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The so-called Hamming distance measures the difference between two binary strings A and B. In simplified form, it measures the number of changes in A to get B. This type of distance is very useful in classical computing in applications such as error correction. It is also advantageous in quantum computing, being for example widely used in quantum machine learning. Since current quantum computers have limited resources, this type of distance is particularly attractive because it can be computed using fewer qubits and operations than other distances such as Euclidean or Manhattan distances. In this paper, two circuits for calculating Hamming distances using exclusively Clifford+T gates are presented. The aim of both circuits is to reduce the quantum cost and number of T gates needed to compute the Hamming distance. The T gate is more expensive than the other gates, so this reduction will have a significant impact on the total cost of the circuits. Furthermore, the proposed circuits are implemented using only Clifford+T gates. The circuits implemented exclusively with this group of gates are compatible with proven error detection and correction codes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The energy consumption of mechanical products in China is enormous, and the energy utilization rate is low, which is increasingly receiving people's attention. Conducting product design for energy optimization is of great significance for improving energy utilization efficiency. The scheme design of a product is the key to achieving innovation in product design, and the evaluation and decision-making of the design scheme directly affect the results of the later stage of the design. Therefore, correctly evaluating and making reliable decisions on product design schemes that are oriented towards fuzzy decision optimization is an important aspect of product innovation conceptual design. The product modeling design quality evaluation is a multiple attribute group decision making (MAGDM) problems. Recently, the Combined Compromise Solution (CoCoSo) method and information entropy method has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for portraying uncertain information during the product modeling design quality evaluation. In this paper, the CoCoSo method is designed for MAGDM under INSs. Then, the interval neutrosophic numbers CoCoSo (INN-CoCoSo) method based on the Hamming distance and Euclidean distance is built for MAGDM. The information Entropy method is employed to produce the weight information based on the Hamming distance and Euclidean distance under INNSs. Finally, a practical numerical example for product modeling design quality evaluation is supplied to show the INN-CoCoSo method. The main contributions of this paper are constructed: (1) This paper builds the novel MAGDM based on CoCoSo model under INSs; (2) The information Entropy method is employed to produce the weight information based on the Hamming distance and Euclidean distance under INNSs; (3) The new MAGDM method is proposed for product modeling design quality evaluation based on INN-CoCoSo. [ABSTRACT FROM AUTHOR]

In 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 Θ. 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. [ABSTRACT FROM AUTHOR]

Combinative distance-based assessment (CODAS) is a multi-criteria decision-making (MCDM) method that is based on the Euclidean and Hamming distances of alternatives from the average scores of attributes. Spherical fuzzy sets, as the recent extensions of ordinary fuzzy sets, were developed based on Pythagorean and neutrosophic sets and enable decision-makers to express their membership, non-membership, and hesitancy degrees independently and in a larger domain than most other fuzzy extensions. This paper proposes a new interval-valued spherical fuzzy CODAS method and provides extra space for catching the vagueness in the nature of the problem. The feasibility and practicality of the proposed model are illustrated with an application for evaluating the reopening readiness of academic units for campus education in the era of COVID-19. Three decision-makers from a higher education institution evaluate four academic units with respect to five strategic criteria and prioritize them according to their readiness levels for the campus type of education. Sensitivity and comparative analyses, theoretical and practical contributions, limitations, and future research avenues are also presented in the study. [ABSTRACT FROM AUTHOR]

In this paper, we present novel approaches to multi-attribute decision-making problems using q -rung normal fuzzy numbers. The q -rung normal fuzzy sets are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets, Pythagorean fuzzy sets and normal Pythagorean fuzzy sets. A combination of the q -rung fuzzy number and the normal fuzzy number becomes q -rung normal fuzzy numbers. The new averaging and geometric operations of q -rung normal fuzzy numbers are studied using the general aggregation function. There are both commutative, associative, idempotent and boundedness compatible using q -rung normal fuzzy numbers. There are four new aggregating operators presented such as q -rung normal fuzzy interaction weighted averaging, q -rung normal fuzzy interaction weighted geometric, q -rung generalized normal fuzzy interaction weighted averaging and q -rung generalized normal fuzzy interaction weighted geometric. Usually, the aggregation functions are taken to be the Euclidean distance and Hamming distance. The existence of these operators enables the development of algorithms that solve multi-attribute decision-making problems. We demonstrate the application of enhanced Euclidean and Hamming distances to problems arising in real-world situations. An important component of a robot sensor is computer science and machine tool technology. There are four factors that can be used to evaluate robotics systems: resolution, sensitivity, error and accuracy. In order to determine the best alternative, expert opinions should be compared to the criteria. The accuracy of these models is better and they are closer to q. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. [ABSTRACT FROM AUTHOR]

