Fuzzy Similarity Measure Research Articles

Smart Cities and Human Development: Analysis Using Fuzzy Similarity Measures

Smart Cities and Human Development: Analysis Using Fuzzy Similarity Measures

Terrorism: Interpol Global Policing Goals and SDGs

In this paper, we determined how well an OECD country is achieving the Received Interpol goals with respect to the SDGs pertinent to them. We found that the Scandinavian countries were at the top in the achievement. In combatting terrorism in general, we found that the Scandinavian countries were at the top. We also show that the fuzzy similarity measure of the ranking of countries used by the SDGs relevant to terrorism compared with SDG 16 alone was high. Let [Formula: see text] and [Formula: see text] be rankings of a set [Formula: see text] and [Formula: see text] and [Formula: see text] the associated fuzzy subsets, respectively. Consider the similarity measures [Formula: see text] and [Formula: see text] [J. N. Mordeson and S. Mathew, Journal of Mahani Mathematical Research 13(1) (2024) 279–291]. Suppose that [Formula: see text] and [Formula: see text] are known, but [Formula: see text] is unknown. It is shown in the reference by J. N. Mordeson and S. Mathew [Mathematics of Uncertainty for Coping with World Challenges, Climate Change, World Hunger, Modern Slavery, Coronavirus, Human Trafficking (Springer, 2021)] that if [Formula: see text] is near [Formula: see text] then [Formula: see text] is near [Formula: see text] In this paper, a similar result for [Formula: see text] is shown.

Knowledge reduction by combining interval Type-2 Fuzzy similarity measures and interval Type-2 Fuzzy formal lattice

Knowledge reduction by combining interval Type-2 Fuzzy similarity measures and interval Type-2 Fuzzy formal lattice

Novel strict intuitionistic fuzzy similarity measures-based on fuzzy negation and their applications

The concept of similarity measure is fundamental for evaluating the consistency between intuitionistic fuzzy sets (IFSs). Several researchers have developed various intuitionistic fuzzy similarity measures (IFSimMs) utilizing intuitionistic fuzzy distance measures (IFDisMs) or combinations of membership and non-membership degrees of IFSs. Nevertheless, there is still ample room for the improvement, as some of these measures do not satisfy the axiomatic properties of IFSimMs and produce unreasonable results. In this paper, we first establish a dual relationship between IFDisMs and IFSimMs based on fuzzy negations, enabling the construction of an infinite number of IFSimMs from a given IFDisM. We then propose two novel IFSimMs by directly manipulating the membership and non-membership degrees of IFSs and prove that they satisfy the axiomatic properties of strict IFSimMs (SIFSimMs). Furthermore, a comparative analysis reveals that the proposed SIFSimMs do not yield any unreasonable results in various scenarios. Finally, we apply these SIFSimMs to pattern recognition, medical diagnosis, and clustering analysis problems, demonstrating their superior performance compared to some existing measures.

Modern Approach in Pattern Recognition Using Circular Fermatean Fuzzy Similarity Measure for Decision Making with Practical Applications

The circular Fermatean fuzzy (CFF) set is an advancement of the Fermatean fuzzy (FF) set and the interval-valued Fermatean fuzzy (IVFF) set which deals with uncertainty. The CFF set is represented as a circle of radius ranging from 0 to 2 with the center at the degree of association (DA) and degree of nonassociation (DNA). If multiple people are involved in making decisions, the CFF set, as an alternative to the FF and IVFF sets, can deal with ambiguity more effectively by encircling the decision values within a circle rather than taking an average. Using algorithms, a pattern can be observed computationally or visually. Machine learning algorithm utilizes pattern recognition as an instrument for identifying patterns and also similarity measure (SM) is a beneficial pattern recognition tool used to classify items, discover variations, and make future predictions for decision making. In this work, we introduce the CFF cosine and Dice similarity measures (CFFDMs and CFFSMs), and their properties are studied. Unlike traditional approaches of decision making, which emphasize a single number, the proposed CFFSMs observe the pattern over the circular region to help in dealing with uncertainty more effectively. We introduce an innovative decision-making method in the FF setting. Available bank loans and applicants’ eligibility levels are represented as CFF set using their FF criteria and are taken as loan patterns and customer eligibility patterns. The loan is allocated to the applicant by measuring the CFFCSM and CFFDSM between the two patterns. Also, laptops are suggested to the customers by measuring the similarity between specification pattern and requirement pattern. The correctness and consistency of the proposed models are ensured by comparison analysis and graphical simulations of the input and similarity CFFNs.

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.

