Hamming Distance Measure Research Articles

Applications of distance measure between dual hesitant fuzzy sets in medical diagnosis and weighted dual hesitant fuzzy sets in making decision

This paper introduces a novel distance measure for dual hesitant fuzzy sets (DHFS) and weighted dual hesitant fuzzy sets (WDHFS), with a rigorous proof of the triangular inequality to ensure its mathematical validity. The proposed measure extends the normalized Hamming, generalized, and Euclidean distance measures to dual hesitant fuzzy elements (DHFE), offering a broader framework for handling uncertainty in fuzzy environments. Additionally, the utilization of a score function is shown to simplify the computation of these distance measures. The practical relevance of the proposed measure is demonstrated through its application in medical diagnosis and decision-making processes. A comparative analysis between the newly introduced distance measure denoted as χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}, and an existing measure, χ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _1$$\\end{document} is performed to underscore the superiority and potential advantages of the new approach in real-world scenarios.

Real-Life Applications of New Type Spherical Fuzzy Sets and Its Extension Using Aggregation Operators

The purpose of this article is to present a novel approach to the multiple attribute decision-making problem (MADM) based on (l1, l2) spherical fuzzy sets (SFS). This is an extension of the SFS. As a result of this article, we will discuss the concept of spherical fuzzy weighted averaging (SFWA), spherical fuzzy weighted geometric (SFWG), generalized spherical fuzzy weighted averaging (GSFWA) and generalized spherical fuzzy weighted geometric (GSFWG). Here is a flowchart that shows how these operators are used in the algorithm we discussed. With the help of a numerical example, we illustrate the extended Euclidean and Hamming distance measures. Additionally, the SFN approach is characterized by idempotency, boundedness, commutativity, and monotonicity. These tools help you find the best option faster, simpler, and more conveniently. The result is a more precise conclusion and a more intimate relationship between (l1, l2). We compare some of the current models with those that have been proposed in order to demonstrate the dependability and utility of the models under investigation. The study also revealed fascinating and intriguing findings.

Interval-valued (p,q,r)-spherical fuzzy sets and their applications in MCGDM and MCDM based on TOPSIS method and aggregation operators

The (p,q,r)-Spherical fuzzy set is a useful generalization of other fuzzy structures such as fuzzy, intuitionistic fuzzy, Pythagorean fuzzy, picture fuzzy, q-rung orthopair fuzzy, spherical fuzzy, and T-spherical fuzzy sets. In this paper, we define concept of interval-valued (p,q,r)-spherical fuzzy set (IVpqr-SFS) and Set-theoretical and arithmetic operations of them. Two aggregation operators named interval-valued (p,q,r)-spherical fuzzy weighted arithmetic (IVpqr-SFWAA) and interval-valued (p,q,r)-spherical fuzzy weighted geometric (IVpqr-SFWGA) aggregation operators are introduced for IVpqr-SF numbers (IVpqr-SFN) and their properties were examined. The proposed operators are explained with examples. Furthermore, the score and accuracy functions of an IVpqr-SFN are introduced. We also define distance measures between two same types IVpqr-SFSs based on Hamming, Euclidean, and Hausdorff distance measures. Moreover, a multi-criteria group decision-making (MCGDM) method is developed based on the TOPSIS method by using the proposed distance measures and score function, and a numerical example is given to show the process of the proposed MCGDM method. In addition, a multi-criteria decision-making (MCDM) method is developed using the proposed IVpqr-SFWAA, IVpqr-SFWGA operators, and an illustrative example is given to show the process of the proposed MCDM method. Finally, a comparative analysis is presented between the proposed methods and the existing methods.

Novel complex fuzzy distance measures with hesitance values and their applications in complex decision-making problems

A complex fuzzy distance measure (CFDMs) plays a significant role in applications involving complex or high-dimensional data where traditional distance measures may not adequately capture the nuances of the data relationships. The significance of CFDMs lies in their ability to handle uncertainty, imprecision, and complexity in various domains. Numerous researchers introduced different concepts of CFDMs, yet these CFDMs fails to convey any information regarding the hesitancy degree associated with an element. The main objective of this paper is to introduce some new distance measures based on complex fuzzy sets, called complex fuzzy hesitance distance measure and complex fuzzy Euclidean Hesitance distance measure, which is the generalization of complex fuzzy normalized Hamming distance measure and complex fuzzy Euclidean distance measure. Some new operations and primay results are discussed in the environment of proposed CFDMs and complex fuzzy operations. Moreover, we discussed the applications of the proposed CFDMs in addressing decision-making problems. We introduced a new decision-making algorithm that integrates CFDMs into decision-making processes, providing a robust methodology for handling real-world complexities. Further, the comparative study of the proposed CFDMs is discussed with some existing CFDMs.

