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Axiomatization is a significant and challenging task in the field of fuzzy variable precision rough sets, where research is currently limited. This paper aims to address this gap by defining and characterizing 14 types of L-fuzzy variable precision rough sets (LFVPRS for short). First, we introduce three fundamental LFVPRSs generated by Euclidean, mediate, and associate L-fuzzy relations. Second, we present their single axiomatic characterizations using the product of L-fuzzy sets. Lastly, we provide single axiomatic characterizations for another 11 types of LFVPRSs, which are generated by various compositions of reflexive, transitive, symmetry, Euclidean, mediate, and associate L-fuzzy relations. These single axiomatic characterizations are entirely innovative and have not been explored, even in the context of classical rough sets and fuzzy rough sets. [ABSTRACT FROM AUTHOR]

As combinations of neighborhood rough sets and multigranulation rough sets (MRSs), optimistic and pessimistic neighborhood MRSs can handle complex information systems and characterize problems from multiple perspectives. Nevertheless, they require complete inclusion between neighborhood granules and target concepts, which may weaken their fault tolerance. To overcome the challenge, this paper proposes neighborhood MRSs based on variable precision neighborhood (VMRSs), which allow a certain degree of misclassification and noise in data. In VMRSs, we assign different weights to different attribute subsets to distinguish their importance in learning. In addition to investigating the properties of the VMRS model, we focus on the methods of obtaining its required multiple attribute subsets and their weights. Next, we introduce two applications of the VMRS model. One is using it to construct an indicator for evaluating attribute clustering and attribute subset weighting methods. The other is employing it for attribute reduction. Based on distribution distances, we develop a heuristic algorithm framework for obtaining the proposed reducts. The mechanism and applications of VMRSs are explained through a case study on a medical diagnosis issue. Finally, the experiments on real datasets illuminate the effectiveness and superiority of the methods and algorithms in the paper. [ABSTRACT FROM AUTHOR]

Axiomatization is a lively research direction in fuzzy rough set theory. Fuzzy variable precision rough set (FVPRS) incorporates fault-tolerant factors to fuzzy rough set, so its axiomatic description becomes more complicated and difficult to realize. In this paper, we present an axiomatic approach to FVPRSs based on residuated lattice (L-fuzzy variable precision rough set (LFVPRS)). First, a pair of mappings with three axioms is utilized to characterize the upper (resp., lower) approximation operator of LFVPRS. This is distinct from the characterization on upper (resp., lower) approximation operator of fuzzy rough set, which consists of one mapping with two axioms. Second, utilizing the notion of correlation degree (resp., subset degree) of fuzzy sets, three characteristic axioms are grouped into a single axiom. At last, various special LFVPRS generated by reflexive, symmetric and transitive L-fuzzy relation and their composition are also characterized by axiomatic set and single axiom, respectively. [ABSTRACT FROM AUTHOR]

The comparable property (or inclusion property) is the basic property of rough set theory. Unfortunately, the well-known granular variable precision fuzzy rough set does not satisfy the comparable property. To remedy this gap, a novel granular variable precision fuzzy rough set model with comparable property is proposed and discussed. Firstly, by analyzing the existing granular precision fuzzy rough set models, we find the reason that they do not satisfy the comparable property. Then, we give a new granular precision fuzzy rough set model with the comparable property. Secondly, we study the basic properties, characterization theorem and accuracy measure of the new model. Thirdly, we apply the novel model in the study of fuzzy decision system. An attribute reduction method is developed, and the corresponding attribute reduction algorithm is designed. Finally, by using public accessible datasets, we make a series of experiments to verify the effectiveness and reliability of our method and make comparisons with some existing attribute reduction methods. [ABSTRACT FROM AUTHOR]