Novel construction method for Pythagorean fuzzy similarity measures

Novel construction method for Pythagorean fuzzy similarity measures

An innovative distance measure for quantifying the dissimilarity between Q-Rung orthopair fuzzy sets

Q-Rung orthopair fuzzy set (Q-ROFSs) is a generation of quartic fuzzy sets (QFSs), Fermatean fuzzy sets (FFSs), Pythagorean fuzzy sets (PFSs), Intuitionistic fuzzy sets (IFSs), and fuzzy sets (FSs). Fuzzy similarity measures find wide-ranging applications in several fields, such as pattern recognition (PR), classification, and multi-criteria decision-making (MCDM). The computation of criteria weights in MCDM heavily relies on the fuzzy environment. Therefore, this study focuses on developing a similarity measure for Q-ROFS based on Hausdorff distance, a valuable tool for establishing object similarities. We introduce an innovative distance measure designed to quantify the dissimilarity between Q-ROFSs. Our approach leverages this distance measure to establish a similarity measure between Q-ROFSs. Furthermore, we present a set of properties associated with the suggested similarity measures. To demonstrate the usefulness of these measures, we provide numerous numerical examples in the fields of PR and linguistic variable characterization. By leveraging our innovative techniques, we also develop a novel algorithm for orthopair fuzzy Tomada de Decisao Iterativa Multicriterio (TODIM), a highly interactive and effective MCDM approach. Moreover, we have successfully applied the newly devised orthopair fuzzy TODIM method to address MCDM challenges encountered in diverse real-life problems. The obtained algebraic outcomes affirm that the suggested similarity measures are appropriate, practical, and applicable for queries involving fuzzy linguistic variables in MCDM contexts.

Multi-criteria decision analysis model using the q-rung orthopair fuzzy similarity measures and the COPRAS method for electric vehicle charging station site selection

Multi-criteria decision analysis model using the q-rung orthopair fuzzy similarity measures and the COPRAS method for electric vehicle charging station site selection

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.

Comparing some plant communities in a region of Türkiye via fuzzy similarity

Abstract In this study, the results obtained from forest vegetation via the research project on plant sociology which was conducted in the Black Sea region of Türkiye is evaluated with the help of a fuzzy similarity measures approach. Via this project, the plant sociology in an area which has not been studied in the Black Sea region of Türkiye is performed to investigate the plant communities and ecological and sociological relationships with each other. The similarity relations among the plant communities and relevés (sampling areas) which they covered are investigated. The issue of fuzzy similarity of sets and elements in sets is studied. According to this point of view, the fuzzy similarity among the plant communities and among the relevés is introduced. This joint study is carried out in a fuzzy environment, considering the classical results found in the project in question to be obtained in more detail for application. It is also understood that such studies can only be best performed with an interdisciplinary working group.

An assessment of fertilizer spraying drones based on hesitancy fuzzy similarity measures for sustainable green development

This research proposes a new similarity measure on hesitancy fuzzy graphs. The similarity measures are crucial concepts to explore the closeness between fuzzy graphs. The available imprecise and inconsistent data were more effectively handled by fuzzy similarity measures and intuitionistic fuzzy similarity measures. With time in decision-making theory, a complex frame of the background that occurs cannot be specified entirely by these fuzzy graphs but generalized fuzzy graphs like the hesitancy fuzzy graph can handle such a situation efficiently. The applicability of Hesitancy Fuzzy Graph (HFG) attracted the researchers to generalize ranking order based on the working procedures I, II of Xu’s approach and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach. For this purpose, we first define hesitancy fuzzy preference relations, Laplacian energy, and similarity measures in these HFG. The decision-making technique is then proposed in which a weighting technique is developed by building an optimal model based on the proposed Laplacian energy and similarity measure under a hesitancy fuzzy environment. This research studies the decision-making problem in which the preference information given by the experts takes the form of Hesitancy Fuzzy Preference Relations (HFPRs) and the information about experts’ weights are completely unknown. This research utilizes the hesitancy fuzzy weighted averaging operator to aggregate all individual HFPRs into a collective HFPR. Then, based on the degree of similarity between the individual HFPRs and the collective ones, we develop an approach to determine the experts’ weights. Moreover, based on HFPRs, in which the similarity measures between the collective preference relation and hesitancy fuzzy ideal solution are used to rank the given alternatives. We provide an illustrative numerical example to illustrate the mentioned approach and also we compare the aggregate results of the two techniques.