An integrated framework for spherical fuzzy MAGDM and applications to english blended teaching quality evaluation

In the information age, teachers are no longer the only source of information for students, and the problems of the traditional lecture mode are becoming more and more obvious. Especially in the process of teaching English in colleges and universities, students’ personalized and diversified needs for English learning are becoming more and more obvious, and if traditional theoretical lectures or theoretical indoctrination are continued, students’ needs and goals will be affected. As a new form of teaching, blended teaching can integrate the advantages of classroom teaching and online teaching and improve the overall quality and effectiveness of English teaching under the premise of changing the orientation of teachers and students. The English blended teaching quality evaluation is a multiple-attribute group decision-making (MAGDM) problem involving multiple qualitative and quantitative attributes. In this paper, on basis of EDAS technique, a novel spherical fuzzy number EDAS (SFN-EDAS) technique based on SFN Hamming distance (SFNHD) and SFN Jaccard similarity measure (SFNJSM) is built for dealing with MAGDM. Moreover, the MEREC technique with SFNHD and SFNJSM is extended to SFSs to acquire the attribute weights. Finally, SFN-EDAS technique is used for English blended teaching quality evaluation to prove practicability of the developed SFN-EDAS technique and SFN-EDAS technique is compared with existing techniques to further demonstrate its superiority. Hence, the research main achievements for this paper are outlined: (1) the novel EDAS technique is extended to the SFSs environment based on the SFNHD and SFNJSM; (2) the MEREC technique is extended to SFSs to acquire the attribute weights based on the SFNHD and SFNJSM; (3) a novel spherical fuzzy number EDAS (SFN-EDAS) technique based on the SFNHD and SFNJSM is built for dealing with MAGDM; (4) an empirical example and several comparative analysis for English blended teaching quality evaluation is offered to demonstrate the SFN-EDAS technique.

Optimized distance measures on hesitant fuzzy numbers: An application

As the rapidly progressing applications of uncertainty theories, the need for modifications to some of their existing mathematical tools or creating new tools to deal correctly with them in various environments is also exposed. Hesitant fuzzy numbers (HFNs), as a particular case of fuzzy numbers, are not an exception to this rule. Considering the necessity of determining the distance between given HFNs in many of their practical applications, this article shows that the existing methods either do not provide correct results or are not able to meet the needs of users. This paper aims to present new methods for distance measures of hesitant fuzzy numbers. To do them, three prevalent distance measures, i.e., the generalized distance measure, the Hamming distance measure, and the Euclidean distance measure, will be optimized into three distinct trinal categories. With the approach of reducing error propagation via reducing some unnecessary mathematical computations, new distance measures on HFNs will be introduced, first. The middle is the modification of the first category, which is more suitable when the given HFNs are equal-distance by the previous formula. Also, as the third category, the weighted form of these distance measures has been proposed, to be used where the real and membership parts of HFNs are not of equal importance. As an application of these, a TOPSIS-based technique for solving multi-attribute group decision-making problems with HFNs has been proposed. A numerical example will be implemented to describe the presented method. Finally, along with the validation of the proposed method, its numerical comparison with some other existing methods will be discussed in detail.

Computer purchasing using new type neutrosophic sets and its extension based on aggregation operators

This article discusses a new approach to multiple attribute decision-making (MADM) based on (l1, l2, l3) neutrosophic sets (NS). This is an extension of the NS. Neuosophic weighted averaging (NWA), neutrosophic weighted geometrics (NWG), generalized neutrosophic weighted averaging (GNWA), and generalized neutrosophic weighted geometrics (GNWG) are the topics of this article. The flowchart we presented during our discussion showed an algorithm that used these operators. Numerical examples are provided for the extended Euclidean and Hamming distance measures. As part of this communication, we will also elaborate on the properties of neutrosophic sets, such as their idempotency, their boundness, their commutativity, and their monotonicity. They make it quicker, easier, and more convenient to find the best option. Thus, there is a stronger connection between (l1, l2, l3) and more precise conclusions. Some of the current models are compared with those that have been proposed in order to demonstrate their dependability and utility. The study also revealed fascinating and intriguing findings.