• A CODAS-based group decision model is designed for the T-spherical fuzzy context. • A T-spherical fuzzy Minkowski distance operator based on Heronian mean is proposed. • A novel ordered weighted Heronian Minkowski distance (TSFOWHMD) operator is advanced. • The TSFOWHMD operator is utilized to improve the CODAS method. • The applicability of the developed methodology is verified through a case study. T-spherical fuzzy sets (TSFSs) are more flexible and efficient tools to deal with ambiguous, uncertain and vague information in complex real-world decision-making problems than various extended intuitionistic fuzzy sets. This paper aims to develop a novel T-spherical fuzzy (TSF) Combinative Distance-Based ASsessment (CODAS) based on the Heronian Minkowski distance aggregation operator, this new method can capture interrelationship between input arguments. Some TSF weighted Heronian Minkowski distance (TSFWHMD) aggregation operators with generalization are developed based on Heronian mean and Minkowski-type distance, their properties are discussed as well as their families are analyzed. Furthermore, the TSF MAGDM methodology based on the improved CODAS is designed, where the Minkowski-type distance is used to define the TSF similarity for computing the expert weights and to construct the maximizing deviation method (MDM) for determining the attribute weights, respectively. The TSF ordered weighted Heronian Hamming distance (TSFOWHHD) and TSF ordered weighted Heronian Euclidean distance (TSFOWHED) operators derived from the TSFOWHMD operator are integrated into the CODAS method, which is an improved method for both measuring the deviation of the negative ideal solution from each alternative and capturing the correlation between attributes. Finally, the feasibility and practicality of developed methodology are illustrated with an example of CAE (Computer Aided Engineering) software selection for lithium-ion power battery (LiPB) design, sensitivity analysis and method comparisons are performed to elucidate the reliability and validity of the developed methodology. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, considering the traditional geometric operation laws and Pythagorean fuzzy information, a varies of new distance measures of Pythagorean fuzzy set are proposed, such as generalized Pythagorean fuzzy ordered geometric distance (GPFOWGD) measures and generalized Pythagorean fuzzy hybrid weighted geometric distance (GPFHWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, a decision-making model is built and illustrated by a mathematical calculation example to evaluate the service quality of sports clubs using Pythagorean fuzzy information. The results display that the approach is uncomplicated, valid and simple to compute. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiple attribute decision making. [ABSTRACT FROM AUTHOR]

The idea of an interval complex neutrosophic soft set (I-CNSS) emerges from the interval neutrosophic soft set (I-NSS) by the extension of its three membership functions (T, I, F) from real space to complex space (unit disc) to better handle uncertainties, vagueness, indeterminacy, and imprecision of information in the periodic nature. The novelty of I-CNSS lies in its more significant range of activity compared to CNS. Measures of similarity and distance are important tools that can be used to solve many problems in real life. Hence, this paper presents some interval complex neutrosophic soft similarities based on Hamming and Euclidean distances of I-CNSSs to deal with real-life problems that include uncertain information such as decision-making issues and medical diagnosis stats. Firstly, this paper reviews the definition of an interval complex neutrosophic soft set. Secondly, we defined distance Hamming measures and distance Euclidean measures on I-CNSSs. Next, the axiomatic definition of similarity measures based on Hamming and Euclidean distances of I-CNSSs is proposed. Moreover, a numerical example is given and relations between these measures are introduced and verified. Meanwhile, some applications are given to show how similarity can be used to help the user in making decisions and making medical diagnoses. Finally, a comparison of some current approaches is used to back up this study. [ABSTRACT FROM AUTHOR]

Generalized hesitant fuzzy numbers (GHFNs) are able to directly manage situations in which we may encounter a finite set of known values with a finite set of degrees of doubt as quantitative approximations of an uncertain situation/quantification of a linguistic expression. They are new extensions of hesitant fuzzy sets, which have been considered in this paper. In fact, in this paper, GHFNs will be utilized to model the uncertainty of the assessment values of options against criteria in multi-attribute decision making (MADM) problems. It means that all of the elements of decision matrix are GHFNs. Then, the technique for order of preference by similarity to ideal solution (TOPSIS) method, as a very successful method in solving MADM problems, will be updated to be used with GHFNs. To this end, the distance between GHFNs must be defined to obtain the distances between given alternatives from each of two subjective alternatives (positive/negative ideal solutions). Thus, three existing famous distance measures, i.e., general distance ( d g ), Hamming distance ( d h ), and Euclidean distance ( d e ) measures, have been updated for GHFNs firstly. Then, the new TOPSIS method will be proposed based on GHFNs. Finally, the numerical examples have been appointed to illustrate the proposed method, analyze comparatively and validate it. [ABSTRACT FROM AUTHOR]

In this paper, various E-learning Apps have been compared and analysed by two distance measures and formulate their comparison with limited number of students and factors with the scope of their extension. Hamming Distance and Euclidean Distance are two distance measures used in this paper. Moreover, the variables considered for this purpose follows the Intuitionistic Fuzzy Set (IFS) theory. [ABSTRACT FROM AUTHOR]

Mining clusters from data is an important endeavor in many applications. The k‐means method is a popular, efficient, and distribution‐free approach for clustering numerical‐valued data, but does not apply for categorical‐valued observations. The k‐modes method addresses this lacuna by replacing the Euclidean with the Hamming distance and the means with the modes in the k‐means objective function. We provide a novel, computationally efficient implementation of k‐modes, called Optimal Transfer Quick Transfer (OTQT). We prove that OTQT finds updates to improve the objective function that are undetectable to existing k‐modes algorithms. Although slightly slower per iteration due to algorithmic complexity, OTQT is always more accurate and almost always faster (and only barely slower on some datasets) to the final optimum. Thus, we recommend OTQT as the preferred, default algorithm for k‐modes optimization. [ABSTRACT FROM AUTHOR]