Using fuzzy similarity measure in content-based video retrieval based on image query

Using fuzzy similarity measure in content-based video retrieval based on image query

Remaining Useful Life Prediction for Pressurized Fluid Pipelines Based on Acoustic Emission Monitoring and an Adaptive Fuzzy Similarity Measure

Remaining Useful Life Prediction for Pressurized Fluid Pipelines Based on Acoustic Emission Monitoring and an Adaptive Fuzzy Similarity Measure

Elementary Function-Based Fermatean Fuzzy Similarity Measures: Applications to Medical Pattern Recognition and Multi-Criteria Decision-Making

Elementary Function-Based Fermatean Fuzzy Similarity Measures: Applications to Medical Pattern Recognition and Multi-Criteria Decision-Making

Linear Diophantine Fuzzy Sets: Image Edge Detection Techniques based on Similarity Measures

In the digital imaging process, fuzzy logic provides many advantages, including uncertainty management, adaptability to variations, noise tolerance, and adaptive classification. One of the techniques of digital image processing is the edge detection. The edge detection process is an essential tool to segment the foreground objects from the image background. So, it facilitates subsequent analysis and comprehension of the image’s underlying structural properties. This process can be moved on with the notion of fuzzy sets and their generalizations. The concept of Linear Diophantine fuzzy sets is a generalization of fuzzy sets where reference parameters correspond to membership and non-membership grades. This study aims to apply linear Diophantine fuzzy sets (LDFSs) to edge detection of images. The novelty of this paper is twofold. The first one is that we conduct a comprehensive evaluation to ascertain the similarity values using the linear Diophantine fuzzy similarity measure by leveraging the gray normalized membership values associated with fundamental edge detection techniques. The other is to modify the image pixels into the LDFSs and then filter the images by using the presented similarity measure operators given in the LDFS environment.

Extraction of evolutionary factors in smart manufacturing systems with heterogeneous product preferences and trust levels

Smart products, as an increasingly significant part of smart manufacturing systems, have brought users extreme experiences. To provide a significantly better user experience and succeed amidst intense market competition, smart products undergo continuous and iterative evolution guided by diverse user requirements. However, users' requirements are heterogeneous, ever-changing, and misleading owing to the heterogeneous familiarity and deceptive interactions, leading to an erroneous identification of product evolutionary factors and inferior subsequent evolution. In existing works, the heterogeneous preferences and trust levels of users are considered superficially, and the extracted product evolutionary factors fail to adequately fulfill users' requirements. To address this issue, a reliable extraction method for evolutionary factors of smart products with heterogeneous product preferences and trust levels is proposed. First, the fuzzy similarity measure is introduced and a group classification method based on this measure is designed to filter out users without reference value. Second, the trust score induced order weighted averaging (TS-IOWA) operator is employed to obtain the comprehensive trust level of an individual user. Third, the dual trust aggregating operator is improved by two corrective factors being incorporated with the Einstein product and the Einstein sum to overcome the deficiency: an over-reduction of trust level and an over-expansion of distrust level, and then employed to aggregate multiple trust/distrust values and sort the evolutionary factors. Finally, two case studies on the App rating system and the evolution of smart wristbands are provided to verify the effectiveness of this proposed method. Throughout the analysis, the ranking accuracy of users' trust levels has increased by 25%, and the matching ratio between the extraction results and user requirements has increased from 57.14% to 85.7% with an improvement of 50%. The results demonstrate that the proposed method is capable of obtaining more credible evolutionary factors of smart products.

Software bug severity and priority prediction using SMOTE and intuitionistic fuzzy similarity measure

A software bug tracking system receives several bug reports in a rapid manner during the maintenance of software. In order to fix the important and urgent bugs, the triager has to assign severity and priority to individual bugs on time. However, there are a lot of uncertainties in the bug reports due to bias, noise, and abnormal data. At the same time, the presence of common terms in multiple severity and priority classes creates confusion in the mind of the triager. Furthermore, machine learning and deep learning approaches generally belong to discriminative learning with a clear-cut outcome. Instances of software bug reports are textual in nature. As a result, these are fuzzy and cannot be classified with a clear-cut outcome. To overcome the above problems, in this paper, an Intuitionistic Fuzzy Similarity Measure (IFSM) based severity prediction technique (IFSMSP) and priority prediction technique (IFSMPP) are proposed for predicting the severity and priority of a new bug by using already labeled bugs. Initially, the Synthetic Minority Oversampling Technique (SMOTE) is used to balance the severity and priority label of software bugs. Then the severity-term dictionary or priority-term dictionary is created by extracting the most frequent terms from the bug summary using text mining and Natural Language Processing (NLP). Then the data is represented using an intuitionistic fuzzy set (IFS) by calculating the membership, non-membership, and hesitancy degrees. Then 15 different IFSM techniques are investigated for predicting the severity and priority of software bugs. Experiments are carried out on large software bug repositories (Eclipse, Mozilla, Apache, and NetBeans) with a 10-fold cross-validation technique. IFSMSP outperformed other state-of-the-art priority models by obtaining an accuracy of 92.3%, 90.6%, 91.9%, and 91.2%, and IFSMPP outperformed other state-of-the-art models by obtaining an accuracy of 93.2%, 91.9%, 92.7%, and 92.3% on the Eclipse, Mozilla, Apache, and NetBeans software bug repositories, respectively.

A modified fuzzy similarity measure for trapezoidal fuzzy number with their applications

A modified fuzzy similarity measure for trapezoidal fuzzy number with their applications

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.