Evaluation of Sustainable Potential Bearing Capacity of Tourism Environment Under Uncertainty: A Multiphase Intuitionistic Fuzzy EDAS Technique Based on Hamming Distance and Logarithmic Distance Measures

Evaluation of Sustainable Potential Bearing Capacity of Tourism Environment Under Uncertainty: A Multiphase Intuitionistic Fuzzy EDAS Technique Based on Hamming Distance and Logarithmic Distance Measures

Selection process based on new building construction work using square root vague sets and their aggregated operators

This study discusses novel approaches for solving multi-attribute decision-making problems using logarithmic square root vague sets. Logarithmic square root vague sets can be considered as an extension of vague sets and square root fuzzy sets provides a more profitable method to express the uncertainties in the data to deal with decision making problems. We developed some novel logarithmic square root vague sets, which can overcome the weaknesses of algebraic operations and capture the relationship between various square root vague sets and vague sets. The purpose of this study is to examine several aggregation operators using logarithmic square root vague sets. The weighted logarithmic averaging distance and weighted logarithmic geometric distance operators are distance measure that is based on aggregating model. We discuss the concepts of logarithmic square root vague weighted averaging, logarithmic square root vague weighted geometric, generalized logarithmic square root vague weighted averaging and generalized logarithmic square root vague weighted geometric operators. We communicate that algebraic structures such as associative, distributive, idempotent, bounded, commutativity and monotonicity properties are satisfied by logarithmic square root vague numbers. We discusses some mathematical properties of logarithmic square root vague sets, as well as the Hamming distance and Euclidean distance measures. It measures the similarity of two strings of information by measuring the Hamming distance. An analysis of the proposed operators is presented, along with alternative formulations and families, as well as their main properties. The weighting vector is characterized by multiple classical measures and we propose alternative solutions for dealing with the logarithmic properties of the operators. As a result of studying the weighting vectors of the operators, we present generalizations of them. We examine vague sets with important properties using algebraic operations in more detail. Furthermore, we develop an algorithm to solve multi-attribute decision-making problems using these operators. We provide real-life examples to illustrate how enhanced Euclidean distances, Hamming distances and score values can be applied in real-world situations. To show the superiority and the validity of the proposed aggregation operations, we compared it with the existing method, and concluded from the comparison and sensitivity analysis that our proposed technique is more effective and reliable. Based on the expert assessments, we compared the criteria with the most appropriate options.

AlexNet Convolutional Neural Network Architecture with Cosine and Hamming Similarity/Distance Measures for Fingerprint Biometric Matching

In information security, fingerprint verification is one of the most common recent approaches for verifying human identity through a distinctive pattern. The verification process works by comparing a pair of fingerprint templates and identifying the similarity/matching among them. Several research studies have utilized different techniques for the matching process such as fuzzy vault and image filtering approaches. Yet, these approaches are still suffering from the imprecise articulation of the biometrics’ interesting patterns. The emergence of deep learning architectures such as the Convolutional Neural Network (CNN) has been extensively used for image processing and object detection tasks and showed an outstanding performance compared to traditional image filtering techniques. This paper aimed to utilize a specific CNN architecture known as AlexNet for the fingerprint-matching task. Using such an architecture, this study has extracted the significant features of the fingerprint image, generated a key based on such a biometric feature of the image, and stored it in a reference database. Then, using Cosine similarity and Hamming Distance measures, the testing fingerprints have been matched with a reference. Using the FVC2002 database, the proposed method showed a False Acceptance Rate (FAR) of 2.09% and a False Rejection Rate (FRR) of 2.81%. Comparing these results against other studies that utilized traditional approaches such as the Fuzzy Vault has demonstrated the efficacy of CNN in terms of fingerprint matching. It is also emphasizing the usefulness of using Cosine similarity and Hamming Distance in terms of matching.