Game theory is a powerful tool in modeling actual decision-making problems. In many cases, it is difficult for players to give a crisp value of payoff. To conquer this issue, various extensions of fuzzy sets have been introduced to represent the payoffs. Although type-2 intuitionistic fuzzy (T2IF) set (T2IFS) can solve the game problem effectively, sometimes players prefer to give the primary (secondary) membership and non-membership degrees with some approximate ranges rather than crisp values. T2IFS cannot express such uncertain payoffs. Thus, this paper initiates a new concept called type-2 interval-valued intuitionistic fuzzy (T2IVIF) set (T2IVIFS) which has stronger ability than T2IFS and interval-valued intuitionistic fuzzy set (IVIFS) in representing uncertain information. Hamacher operations of T2IVIFSs are given. Hamming and Euclidean distances between T2IVIFSs are defined respectively. Some Hamacher aggregation operators for T2IVIFSs are developed and some desirable properties are analyzed. Afterwards, an effective method is proposed for solving T2IVIF matrix game, which can make game results more accurate and reliable. An example of new energy vehicle industry development is provided to validate the proposed T2IVIF matrix game. Comparative analyses reveal that the matrix game in T2IVIF environment has better flexibility and reliability than that in T2IF and IVIF environments. [ABSTRACT FROM AUTHOR]

Main problems in FPGA-based ring oscillator (RO) PUFs are that the RO frequencies are highly sensitive to operating conditions and other types of global variations. In addition, the RO frequencies are highly correlated by local variations. Therefore, in practice, conventional RO-PUF application schemes using Hamming distance normally require complex identification (ID) extraction algorithms and/or a large number of ROs to ensure a high level of uniqueness and reliability of the extracted IDs. In this work, we proposed a novel scheme of ID extraction based on Euclidean distances. Our proposed scheme stably and reliably generates the ID using a non-selective small number of ROs. Specifically, the generated IDs are mostly non-sensitive to global variables and operating conditions such as ambient temperature. In oppose to Hamming-based extraction, the close-frequencies ROs are normally removed to avoid flipping bits, our proposed scheme takes all those into account and simplifies the extraction process. Experiments on our available hardware have shown a very good level of reliability and uniqueness with ID collision rate is estimated less than 2 × 10 − 9 . • A unique ID extraction scheme using RO based on Euclidean distance. • IDs can be reliably generated utilizing a non-selective small number of ROs. • The ID extraction scheme is experimentally verified on FPGA devices. • The ID collision rate from the experiment is estimated to be less than 2-9. • The ID stability is confirmed under different operating conditions. [ABSTRACT FROM AUTHOR]

The similarity measure is used to tackle many issues that include indistinct as well as blurred information excluding is not in a position to deal with the general fuzziness along with obscurity of the problems that have various information. The main purpose of this research is to propose a multipolar interval-valued neutrosophic soft set (mPIVNSS) with operations and basic properties. We also develop Hamming distance and Euclidean distance by using mPIVNSS and numerical examples and use the developed distances to introduce similarity measures. By using the developed similarity measures a decision-making approach is presented for mPIVNSS. Finally, we used the developed decision-making approach for medical diagnosis. [ABSTRACT FROM AUTHOR]

In this study, considering the traditional geometric operation laws and Pythagorean fuzzy information, we propose a variety of new distance measures of Pythagorean fuzzy sets such as generalized Pythagorean fuzzy geometric distance (GPFGD) measures and generalized Pythagorean fuzzy weighted geometric distance (GPFWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance, and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, we build a decision-making model illustrated by a mathematical calculation example to evaluate the sustainable development of new urbanization from the perspective of urban agglomeration using Pythagorean fuzzy information. [ABSTRACT FROM AUTHOR]

Image representation and approximate query is always a research challenge and is affected greatly by the dimension and size of images. Since hash-based methods and binary encodings in combination with other techniques, such as kernel tricks, a longer binary code and mapping vectors rotation, can maintain a linear query time and query accuracy, they have been used in this area broadly. This paper develops principal component analysis hashing (PCAH) and unequal length of binary coding to divide images into more categories, denoted as PCA-MD, to improve accuracy of the representation and lookup of images. This paper firstly proves that the eigenvector mapping is locality sensitive, which is the basis for more classes division. For the anisotropy of the eigenvectors, PCA-MD utilizes an unequal length of binary coding and fewer eigenvectors, rather than an equal code, to divide the images mapped on every eigenvector to more categories. Moreover, L1-norm distance is applied to measure the distances of images to avoid the enormous computation of Euclidean distance. Theoretical analysis and extensive experimental results demonstrate that the PCA-MD has a higher query performance and a slight longer run time than the state-of-the-art approaches based on the Hamming distance. This in turn verifies that PCAH is a locality sensitive hash and that partitioning into more categories rather than only two categories is reasonable. [ABSTRACT FROM AUTHOR]