As the utilization of CNN increases, many studies on lightweight, such as pruning, quantization, and compression, have been conducted to use CNN models in servers and edge devices. Studies have revealed that quantization greatly reduces the complexity of CNN models while lowering accuracy to a negligible level. CNN models with bit precision lowered from the existing 64/32 floating point to 16, 8, and 4 fixed points are being announced. Therefore, this paper proposes a variable precision multiplier that can select between 16 bits and 8 bits of precision. It consists of four 8-bit booth multipliers. When 16-bit multiplication is selected, the final product is calculated from four partial products, and when 8-bit multiplication is selected, four multiplications are possible simultaneously. The proposed multiplier was designed with Verilog HDL, and its function was verified in ModelSim. And it was synthesized for Altera Cyclone III EP3C16F484C6 using Quartus II 13.1.0 Web Edition. The proposed variable multiplier has increased combinational logic compared to general 8-bit/16-bit booth multipliers, and the clock speed is reduced by 65% and 82%, respectively. However, it can process four 8-bit multiplications within 1.68 times of normal 8-bit multiplication processing time and can process 16-bit multiplication within 75% of the normal 16-bit multiplication processing time. Therefore, the proposed multiplier is expected to increase speed and energy efficiency by selecting bit precision according to the layer in the CNN model. [ABSTRACT FROM AUTHOR]

As a useful extension of rough sets, multigranulation rough sets (MGRSs) can be used to deal with a variety of complex data. Numerous significant advances have been achieved by generalizing MGRSs. However, most of the existing findings of MGRSs are sensitive to misclassification and noise in data. Furthermore, the studies of attribute reduction based on MGRSs have received little attention. To fill such gaps, this paper proposes an extended model of MGRSs named variable precision multigranulation rough sets (VPMGRSs) by introducing rough membership function and approximation parameters in variable precision rough sets (VPRSs) into the multigranulation environment. After giving some basic properties of VPMGRSs, we investigate the relationships between VPMGRSs and VPRSs, pessimistic MGRSs, and generalized MGRSs. In addition, several VPMGRSs-based attribute reductions are introduced, and it is proved that some of them are equivalent when the parameters in the model meet specific requirements. Finally, we propose a heuristic algorithm for α -lower distribution reduct and illustrate its effectiveness and efficiency by a comparative experiment on real datasets. [ABSTRACT FROM AUTHOR]

In this brief, a variable-precision approximate floating-point multiplier is proposed for energy efficient deep learning computation. The proposed architecture supports approximate multiplication with BFloat16 format. As the input and output activations of deep learning models usually follow normal distribution, inspired by the posit format, for numbers with different values, different precisions can be applied to represent them. In the proposed architecture, posit encoding is used to change the level of approximation, and the precision of the computation is controlled by the value of product exponent. For large exponent, smaller precision multiplication is applied to mantissa and for small exponent, higher precision computation is applied. Truncation is used as approximate method in the proposed design while the number of bit positions to be truncated is controlled by the values of the product exponent. The proposed design can achieve 19% area reduction and 42% power reduction compared to the normal BFloat16 multiplier. When applying the proposed multiplier in deep learning computation, almost the same accuracy as that of normal BFloat16 multiplier can be achieved. [ABSTRACT FROM AUTHOR]

The performance of transcendental functions is important to high-performance applications. Various customized implementations of transcendental functions in practice to obtain better performance for some particular applications, but specializing the transcendental functions for each individual application cannot scale with the increase and diversity of the latter. It is thus of vital importance to design and implement an automatic generator for transcendental functions. This article implements an automatic generator TGen (transcendental function generator) for variable precision transcendental functions. Given a specific computation interval, TGen can automatically generate independent implementations with different precisions for a transcendental function, and select the most suitable version for the target by means of a code filtering strategy. Our generator can now support the automatic generation of 18 representative transcendental functions. The experimental results show that TGen can generate code with the unfixed accuracy, and the performance of the generated code is superior to that of the code generated by metalibm. More specifically, when compiled with the GCC compiler, the code generated by TGen can provide a mean speedup of 1.84 × over that of a metalibm's version, while the speedup of TGen's code over that of the metalibm is 1.27 × when compiled with the SW5CC compiler. [ABSTRACT FROM AUTHOR]

Multi-label attribute reduction as a common dimensionality reduction technique has obtained widely research in recent years. Most existing multi-label attribute reduction methods adopt discretization to deal with mixed data and have strict requirements on the condition of sample classification. However, the process of discretization may lead to information loss, moreover, strict conditions will increase the possibility of a sample classified into a wrong class. Based on this, we construct a multi-label attribute reduction method based on variable precision fuzzy neighborhood rough set. The main motivation is that the variable precision fuzzy neighborhood rough set can process multiple types of data without discretization and tolerate noisy data. Specifically, we first use the parameterized fuzzy neighborhood granule to define the fuzzy decision and decision class of each sample under different labels. Then, the fuzzy decision and decision classes under different labels are fused into the entire multi-label learning space. Finally, a multi-label attribute reduction algorithm is designed according to the defined maximum attribute significance criterion. Our experiments are conducted on a series of multi-label datasets, and the experimental results verify that the proposed algorithm achieves better classification performance than other state-of-the-art comparison algorithms.

