Similarity Measures Of Fuzzy Sets Research Articles

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.

A novel similarity measure for intuitionistic fuzzy sets and its application to pattern recognition

A novel similarity measure for intuitionistic fuzzy sets and its application to pattern recognition

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.

The generalized dice similarity measures for comprehensive evaluation of graphic design effects based on color psychology with t-spherical fuzzy sets

Traditional Chinese art is vast and profound, with various colors having rich meanings. The combination of colors can vividly and intuitively represent various characteristics of things. Fully reflecting the characteristics of traditional Chinese folk art in graphic design can achieve extremely strong expressive effects. In current graphic design, the artistic colors of traditional Chinese folk art have not yet been fully displayed, and there is a lack of understanding of the profound connotation of traditional Chinese art. The graphic design industry has a very broad development space. The comprehensive evaluation of graphic design effects based on color psychology is a classical multiple attribute group decision making (MAGDM) problems. In this work, we shall present some novel Dice similarity measures (DSM) of T-spherical fuzzy sets(T-SFSs) and the generalized Dice similarity measures (GDSM) of and indicates that the DSM and asymmetric measures (projection measures) are the special cases of the GDSM in some parameter values. Then, we propose the GDSM-based MAGDM models with T-SFSs. Then, we apply the GDSMs between T-SFSs to MAGDM. Finally, an illustrative example for comprehensive evaluation of graphic design effects based on color psychology is given to demonstrate the efficiency of the GDSMs. The main contributions of this paper are summarized: (1) some novel Dice similarity measures (DSM) and the generalized Dice similarity measures (GDSMs) of T-spherical fuzzy sets(T-SFSs) are proposed; (2) The weighted Dice similarity measures (WDSM) and the weighted generalized Dice similarity measures (WGDSMs) of T-spherical fuzzy sets(T-SFSs) are proposed to solve the MAGDM; (3) an illustrative example for comprehensive evaluation of graphic design effects based on color psychology is given to demonstrate the efficiency of the WGDSM; (4) Some comparative analysis are used to show the effectiveness of the proposed Dice similarity measures.

Detection of plant diseases using image-based similarity measures of Pythagorean fuzzy sets

<span>In image processing, data extraction from any image with deviation is difficult to pursue. Especially in identification of radiological images, many issues have been involved in the choosing of right image from the available images. In this paper, new similarity measure model for images is proposed that have application in the identification of the images of plant diseases. The application of the similarity measures is compared with existing models. The results reports that the proposed Pythagorean entropy measures have application in the detection of plant diseases. Even, the quality ofextraction of data from images is enhanced. Further, the study concludes that the proposed measures are better than the existing measures in case of image processing problems.</span>

Construction of similarity measure for intuitionistic fuzzy sets and its application in face recognition and software quality evaluation

As a generalization of fuzzy sets, intuitionistic fuzzy sets (IFSs) are more capable of representing and addressing uncertainty in real-world problems. As a result, IFSs have been utilized in various areas of application. However, the distance and similarity measures between the two IFSs are still an open issue that has drawn much attention over the past few decades. Even though several intuitionistic fuzzy similarity measures (IFSMs) have been developed, a number of issues still exist, including counter-intuitive results, ‘the zero divisor problem,’ violation of similarity measure axioms, and being incompetent to detect minor changes in membership or non-membership. To overcome these shortcomings, a novel intuitionistic fuzzy similarity measure (IFSM) has been introduced in this study. Unlike existing measures, this method considered the global maximum and minimum of differences in memberships and differences in non-memberships, along with their individual differences, to construct an IFSM. Moreover, it has been shown that a convex combination of two similarity measures is also a similarity measure. Some numerical examples are employed to emphasize the advantages and strengths of the proposed method over existing ones. The suggested IFSM has been implemented on a few pattern classification issues to demonstrate its efficacy and a new face recognition method is also presented. Moreover, an entropy measure is introduced using the proposed IFSM, which is further used to construct the weights of attributes in the MADM method. Furthermore, the MADM technique, IF-E-TOPSIS, is constructed using the suggested IFSM and entropy measure. The effectiveness of this method is shown by utilizing it for software quality assessment, and the results are compared with existing ones to highlight the superiority of the proposed method.

Similarity measures of Pythagorean fuzzy sets based on Lp metric and its applications to multicriteria decision-making with Pythagorean VIKOR and clustering

Similarity measures of Pythagorean fuzzy sets based on Lp metric and its applications to multicriteria decision-making with Pythagorean VIKOR and clustering

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.

SOME TRIGONOMETRIC SIMILARITY MEASURES OF COMPLEX FUZZY SETS WITH APPLICATION

Similarity measures of fuzzy sets are applied to compare the closeness among fuzzy sets. These measures have numerous applications in pattern recognition, image processing, texture synthesis, medical diagnosis, etc. However, in many cases of pattern recognition, digital image processing, signal processing, and so forth, the similarity measures of the fuzzy sets are not appropriate due to the presence of dual information of an object, such as amplitude term and phase term. In these cases, similarity measures of complex fuzzy sets are the most suitable for measuring proximity between objects with two-dimensional information. In the present paper, we propose some trigonometric similarity measures of the complex fuzzy sets involving similarity measures based on the sine, tangent, cosine, and cotangent functions. Furthermore, in many situations in real life, the weight of an attribute plays an important role in making the right decisions using similarity measures. So in this paper, we also consider the weighted trigonometric similarity measures of the complex fuzzy sets, namely, the weighted similarity measures based on the sine, tangent, cosine, and cotangent functions. Some properties of the similarity measures and the weighted similarity measures are discussed. We also apply our proposed methods to the pattern recognition problem and compare them with existing methods to show the validity and effectiveness of our proposed methods.

A Parametric Family of Fuzzy Similarity Measures for Intuitionistic Fuzzy Sets

A Parametric Family of Fuzzy Similarity Measures for Intuitionistic Fuzzy Sets

Normal [formula omitted] functions-based fuzzy information measures with applications in MADM and pattern recognition

Fuzzy and non-standard fuzzy information measures act upon vague information entailed in linguistic variables or uncertain numerical data following some goal for which they discover the “best alternative” or “correct pattern”. This paper introduces the concept of normalKN functions instrumental to generate a class of fuzzy knowledge measures. In addition to the axiomatic approach, we investigate various general methods to obtain normalKN functions from the notions of auto-morphisms, restricted equivalence functions, and restricted dissimilarity functions. Further, aggregatingnormal KNfunctions, we propose three knowledge measures of a fuzzy set and exploit their significance in practical applications. This concerns Multiple Attribute Decision Making (MADM) problems, the issue of appropriate weight computation, and the understanding of structured linguistic variables. Additionally, we consider the real case study for the ranking of universities. A novel methodology to transform a given fuzzy knowledge measure into a family of similarity measures of fuzzy sets is also suggested. Furthermore, we discuss an application of the proposed similarity measures in the context of pattern recognition and the MADM problem using artificial and real data sets. The comparative study of the proposed measures shows their advantage over existing ones because of specific theoretical and practical aspects.

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.

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

Multi-criteria decision making based on vector similarity measures of picture type-2 hesitant fuzzy sets

Multi-criteria decision making based on vector similarity measures of picture type-2 hesitant fuzzy sets