Probabilistic uncertain linguistic sets (PULTSs) have widely been used in MADM or MAGDM. The CODAS method, which is a novel MADM or MAGDM tool, aims to acquire the optimal choice which have the largest Euclidean & Hamming distances from the NIS. This paper designs the probabilistic uncertain linguistic CODAS (PUL-CODAS) method with sine entropy weight. Finally, a numerical example for green supplier selection is given and the obtained results are compared with some existing models. [ABSTRACT FROM AUTHOR]

As a generalization of complex fuzzy set (CFS), interval-valued complex fuzzy set (IVCFS) is a new research topic in the field of CFS theory, which can handle two different information features with the uncertainty. Distance is an important tool in the field of IVCFS theory. To enhance the applicability of IVCFS, this paper presents some new interval-valued complex fuzzy distances based on traditional Hamming and Euclidean distances of complex numbers. Furthermore, we elucidate the geometric properties of these distances. Finally, these distances are used to deal with decision-making problem in the IVCFS environment. [ABSTRACT FROM AUTHOR]

Currently, an important issue in multi-criteria decision-making (MCDM) problems are vagueness and lack of precision of decision- -making information because of insufficient data and incapability of the decision maker to process the information. Intuitionistic fuzzy sets (IFS) are a solution to eliminate the vagueness and the uncertainty. While fuzzy sets (FS) deal with ambiguity and vagueness problem, IFSs have more advantages. Moreover, the CODAS-SORT method cannot handle the uncertainty and ambiguity of information provided by human judgments. The aim of this study is to develop an IF extension of CODAS-SORT combining this method with the IFS theory. To achieve this, we use the fuzzy weighted Euclidean distance and fuzzy weighted Hamming distance instead of the crisp distances. A case study of a supplier selection assessment is used to clarify the details of our proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the complex fuzzy ordered weighted distance (CFOWD) measure. It is a new measure that uses the main characteristics of the the ordered weighted averaging (OWA) operator and uncertain information represented as complex fuzzy values. This measure includes a wide range of distance measures such as the complex fuzzy maximum distance, the complex fuzzy minimum distance, the normalized complex fuzzy distance (NCFD), the complex fuzzy ordered weighted Hamming distance (CFOWHD), complex fuzzy ordered weighted Euclidean distance (CFOWED), complex fuzzy ordered weighted geometric distance (CFOWGD), the normalized complex fuzzy Ham- ming distance (NCFHD) and the normalized complex fuzzy Euclidean distance (NCFED). We study some of its main properties. Finally, based on CFOWD measures, we give an illustrative example regarding the selected problem. [ABSTRACT FROM AUTHOR]

In this article, we propose a limited feedback-based space-shift keying (SSK) modulation scheme where transmitter (Tx) obtains partial channel state information (CSI) via a feedback link from receiver (Rx). More specifically, the Tx does not receive perfect information of channel gain, but is aware only of channel gain ordering. Based on the received partial CSI, the Tx adapts the spatial constellation and allocates different transmit weights to each transmit antenna representing spatial constellation points. Furthermore, the power adapted spatial constellation points are encoded by using gray coding scheme, which results in unit hamming distance between adjacent spatial constellation points. Next, a multiple-input single-output (MISO) system with maximum–likelihood detection is investigated. Accurate expressions for the average bit error rate (ABER) for ${2}\times {1}$ and ${4}\times {1}$ MISO systems over Rayleigh fading channel are derived. Further, an approximate expression for the ABER of a generalized MISO system is also obtained. It is shown analytically that the ABER performance of the proposed SSK scheme can be improved by applying a non-uniform power allocation to make transmit links more distinguishable at the Rx. Moreover, we demonstrate analytically that the proposed scheme attains a diversity order which is twice of the conventional SSK scheme. Numerical results, corroborated by Monte Carlo simulations, verify the proposed analysis and clearly highlight that, the proposed scheme significantly outperforms existing closed-loop spatial constellation-based schemes relying on full CSI in Tx and conventional open-loop SSK scheme. [ABSTRACT FROM AUTHOR]

In this study, hard turning tests are carried out on the hardened AISI 4140 steel material. Power consumption, sound intensity, processing time and surface roughness values are measured for all combinations of cutting conditions such as three different cutting speeds, three different feed rates, three different depths of cut and two different tool cutting edge angle. According to these measurements, the ideal cutting condition is found by using the TOPSIS method which is integrated by fuzzy Hamming distance, Euclidean distance and Hausdorff distance measure methods. Also in case that machinability parameters have different importance degrees, ideal cutting condition is determined by using the weighted fuzzy distance measure method. According to the experimental results obtained, it is observed that the surface roughness value increased with the increasing feed rate. Roughness values obtained at 90 degree tool cutting edge angle are lower than 62.5 degrees. It is observed that the sound intensity increases with the increasing feed rate. The machining time is reduced with increasing feed rate, depth of cut and cutting speed. Thus, total power consumption is reduced. [ABSTRACT FROM AUTHOR]