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The wide application of artificial intelligence technology in various fields has accelerated the pace of people exploring the hidden information behind large amounts of data. People hope to use data mining methods to conduct effective research on higher education management, and decision tree classification algorithm as a data analysis method in data mining technology, high-precision classification accuracy, intuitive decision results, and high generalization ability make it become a more ideal method of higher education management. Aiming at the sensitivity of data processing and decision tree classification to noisy data, this paper proposes corresponding improvements, and proposes a variable precision rough set attribute selection standard based on scale function, which considers both the weighted approximation accuracy and attribute value of the attribute. The number improves the anti-interference ability of noise data, reduces the bias in attribute selection, and improves the classification accuracy. At the same time, the suppression factor threshold, support and confidence are introduced in the tree pre-pruning process, which simplifies the tree structure. The comparative experiments on standard data sets show that the improved algorithm proposed in this paper is better than other decision tree algorithms and can effectively realize the differentiated classification of higher education management. [ABSTRACT FROM AUTHOR]

The model of a generalized variable precision rough set is one of the variable precision rough sets used to solve some problems and measurements confront us that was difficult from the view point of science. The behavior of the radio contaminants in the environment is one of these measurements. Throughout this paper, we introduce and study a generalization variable precision rough set via a topological minimal structure. Some characteristics related to generalized upper and lower approximation with a variable precision by minimal structures will be discussed. A dispersion model which is the necessity to predict atmospheric path and danger from an atmospheric plume of hazardous materials will be applied with different types of examples. [ABSTRACT FROM AUTHOR]

While convolutional neural networks (CNNs) continue to renew state-of-the-art performance across many fields of machine learning, their hardware implementations tend to be very costly and inflexible. Neuromorphic hardware, on the other hand, targets higher efficiency but their inference accuracy lags far behind that of CNNs. To bridge the gap between deep learning and neuromorphic computing, we present bitstream-based neural network, which is both efficient and accurate as well as being flexible in terms of arithmetic precision and hardware size. Our bitstream-based neural network (called SC-CNN) is built on top of CNN but inspired by stochastic computing (SC), which uses bitstreams to represent numbers. Being based on CNN, our SC-CNN can be trained with backpropagation, ensuring very high inference accuracy. At the same time our SC-CNN is deterministic, hence repeatable, and is highly accurate and scalable even to large networks. Our experimental results demonstrate that our SC-CNN is highly accurate up to ImageNet-targeting CNNs, and improves efficiency over conventional digital designs ranging through 50–100% in operations-per-area depending on the CNN and the application scenario, while losing <1% in recognition accuracy. In addition, our SC-CNN implementations can be much more fault-tolerant than conventional digital implementations. [ABSTRACT FROM AUTHOR]

Recently some scientific computing users have discovered that they can replace 64-bit with 32-bit operations for carefully selected portions of the computation, and still retain acceptable accuracy in the final results. In addition, developers of some emerging applications such as machine learning have discovered that they can achieve acceptable results with only 16-bit precision in certain portions of the code. At the other end of the precision spectrum, some users have explored using 128-bit arithmetic in some particularly demanding applications, while others have done computations using much higher precision—hundreds or even thousands of digits. Such work has underscored the need to develop new mathematical and software frameworks to support a dynamically variable level of precision, and, more generally, to rethink what "reproducibility" means in a variable precision environment. This article summarizes some of the work being done in this arena, and lists research problems that need to be solved. [ABSTRACT FROM AUTHOR]

Stochastic computing offers an area‐efficient solution for power‐greedy computations in error‐resilient applications such as image processing. However, stochastic computing produces only approximated results and suffers from long latency especially for multiplication. The authors present a multiplier design technique for stochastic computing which guarantees exact output and has latency in the order of 2N (N = input precision), utilising the counter for unary‐to‐binary conversion. Compared to state‐of‐the‐art deterministic methods the proposed design is faster by a factor of 2N. Besides, the area of proposed design scales up in proportion to N instead of N2, as opposed to conventional binary multipliers. The design technique can be further extended for multiple inputs and parallel computing, Extensive mathematical analysis and simulation results are presented for each variation throughout this Letter. [ABSTRACT FROM AUTHOR]