Comparison of Performance of Four Distance Metric Algorithms in K-Nearest Neighbor Method on Diabetes Patient Data

Diabetes is a chronic disease that occurs when the pancreas no longer produces insulin or when the body cannot effectively use the insulin it produces. The aim of this study is to analyze and compare the classification performance on diabetes patient dataset using four distance metric algorithms in the K-Nearest Neighbor (K-NN) method. Based on previous research, the performance values obtained were not sufficiently high, not exceeding 80%. Therefore, some actions are needed with the hope of obtaining new performance values and making comparisons with previous studies. Based on the test results using the confusion matrix, the accuracy level using Euclidean distance measurement obtained the best performance value at k=17 with 10-k fold, with an accuracy of 85.71%, precision of 86.24%, recall of 85.71%, and F-measure of 85.12%. The Manhattan distance measurement obtained the best performance value at k=25 with 10-k fold, with an accuracy of 85.53%, precision of 85.54%, recall of 85.53%, and F-measure of 85.10%. The Minkowski distance measurement obtained the best performance value at k=17 with 10-k fold, with an accuracy of 85.71%, precision of 86.24%, recall of 85.71%, and F-measure of 85.12%. On the other hand, the Hamming distance measurement obtained the best performance value at k=23 with 10-k fold, with an accuracy of 75.32%, precision of 79.27%, recall of 75.32%, and F-measure of 71.45%.

Some p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-cubic quasi-rung orthopair fuzzy operators for multi-attribute decision-making

This paper aims to support decision-makers improve their ability to accurately capture and represent their judgment in a wide range of situations. To do this, we propose a new type of fuzzy set called a p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-cubic quasi-rung orthopair fuzzy set (p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-CQOFS). The p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-CQOFS allows for a more flexible and detailed expression of incomplete information through the use of an additional parameter. The paper describes the concept of p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-CQOFS and its relationship to other types of fuzzy sets, introduces score and accuracy functions for p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-CQOFS and analyzes some of its mathematical properties, defines the Hamming distance measure between two p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-CQOFSs and examines some of its important properties, investigates the basic operations of p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-CQOFSs and extends these laws to aggregation operators, and introduces weighted averaging and geometric aggregation operators for combining p,q\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p,q$$\\end{document}-cubic quasi-rung orthopair fuzzy data.

Improved CoCoSo Method Based on Frank Softmax Aggregation Operators for T-Spherical Fuzzy Multiple Attribute Group Decision-Making

In this article, a novel CoCoSo (Combined compromise solution) method based on Frank operational laws and softmax function is investigated to handle multiple attribute group decision-making problems for T-spherical fuzzy sets. We extend Frank operations in T-spherical fuzzy environment and develop a series of aggregation operators, including T-spherical fuzzy Frank softmax (T-SFFS) average and geometric operators, and their weighted forms, i.e., T-SFFS weighted averaging (T-SFFSWA) and T-SFFS weighted geometric (T-SFFSWG) operators. Some of their basic properties and particular cases are discussed. Meanwhile, the monotonicity of proposed operators is also analyzed, and it is discussed that how they indicate the decision-makers’ optimistic and pessimistic decision attitudes with risk preference. Furthermore, a novel CoCoSo method based on Hamming distance measure is proposed, which considers both decision-maker’s decision attitude and attribute priority, and a multiple attribute group decision-making framework with two independent and parallel T-spherical fuzzy information processing processes are designed. Lastly, a real case of spent power battery recycling technology (SPBRT) selection is presented to show the practicability of the proposed method. Also sensitivity and comparative analyses are carried out to prove the reliability, effectiveness, and superiority of our proposed method.

Fuzzy hypersoft contra maps, homeomorphisms, and application in Covid-19 diagnosis using Hamming distance

This paper aims to introduce and study fuzzy hypersoft contra open, fuzzy hypersoft contra semi open, fuzzy hypersoft contra closed, and fuzzy hypersoft contra semi closed maps in fuzzy hypersoft topological spaces. Basic properties of fuzzy hypersoft contra open, contra semi open, contra closed and contra semi closed maps are analyzed with examples. Also, the relation between fuzzy hypersoft contra open maps, contra semi open maps, contra closed maps and contra semi closed maps is discussed. It is extended to fuzzy hypersoft contra homeomorphism, contra semi homeomorphism, contra C-homeomorphism and its related characteristics are also investigated. The fuzzy hypersoft set measure Hamming distance can be applied in real-world decision-making problems containing more uncertain and inadequate data. By applying Hamming distance between the Covid-19 patients and the other patients, a better decision can be taken in the Covid-19 diagnosis. This paper proposes a method to diagnose Covid-19 using Hamming distance of fuzzy hypersoft sets. The association between the patients and the symptoms is formulated as fuzzy hypersoft sets in which the Hamming distance measure is applied to decide on Covid-19 diagnosis.