This study proposes a method to distinguish between healthy people and Parkinson's disease patients using sole pressure sensor data, neural network with weighted fuzzy membership (NEWFM), and preprocessing techniques. The preprocessing techniques include fast Fourier transform (FFT), Euclidean distance, and principal component analysis (PCA), to remove noise in the data for performance enhancement. To make the features usable as inputs for NEWFM, the Euclidean distances between the left and right sole pressure sensor data were used at the first step. In the second step, the frequency scales of the Euclidean distances extracted in the first step were divided into individual scales by the FFT using the Hamming method. In the final step, 1–15 dimensions were extracted as the features of NEWFM from the individual scales by the FFT extracted in the second step by the PCA. An accuracy of 75.90% was acquired from the eight dimensions as the inputs of NEWFM. [ABSTRACT FROM AUTHOR]

In this paper, a set of generators (in a unique from) called the distinguished set of generators, of a cyclic code C of length n = 2 k (where k is a natural number) over Z 2 m is obtained. This set of generators is used to find the rank of the cyclic code C. It is proved that the rank of a cyclic code C of length n = 2 k over Z 2 m is equal to n − v , where v is the degree of a minimal degree polynomial in C. Then a description of all MHDR (maximum hamming distance with respect to rank) cyclic codes of length n = 2 k over Z 2 m is given. An example of the best cyclic codes over Z 8 of length 4 having largest minimum Hamming, Lee and Euclidean distances among all cyclic codes of the same rank is also given. Further, using an isomorphism between cyclic and negacyclic codes of odd length over finite chain rings given by Dinh, Lopez and Szabo, the above results are extended to cyclic and negacyclic codes of length p k over Z p m for an odd prime p. [ABSTRACT FROM AUTHOR]

The concept of distance between Pythagorean fuzzy sets (PFSs) has been proven to be relevant in the applications of PFSs as seen in the literature. The main purpose of this paper is to show that Zhang and Xu's distance measure between PFSs fails the conditions of distance measure; hence, it is not an appropriate distance measure for PFSs. Some numerical examples are used to validate this stance. In order to remedy this shortcoming, Zhang and Xu's distance measure for PFSs is normalised/modified to cater for the limitation by employing the technique used to normalise both Hamming and Euclidean distances between intuitionistic fuzzy sets by Szmidt and Kacprzyk. The modified Zhang and Xu's distance measure for PFSs satisfies the conditions of the axiomatic definition of distance measure for PFSs; hence, it is an appropriate/reliable distance measure for PFSs. Finally, the modified Zhang and Xu's distance measure for PFSs is applied to pattern recognition problems of classification of building materials and mineral fields. [ABSTRACT FROM AUTHOR]

Social Networks is an essential phenomenon in all aspects through various perspectives. These networks contain a large number of users better termed as nodes and the connections between the users termed as edges. For efficient information processing and retrieving, accessing the influential node is essential for improving the diffusion process. To identify the influential node inside a heterogeneous community, incorporating probability metrics with regression classifier is put forth stated by proposed method Support Vector Bayesian Machine (SVBM). Node metrics such as degree centrality, closeness centrality is measured for eliminating the nodes primarily. A standardized index based on the centrality values computed for enhancing into SVBM. After the standardized index, similarity dissimilarity index values evaluated by combining the Euclidean, Hamming, Pearson coefficient for valued relations and Jaccard for binary relations which results in a single index value considered as the power degree value(p). The value p determines the node's boundedness, which indicates the range of influence within the community. The outlier nodes in the bounded region get eliminated, and the nodes remaining taken for the final phase of SVBM, probability regression line predicts the node inhibiting the most influential nature. Experimental evaluation of the proposed system with the existing Support Vector Machine (SVM) technique resulted in 0.95 and 0.41 respectively for Area Under Curve (AUC) denoting that the true positive influential node classification process from the other existing nodes was higher than SVM. In comparison with the existing SVM, the proposed methodology SVBM attained a node detection, which influenced a higher diffusion rate within the networks. [ABSTRACT FROM AUTHOR]

It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their drawbacks and pursue more accuracy and effectiveness, in this paper, we propose a new inclusion relation of IFSs and a new definition called strict distance measure. Based on this new relation, an analysis is given to point out that the common shortcoming of Hamming distance measure and Euclidean distance measure is the mishandling of hesitancy degree. Therefore, the role of hesitancy degree in distance measure is studied deeply and then three strict distance measures are put forward to overcome the above shortcoming. In addition, a novel definition called the characteristic function of distance measure is defined to describe the character of strict distance measure. On this basis, a theorem is presented to illustrate the inevitability of the occurrence of unrecognized result in pattern recognition problems in some special cases. This theorem also shows that the problem cannot be entirely attributed to distance measures. In view of this condition, we provide an appropriate solution. Compared with other existing distance measures in some examples, the superiorities of our improved distance measures are demonstrated to be more effective and more significant. [ABSTRACT FROM AUTHOR]

