure their good performance. Also, they are applied to the clustering problem and the results are analyzed. A comparative study is established and thus several advantages of the proposed similarity measures are discussed.

Nonlinear strict distance and similarity measures for intuitionistic fuzzy sets with applications to pattern classification and medical diagnosis

In this paper, we propose a new type of nonlinear strict distance and similarity measures for intuitionistic fuzzy sets (IFSs). Our proposed methods not only have good properties, but also improve the drawbacks proposed by Mahanta and Panda (Int J Intell Syst 36(2):615–627, 2021) in which, for example, their distance value of d_{_{textrm{MP}}}(langle mu , nu rangle , langle 0, 0rangle ) is always equal to the maximum value 1 for any intuitionistic fuzzy number langle mu , nu rangle ne langle 0, 0rangle . To resolve these problems in Mahanta and Panda (Int J Intell Syst 36(2):615–627, 2021), we establish a nonlinear parametric distance measure for IFSs and prove that it satisfies the axiomatic definition of strict intuitionistic fuzzy distances and preserves all advantages of distance measures. In particular, our proposed distance measure can effectively distinguish different IFSs with high hesitancy. Meanwhile, we obtain that the dual similarity measure and the induced entropy of our proposed distance measure satisfy the axiomatic definitions of strict intuitionistic fuzzy similarity measure and intuitionistic fuzzy entropy. Finally, we apply our proposed distance and similarity measures to pattern classification, decision making on the choice of a proper antivirus face mask for COVID-19, and medical diagnosis problems, to illustrate the effectiveness of the new methods.

A Parametric Family of Fuzzy Similarity Measures for Intuitionistic Fuzzy Sets

A Parametric Family of Fuzzy Similarity Measures for Intuitionistic Fuzzy Sets

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”

Pattern recognition and medical diagnosis based on trigonometric similarity measures for bipolar complex fuzzy soft sets

Pattern recognition and medical diagnosis based on trigonometric similarity measures for bipolar complex fuzzy soft sets

New similarity measure of Pythagorean fuzzy sets based on the Jaccard index with its application to clustering

A similarity measure is being widely used as a tool to create the degree of similarity between two different objects or sets. Several similarity measures between two Pythagorean fuzzy sets (PFSs) are suggested in literature. As far as our knowledge is concerned no one has considered similarity measure between two Pythagorean fuzzy sets (PFSs) based on Jaccard index (JI) so far. Therefore, in this manuscript a novel similarity measure based on JI between two PFSs is suggested. The JI is statics used to compare similarity as well as variety of simple sets. The advantages of proposed similarity based on Jaccard index includes: (i) It can be utilized to compare any two sets and it can also be applied to text data, numerical data and even categorical data. (ii) It is robust to outliers, which means that it is not significantly affected by presence of rare or unusual items exist in the data. This makes it useful in variety of applications including clustering and anomaly detection (iii) It is simple and efficient in computation which make it right choice in many applications where fast processing time is important. Then we gave several numerical examples to show the reliability of suggested similarity measures. Our proposed similarity measure between PFSs based on JI give better properties with respect to numerical results. Based on the numerical analysis, our proposed method is reliable, reasonable and better than the existing ones. Furthermore, we utilized proposed similarity measure with Pythagorean Fuzzy Technique of Order Preference by Similarity to Ideal Solution (PF-TOPSIS) in handling complex daily life issues involving multicriteria decision-making (MCDM) processes. Furthermore, similarity measure between two PFSs is also very useful in clustering. Therefore, we also apply our proposed similarity measure in an application to clustering based on Pythagorean fuzzy data set. Final results revealed that our suggested methods are well suited and reasonable in multicriteria decision-making and clustering environment.

A new definition for quartic fuzzy sets with hesitation grade applied to multi-criteria decision-making problems under uncertainty

Pythagorean fuzzy sets and Fermatean fuzzy sets are used to enhance the flexibility of intuitionistic fuzzy sets for decision-making under uncertainty in fuzzy environments. This study presents and compares a new definition of quartic fuzzy sets with intuitionistic, Pythagorean, and Fermatean fuzzy sets. In addition, we study set operations, score function, and accuracy function of the quartic fuzzy sets. Euclidean distance and similarity measures for quartic fuzzy sets are proposed, which will help solve many real-life problems under uncertainty. We then develop an algorithm to tackle the problem of multiple criteria decision-making. A comparison of the novel quartic fuzzy sets with the existing intuitionistic, Pythagorean, and Fermatean fuzzy sets is provided to demonstrate the advantages of the proposed quartic fuzzy sets. Finally, a practical example is presented to demonstrate the applicability and efficacy of the proposed fuzzy sets. The results of the study indicate that new definition of quartic fuzzy sets produce the most consistent and reliable ranking for handling uncertain and indeterminate information.