Ensembling Scale Invariant and Multiresolution Gabor Scores for Palm Vein Identification

Biometric recognition based on palm vein trait has the advantages of liveness detection and high level of security. An improved human palm vein identification system based on ensembling the scores computed from scale invariant features and multiresolution adaptive Gabor features is proposed. In the training phase, from the input palm vein images, the interested palm regions are segmented using 3-valley point maximal palm extraction strategy, an improved method that extracts the maximal region of interest (ROI) easily and properly. Extracted ROI is enhanced using contrast limited adaptive histogram equalization method. From the enhanced image, local invariant features are extracted by applying scale invariant feature transform (SIFT). The texture and multiresolution features are extracted by employing adaptive Gabor filter over the enhanced image. These two features, scale invariant and multiresolution Gabor features act as the templates. In the testing phase, for the test images, ROI extraction, image enhancement, and two different feature extractions are performed. Using cosine similarity and match count-based classification, the score, Ss is computed for the SIFT features. Another score, Sg is computed using the normalized Hamming distance measure for the Gabor features. Both these scores are ensembled using the weighted sum rule to produce the final score, SF for identifying the person. Experiments conducted with CASIA multispectral palmprint image database version 1.0 and VERA palm vein database show that, the proposed method achieves equal error rate of 0.026% and 0.0205% respectively. For these databases, recognition rate of 99.73% and 99.89% respectively are obtained which is superior to the state-of-the-art methods in authentication and identification. The proposed work is suitable for applications wherein the authenticated person should not be considered as imposter.

Effective prediction of fake news using a learning vector quantization with hamming distance measure

It never happened before in human history the spreading of fake news; now, the development of the Worldwide Web and the adoption of social media have given a pathway for people to spread misinformation to the world. Everyone is using the Internet, creating and sharing content on social media, but not all the information is valid, and no one is verifying the originality of the content. It is sometimes complicated for researchers and intelligence to identify the essence of the content. For example, during Covid-19, misinformation spread worldwide about the outbreak, and much false information spread faster than the virus. This misinformation will create a problem for the public and mislead people into taking the proper medicine. This work will help us to improve the prediction rate. The proposed algorithm is compared with three existing algorithms, and the result is better than the other three current algorithms. The prediction rate of impact for the proposed algorithms is 93.54%

Multiple‐attribute decision‐making spherical vague normal operators and their applications for the selection of farmers

AbstractIn this article, we discuss a few fresh approaches to the spherical vague normal set (SVNS) approach to multiple attribute decision‐making (MADM) problems. A new generalization of the vague set (VS) and the spherical interval valued fuzzy set (SIVFS) is the spherical vague set (SVS). The spherical vague number (SVN) concepts consolidate normal fuzzy number (NFN) and we defined the spherical vague normal number (SVNN) and some of its intriguing fundamental operations. The purpose of this article is to discuss a novel idea of spherical vague normal weighted averaging (SVNWA), spherical vague normal weighted geometric (SVNWG), generalized spherical vague normal weighted averaging (GSVNWA) and generalized spherical vague normal weighted geometric (GSVNWG) operators. We talked about a flowchart with an algorithm that uses this operators and the MADM approach. With the help of a numerical example, we interact the extended euclidean and hamming distance measures. In this communication, it is also important to elaborate on some key SVN approach characteristics based on various algebraic operations, such as idempotency, boundedness, commutativity, and monotonicity. They are quicker to find the best option, more straightforward and practical. Think about five farmers. The four factors that are taken into account for each of the five farmers are climate, water, soil, disease, and flood, and their corresponding weights are displayed. We want to select the best option from a large number of choices by comparing expert assessments with the criteria. As a result, the conclusions of the defined models are more precise and closely related to . We contrast some of the current models with the ones that have been proposed in order to demonstrate the dependability and utility of the models under investigation. The study's findings are also intriguing and fascinating.