This paper deals with two related problems, namely distance‐preserving binary embeddings and quantization for compressed sensing. First, we propose fast methods to replace points from a subset Χ ⊂ ℝn, associated with the euclidean metric, with points in the cube {±1}m, and we associate the cube with a pseudometric that approximates euclidean distance among points in Χ. Our methods rely on quantizing fast Johnson‐Lindenstrauss embeddings based on bounded orthonormal systems and partial circulant ensembles, both of which admit fast transforms. Our quantization methods utilize noise shaping, and include sigma‐delta schemes and distributed noise‐shaping schemes. The resulting approximation errors decay polynomially and exponentially fast in m, depending on the embedding method. This dramatically outperforms the current decay rates associated with binary embeddings and Hamming distances. Additionally, it is the first such binary embedding result that applies to fast Johnson‐Lindenstrauss maps while preserving ℓ2 norms. Second, we again consider noise‐shaping schemes, albeit this time to quantize compressed sensing measurements arising from bounded orthonormal ensembles and partial circulant matrices. We show that these methods yield a reconstruction error that again decays with the number of measurements (and bits), when using convex optimization for reconstruction. Specifically, for sigma‐delta schemes, the error decays polynomially in the number of measurements, and it decays exponentially for distributed noise‐shaping schemes based on beta encoding. These results are near optimal and the first of their kind dealing with bounded orthonormal systems. © 2019 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In this paper, we present the 2-tuple linguistic neutrosophic CODAS model based on the traditional fuzzy CODAS (combinative distance-based assessment) model and some fundamental theories of 2-tuple linguistic neutrosophic information. Firstly, we briefly review the definition of 2-tuple linguistic neutrosophic sets (2TLNSs) and introduce the score function, the accuracy function, operation laws and some aggregation operators of 2TLNNs. Then, the calculation steps of traditional fuzzy CODAS model are briefly presented. Furthermore, by combining the traditional fuzzy CODAS model with 2TLNNs information, the 2-tuple linguistic neutrosophic CODAS model is established and the computing steps for multiple attribute group decision making (MAGDM) are simply depicted. Our presented model is more accurate and effective for considering the combinative form of two distance measurements, including fuzzy weighted Hamming distance (HD) and fuzzy weighted Euclidean distance (ED). Finally, a numerical example for safety assessment of construction project has been given to illustrate this new model and some comparisons between 2TLNNs CODAS model and two 2TLNNs aggregation operators are also made to further illustrate the advantages of the new method. [ABSTRACT FROM AUTHOR]

Topologically associating domains (TADs) are the most fundamental elements and significant structures of the eukaryotic genome. Currently, algorithms have been developed to find the TADs. But few algorithms are reported to compare the similarity of TADs between genomes. In this study, mice Hi-C sequencing data of four contrasts were enrolled. Seventeen algorithms, including BPscore, Jaccard index (JI) distance, VI distance, image hash, image subtraction, image variance, and so on, were used to quantify the genomic similarity of TADs. Image subtraction, Euclidean distance, and Manhattan distance were significantly better for TAD difference detection than the others. Deferent Hash (dHash) with the best zoom size ranked the second, followed by improved Hamming distance algorithm and JI distance. Advantages and disadvantages of various algorithms for quantifying the similarity of TADs were compared. Our work could provide the fundament for TADs comparison. [ABSTRACT FROM AUTHOR]

Intuitionistic Fuzzy Sets (IFSs) have extensively been employed in multi-criteria decision making (MCDM). COmbinative Distance-based Assessment (CODAS) method, which is relatively a new MCDM technique, aims to select the alternative having the largest Euclidean and Taxicab (Hamming) distances to the negative- ideal point. This paper develops an intuitionistic fuzzy CODAS method, namely Interval-Valued Intuitionistic Fuzzy CODAS (IVIF-CODAS), and introduces it to the literature first time. The objective of our paper is to make a multi-criteria decision under intuitionistic fuzzy uncertainty by taking the hesitancy of decision makers into consideration based on both Euclidean and Taxicab distances according to the negative-ideal point. To show the effectiveness of the developed method, an application is given for wave energy facility location selection in Turkey and the obtained results are compared with crisp CODAS method's. [ABSTRACT FROM AUTHOR]

Recently, cross-modal search has attracted considerable attention but remains a very challenging task because of the integration complexity and heterogeneity of the multi-modal data. To address both challenges, in this paper, we propose a novel method termed hetero-manifold regularisation (HMR) to supervise the learning of hash functions for efficient cross-modal search. A hetero-manifold integrates multiple sub-manifolds defined by homogeneous data with the help of cross-modal supervision information. Taking advantages of the hetero-manifold, the similarity between each pair of heterogeneous data could be naturally measured by three order random walks on this hetero-manifold. Furthermore, a novel cumulative distance inequality defined on the hetero-manifold is introduced to avoid the computational difficulty induced by the discreteness of hash codes. By using the inequality, cross-modal hashing is transformed into a problem of hetero-manifold regularised support vector learning. Therefore, the performance of cross-modal search can be significantly improved by seamlessly combining the integrated information of the hetero-manifold and the strong generalisation of the support vector machine. Comprehensive experiments show that the proposed HMR achieve advantageous results over the state-of-the-art methods in several challenging cross-modal tasks. [ABSTRACT FROM PUBLISHER]

In this paper, a new version of distance measure for hesitant fuzzy linguistic term sets is developed. The new version of distance measure provides an objective way to handle the diverse dimensions of two HFLTSs, i.e., without shortening the HFLTS to be a linguistic interval or extending the shorter one by adding linguistic terms. The Hamming distance, the Euclidean distance and the corresponding forms are put forward. By the relationship between the distance measure and the similarity measure, some parallel similarity measures are also investigated. As applications of the proposed measures, the issues of pattern recognition, clustering analysis and multi-criteria decision making are considered. [ABSTRACT FROM AUTHOR]

