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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]

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]

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]