Complex intuitionistic fuzzy ordered weighted distance measure

Compared with the complex fuzzy set (CFS) and the intuitionistic fuzzy set (IFS), the complex intuitionistic fuzzy set (CIFS) can handle the two-dimensional and uncertain information simultaneously, and thus strengthen the capability of capturing useful information. In this paper, we consider the situation with complex intuitionistic fuzzy environment, where the importance of certain information is also taken into consideration. To deal with these situations, we develop the complex intuitionistic fuzzy ordered weighted distance (CIFOWD) measure and investigate its main properties. We find that the CIFOWD measure provides a parameterized family of aggregation distance measures, which includes, for example, complex intuitionistic fuzzy ordered weighted geometric distance (CIFOWGD) measure, complex intuitionistic fuzzy ordered weighted Hamming distance (CIFOWHD) measure, and complex intuitionistic fuzzy ordered weighted Euclidean distance (CIFOWED) measure as special types. The CIFOWD measure is capable of alleviating the influence of excessively large or excessively small deviations on the aggregation results via weight vector. Based on these distance measures, a multiple criteria group decision-making approach is presented under the CIFSs environment. An illustrative example regarding coronavirus vaccine selection on COVID-19 is taken for demonstrating the effectiveness of the proposed approach. Finally, the proposed results are compared with the results obtained from the existing methods.

Novel Distance-Measures-Based Extended TOPSIS Method under Linguistic Linear Diophantine Fuzzy Information

The advantages of the intuitionistic fuzzy set, Pythagorean fuzzy set, and q-rung orthopair fuzzy set are all carried over into the linear Diophantine fuzzy set by extending the restrictions on the grades. Linear Diophantine fuzzy sets offer a wide range of practical applications because the reference parameters allow evaluation andto express their judgments about membership and nonmembership degrees in a variety of ways. Linguistic-valued information cannot be described by linear Diophantine fuzzy numbers since precise numbers are used in linear Diophantine fuzzy systems. In this paper, we first present the novel idea of a linguistic linear Diophantine fuzzy set, which is the hybrid structure of the linear Diophantine fuzzy set and the linguistic term set. Furthermore, some basic operational rules with novel distance measures, namely, Hamming, Euclidean, and Chebyshev distance measures, are established. Based on the newly defined concept of distance measure, an extended TOPSIS technique is presented to tackle the linguistic uncertainty in real-world decision support problems. A numerical example is illustrated to support the applicability of the proposed methodology and to analyze symmetry of the optimal decision. A comparison analysis is constructed to show the symmetry, validity, and effectiveness of the proposed method over the existing decision support techniques.

Multiple attribute group decision making based on quasirung orthopair fuzzy sets: Application to electric vehicle charging station site selection problem

This paper aims to greatly improve decision makers’ capability of capturing their judgment in a broader space. In order to achieve this, we introduce the notion of a p,q-quasirung orthopair fuzzy set (p,q-QOFS), which is an extension of the q-rung orthopair fuzzy set. In p,q-QOFS, the sum of the pth power of membership degree and qth power of nonmembership degree is less than or equal to 1, where p and q are natural numbers. Thus, due to the additional parameter p, the p,q-QOFS can express incomplete information more flexibly and elaborately. This paper first develops the concept of p,q-QOFS and establishes that it is an extension of several existing fuzzy sets. Then, we introduce the score and accuracy functions of p,q-QOFS and analyze a few mathematical properties. Next, we define the Hamming distance measure between two p,q-QOFSs and some important properties. After that, we investigate the basic operations of p,q-QOFSs and extend these operational laws to aggregation operators. Further, we introduce the weighted averaging and geometric aggregation operators to aggregate p,q-quasirung orthopair fuzzy data. Moreover, we establish a p,q-quasirung orthopair fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method for solving multi-attribute group decision-making problems with unknown attribute weights. The present study also discusses a case study illustrating the applicability of the method through the selection of the most appropriate site for an electric vehicle charging station in an Indian city. In this case study, we consider seven alternative sites, including Raniganj, Jamuria, Kulti, and Burnpur. As a result of this study, Jamuria appears to be the best location to build an electric vehicle charging station. Finally, we illustrate the validity and practicability of our developed method through a comparative analysis with existing methods.