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An improved ORB feature point purification method has been proposed to address the problem of large feature point matching error and low image registration rate in the oriented FAST and rotated BRIEF (ORB) feature point color image matching algorithm. Pure virtual quaternions were used to represent the color image pixels in this method, and an improved FAST algorithm was used to detect the color feature points at first. The firework algorithm has been used to divide the detected feature points into key areas, auxiliary areas, and small influence areas, depending on the degree of attachment. The feature points of the key area and the subsidiary area are the required feature points. In order to further improve the efficiency of matching the color image feature points, the firework explosion radius formula and the explosion number formula in the firework algorithm have been improved, and an improved firework algorithm is proposed. This improved algorithm purifies the quaternion-represented color image feature points. For feature matching, the hamming distance was used. Experiments show that, when compared to the traditional ORB algorithm, the improved algorithm retains the key feature points of the color image with high accuracy, removes a large number of irrelevant feature points and noise points, and provides significantly higher accuracy and efficiency of color image matching. [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]

The Oriented FAST and Rotated BRIEF (ORB) algorithm has the problem that the extracted feature points are overconcentrated or even overlapped, leading to information loss of local image features. A homogenized ORB algorithm using dynamic thresholds and improved quadtree method is proposed in this paper, named Quadtree ORB (QTORB). In the feature point extraction stage, a new dynamic local threshold calculation method is proposed to enhance the algorithm's ability to extract feature points at homogeneous regions. Then, a quadtree method is improved and adopted to manage and optimize feature points to eliminate those excessively concentrated and overlapping feature points. Meanwhile, in the feature points optimization process, different quadtree depths are set at different image pyramid levels to prevent excessive splitting of the quadtree and increase calculation speed. In the feature point description stage, local gray difference value information is introduced to enhance the saliency of the feature description. Finally, the Hamming distance is used to match points and RANSAC is used to avoid mismatches. Two datasets, namely, the optical image dataset and SAR image dataset, are used in the experiment. The experimental result shows that, considering accuracy and real-time efficiency, the QTORB can effectively improve the distribution uniformity of feature points. [ABSTRACT FROM AUTHOR]

With respect to multicriteria group decision-making (MCGDM) problems in which the experts have different priority levels, the criteria values are in the form of Pythagorean fuzzy uncertain linguistic variables (PFULVs), and the information about weights of experts and criteria is completely unknown, a novel decision-making method is developed. Firstly, the concept of PFULV is defined, and some operational laws, score function, accuracy function, and normalized Hamming distance of PFULVs are presented. Then, to aggregate information given by all experts, the Pythagorean fuzzy uncertain linguistic prioritized weighted averaging aggregation (PFULPWAA) operator and the Pythagorean fuzzy uncertain linguistic prioritized weighted geometric aggregation (PFULPWGA) operator are proposed. Furthermore, in order to get a comprehensive evaluation value for each alternative, the Pythagorean fuzzy uncertain linguistic Maclaurin symmetric mean aggregation (PFULMSMA) operator and the weighted PFULMSMA (WPFULMSMA) operator are proposed. Moreover, to obtain the information about the weights of criteria, the model based on grey relational analysis (GRA) method is established. Finally, a method of MCGDM with PFULVs is developed, and an application example is given to illustrate the validity and feasibility of the provided procedure. [ABSTRACT FROM AUTHOR]

A stochastic algorithm for obtaining feasible initial populations to the Vehicle Routing Problem with Time Windows is presented. The theoretical formulation for the Vehicle Routing Problem with Time Windows is explained. The proposed method is primarily divided into a clustering algorithm and a two-phase algorithm. The first step is the application of a modified k-means clustering algorithm which is proposed in this paper. The two-phase algorithm evaluates a partial solution to transform it into a feasible individual. The two-phase algorithm consists of a hybridization of four kinds of insertions which interact randomly to obtain feasible individuals. It has been proven that different kinds of insertions impact the diversity among individuals in initial populations, which is crucial for population-based algorithm behavior. A modification to the Hamming distance method is applied to the populations generated for the Vehicle Routing Problem with Time Windows to evaluate their diversity. Experimental tests were performed based on the Solomon benchmarking. Experimental results show that the proposed method facilitates generation of highly diverse populations, which vary according to the type and distribution of the instances. [ABSTRACT FROM AUTHOR]

For a multiple-attribute group decision-making problem with interval intuitionistic fuzzy sets, a method based on extended TODIM is proposed. First, the concepts of interval intuitionistic fuzzy set and its algorithms are defined, and then the entropy method to determine the weights is put forward. Then, based on the Hamming distance and the Euclidean distance of the interval intuitionistic fuzzy set, both of which have been defined, function mapping is given for the attribute. Finally, to solve multiple-attribute group decision-making problems using interval intuitionistic fuzzy sets, a method based on extended TODIM is put forward, and a case that deals with the site selection of airport terminals is given to prove the method. [ABSTRACT FROM AUTHOR]

Frequency diversity is used to reduce the effect of destructive fading, so as to improve the communication quality, by passing the information symbols through multiple independently faded paths, and ensure that reliable communication is possible as long as one of these paths is strong. In this paper a multiorder orthogonal frequency division multiplexing (OFDM) frequency diversity approach using properties of order theory and Hamming distance is proposed. The frequency diversity is obtained by specifying proper correlations among the transmitted symbols. As subchannels experience independent fading, at least one of the symbols may have robust signal, which can be used by the receiver to detect other symbols. Considering bit error rate (BER) performance, power consumption, bandwidth utilization, and practical implementation expense, simulation results show that the proposed approach outperforms other OFDM diversity techniques, such as Maximal Ratio Combination (MRC) and Space Frequency Block Coding (SFBC). [ABSTRACT FROM AUTHOR]

Selection and scheduling are an important topic in production systems. To tackle the order acceptance and scheduling problem on a single machine with release dates, tardiness penalty, and sequence-dependent setup times, in this paper a diversity controlling genetic algorithm (DCGA) is proposed, in which a diversified population is maintained during the whole search process through survival selection considering both the fitness and the diversity of individuals. To measure the similarity between individuals, a modified Hamming distance without considering the unaccepted orders in the chromosome is adopted. The proposed DCGA was validated on 1500 benchmark instances with up to 100 orders. Compared with the state-of-the-art algorithms, the experimental results show that DCGA improves the solution quality obtained significantly, in terms of the deviation from upper bound. [ABSTRACT FROM AUTHOR]