Aristotelian diagrams visualize the logical relations among a finite set of objects. These diagrams originated in philosophy, but recently, they have also been used extensively in artificial intelligence, in order to study (connections between) various knowledge representation formalisms. In this paper, we develop the idea that Aristotelian diagrams can be fruitfully studied as geometrical entities. In particular, we focus on four polyhedral Aristotelian diagrams for the Boolean algebra B4, viz. the rhombic dodecahedron, the tetrakis hexahedron, the tetraicosahedron and the nested tetrahedron. After an in-depth investigation of the geometrical properties and interrelationships of these polyhedral diagrams, we analyze the correlation (or lack thereof) between logical (Hamming) and geometrical (Euclidean) distance in each of these diagrams. The outcome of this analysis is that the Aristotelian rhombic dodecahedron and tetrakis hexahedron exhibit the strongest degree of correlation between logical and geometrical distance; the tetraicosahedron performs worse; and the nested tetrahedron has the lowest degree of correlation. Finally, these results are used to shed new light on the relative strengths and weaknesses of these polyhedral Aristotelian diagrams, by appealing to the congruence principle from cognitive research on diagram design. [ABSTRACT FROM AUTHOR]

Constrained interleaved coded modulation (CICM) is introduced to map coded bits onto higher order signal constellations. A reverse Gray coding (RGC) constellation mapping policy is introduced to map groups of bits onto a selected signal constellation. Then, a CICM interleaver is designed to jointly achieve both the highest possible minimum symbol Hamming distance (MSHD) and the highest possible minimum squared Euclidean distance (MSED) for use with the selected RGC-encoded constellation. It is demonstrated that CICM schemes constructed with simple block codes can be decoded with reduced coding complexity while performing better than more-complicated TCM and BICM-ID schemes known in the literature. [ABSTRACT FROM PUBLISHER]

Locality sensitive hashing (LSH) is an efficient method for solving the problem of approximate similarity search in high-dimensional spaces. Through LSH, a high-dimensional similarity join can be processed in the same way as hash join, making the cost of joining two large datasets linear. By judicially analyzing the properties of multiple LSH algorithms, we propose a generic method to speed up the process of joining two large datasets using LSH. The crux of our method lies in the way which we identify a set of representative points to reduce the number of LSH lookups. Theoretical analyzes show that our proposed method can greatly reduce the number of lookup operations and retain the same result accuracy compared to executing LSH lookups for every query point. Furthermore, we demonstrate the generality of our method by showing that the same principle can be applied to LSH algorithms for three different metrics: the Euclidean distance (QALSH), Jaccard similarity measure (MinHash), and Hamming distance (sequence hashing). Results from experimental studies using real datasets confirm our error analyzes and show significant improvements of our method over the state-of-the-art LSH method: to achieve over 0.95 recall, we only need to operate LSH lookups for at most 15 percent of the query points. [ABSTRACT FROM AUTHOR]

In high-dimensional spaces, accuracy and similarity search by low computing and storage costs are always difficult research topics, and there is a balance between efficiency and accuracy. In this paper, we propose a new structure Similar-PBF-PHT to represent items of a set with high dimensions and retrieve accurate and similar items. The Similar-PBF-PHT contains three parts: parallel bloom filters (PBFs), parallel hash tables (PHTs), and a bitmatrix. Experiments show that the Similar-PBF-PHT is effective in membership query and K-nearest neighbors (K-NN) search. With accurate querying, the Similar-PBF-PHT owns low hit false positive probability (FPP) and acceptable memory costs. With K-NN querying, the average overall ratio and rank-i ratio of the Hamming distance are accurate and ratios of the Euclidean distance are acceptable. It takes CPU time not I/O times to retrieve accurate and similar items and can deal with different data formats not only numerical values. [ABSTRACT FROM AUTHOR]

• Proposing of new method for measuring the distance between pairs of clusters in the dataset. • The proposed distance accurately captures both the variability of the cluster centers as well as the variability of shapes and directions of their respective covariance matrices • The method has a number of advantages including simplicity, interpretability, and computational efficiency • Both the classical and the robust versions of the distances are provided • The distance is illustrated by several motivating examples that demonstrate the need of the new proposed distance and applied to both real and synthetic data • Proving that the Ward distance and the Euclidian distance are equivalent. Clustering methods are based on the computations of both the distances between every pair of the n observations in a multivariate dataset as well as the distances between every pair of clusters in the dataset. The clusters can have different locations and varying elliptical shapes and directions. Numerous methods have been proposed in the literature for computing both of these two types of distances. The contributions of this paper are two folds. First, we propose a new elliptical distance between pairs of clusters in a dataset with different cluster centers and elliptical shapes and directions, Second, we proved analytically that the Ward distance and the Euclidean distance are equivalent. We propose a new classical method for computing the distance between a pair of clusters in the dataset. It is the only distance that does not assume spherical clusters. The proposed classical distances could also be made robust by replacing estimates of location and scale by their respective robust estimators. The proposed distance has a number of advantages including simplicity, interpretability, computational efficiency as well as the ability to accurately capture both the variability of the cluster centers as well as the variability of shapes and directions of their respective covariance matrices. The method is also illustrated by several motivating examples that demonstrate the need of the new proposed distance. The superiority of the proposed method is also demonstrated by application to real-life as well as challenging synthetic data. [ABSTRACT FROM AUTHOR]

In spatial modulation (SM), the information bit stream is divided into two different sets: the transmit antenna index bits (TA-bits) and the amplitude and phase modulation bits (APM-bits). However, the conventional bit-to-symbol mapping (BTS-MAP) scheme maps the APM-bits and the TA-bits independently. For exploiting their joint benefits, we propose a new BTS-MAP rule based on the traditional 2-D Gray mapping rule, which increases the Hamming distance (HD) between the symbol pairs detected from the same transmit antenna (TA) and simultaneously reduces the average HD between the symbol pairs gleaned from different TAs. Based on the analysis of the distribution of minimum Euclidean distance (MED) of SM constellations, we propose a criterion for the construction of a meritorious BTS-MAP for a specific SM setup, with no need for additional feedback links or extra computational complexity. Finally, Monte Carlo simulations are conducted for confirming the accuracy of our analysis. [ABSTRACT FROM AUTHOR]

It is shown that under suitable regularity conditions, differential entropy is O(\sqrt n) -Lipschitz as a function of probability distributions on \mathbb R^n with respect to the quadratic Wasserstein distance. Under similar conditions, (discrete) Shannon entropy is shown to be $O(n)$ -Lipschitz in distributions over the product space with respect to Ornstein’s $\bar d$ -distance (Wasserstein distance corresponding to the Hamming distance). These results together with Talagrand’s and Marton’s transportation-information inequalities allow one to replace the unknown multi-user interference with its independent identically distributed approximations. As an application, a new outer bound for the two-user Gaussian interference channel is proved, which, in particular, settles the missing corner point problem of Costa (1985). [ABSTRACT FROM PUBLISHER]

Clustering is the process of grouping a set of physical or abstract objects into classes of similar objects. The k nearest neighbors is selected by using a predefined distance metric (Hamming distance, Euclidean distance etc) to sense the selected similarity metrics. With KNN technique dimensionality reduction is applied to avoid the effects of the curse of dimensionality. The PSO algorithm optimizes the performance of a KNN classifier by finding the best k values for production of the best clustering performance. This paper presents enhanced method of clustering using K-Nearest neighbor with particle swarm optimization (KNN_PSO) over KNearest neighbor (KNN) algorithms which can be traceable even for large datasets. The KNN, PSO and KNN PSO clustering algorithms are analyzed for different datasets using accuracy as the performance measure. The experimental results exhibit that the clustering using K-Nearest Neighbor with PSO approach outperforms K-Nearest Neighbor algorithm with respect to overall accuracy. [ABSTRACT FROM AUTHOR]

In this article we have introduced the concept of similarity measure for interval-valued intuitionistic fuzzy soft sets based on distance between two interval-valued intuitionistic fuzzy soft sets, some examples and basic properties are also studied. An algorithm is developed in intuitionistic fuzzy soft set setting for a decision making method. Lastly a fictitious numerical example is given to illustrate possible application in a medical diagnosis problem. [ABSTRACT FROM AUTHOR]

In this article I will start in the first part with an introduction to unsupervised learning methods, specifically the K-Means clustering algorithm, the algorithm achieved using the Euclidean distance. In the second part, we modified the K-Means algorithm, which is to say, I realized it with the help of Hamming, and then we compared the clustering time, and we made a parallel between the two algorithms (the K-means algorithm conducted with the Euclidean distance and the algorithm K-Means achieved using the Hamming distance). [ABSTRACT FROM AUTHOR]

This paper presents an extension of the Elias bound on the minimum distance of codes for discrete alphabets with general, possibly infinite valued, distances. The bound is obtained by combining a previous extension of the Elias bound, introduced by Blahut, with an extension of a bound previously introduced by the author which builds upon ideas of Gallager, Lovász, and Marton. The result can in fact be interpreted as a unification of the Elias bound and of Lovász’s bound on graph (or zero-error) capacity, both being recovered as particular cases of the one presented here. Previous extensions of the Elias bound by Berlekamp, Blahut, and Piret are shown to be included as particular cases of our bound. Applications to the reliability function are then discussed. [ABSTRACT FROM AUTHOR]

Traditional centroid-based clustering algorithms for heterogeneous data with numerical and non-numerical features result in different levels of inaccurate clustering. This is because the Hamming distance used for dissimilarity measurement of non-numerical values does not provide optimal distances between different values, and problems arise from attempts to combine the Euclidean distance and Hamming distance. In this study, the mutual information (MI)-based unsupervised feature transformation (UFT), which can transform non-numerical features into numerical features without information loss, was utilized with the conventional k-means algorithm for heterogeneous data clustering. For the original non-numerical features, UFT can provide numerical values which preserve the structure of the original non-numerical features and have the property of continuous values at the same time. Experiments and analysis of real-world datasets showed that, the integrated UFT-k-means clustering algorithm outperformed others for heterogeneous data with both numerical and non-numerical features. [ABSTRACT FROM AUTHOR]