The high performance, power efficiency and reconfigurable characteristic of FPGA attract more and more attention in big data processing. In scientific data analytics, besides the consideration of computing performance, accuracy of the results and dynamic range of data representation are critical features that must be considered. At present, the floating-point IP cores in FPGA design use IEEE standard for floating-point arithmetic – IEEE 754. For FPGA based scientific data application, improving existing floating-point IP cores is a significant way to obtain better results. Posit is a floating-point arithmetic format first proposed by John L. Gustafson in 2017. In posit, the variable precision and efficient representation of exponent contribute a higher accuracy and larger dynamic range than IEEE 754. This work researches on the FPGA implementation of posit arithmetic for extending floating-point IP cores for FPGA based scientific data analytics. We design the logic for hardware implementation and implement it on FPGA. We compare the precision representation, dynamic range and performance of implemented posit FPU (Floating-Point Unit) with IEEE 754 floating-point IP cores. Posit exhibits better superiority in precision representation and dynamic range than IEEE 754, and through further optimization of the implementation, posit can be a good candidate for floating-point IP cores. [ABSTRACT FROM AUTHOR]

Given the same sensory stimuli in the same task, human observers do not always make the same response. Well-known sources of behavioral variability are sensory noise and guessing. Visual short-term memory (STM) studies have suggested that the precision of the sensory noise is itself variable. However, it is unknown whether precision is also variable in perceptual tasks without a memory component. We searched for evidence for variable precision in 11 visual perception tasks with a single relevant feature, orientation. We specifically examined the effect of distractor stimuli: distractors were absent, homogeneous and fixed across trials, homogeneous and variable, or heterogeneous and variable. We first considered 4 models: with and without guessing, and with and without variability in precision. We quantified the importance of both factors using 6 metrics: factor knock-in difference, factor knock-out difference, and log factor posterior ratio, each based on AIC or BIC. According to all 6 metrics, we found strong evidence for variable precision in 5 experiments. Next, we extended our model space to include potential confounding factors: the oblique effect and decision noise. This left strong evidence for variable precision in only 1 experiment, in which distractors were homogeneous but variable. Finally, when we considered suboptimal decision rules, the evidence also disappeared in this experiment. Our results provide little evidence for variable precision overall and only a hint when distractors are variable. Methodologically, the results underline the importance of including multiple factors in factorial model comparison: Testing for only 2 factors would have yielded an incorrect conclusion. [ABSTRACT FROM AUTHOR]

Exploring rough set theory in the viewpoint of multi-granulation gradually attracts scholars attention in recent years. To handle uncertainty problems with grey information, in this paper, we devise a variable precision grey multi-granulation rough set (VPG-MGRS) by combining with grey system theory and multi-granulation rough set. We utilize the grey relational relation for further establishing multiple granular structures and then adopt a threshold to control the number of condition satisfied. After discussing several important properties of VPG-MGRS, we discover that the proposed VPG-MGRS model is a generalized classical MGRS. Meanwhile, we redefine the significance measures of attribute based on VPG-MGRS for attribute reduction. Last but not least, theoretical studies and numerical experiments have demonstrated that the VPG-MRGS-based attribute reduction algorithm is of feasibility and effectivity in handling uncertainty problems with grey information and provides a new technique for knowledge discovery, and the VPG-MGRS model enlarges the application fields of MGRS. [ABSTRACT FROM AUTHOR]

With the development of the diversified economic union, the power grid enterprises’ auxiliary industries are continuing to grow and develop faster. However, in the process of development, power grid enterprises are still faced with the problem of low efficiency of the management of main and auxiliary and resource allocation and utilization. Thus, the synergistic development evaluation for power grid enterprises’ main and auxiliary industries has a strong practical significance. It can help the managers to find the short board of each industry and search for the exploration direction for improvement to promote the sustainable development of the main and auxiliary industries comprehensively. It can also provide the reference for improving the management level of power grid enterprises. Information fusion technology, as a process of information processing for decision making, can make use of multi-source information synergistically to get a more objective and more essential understanding of the same thing or the same goal. It has been applied to many fields in a mature way. Based on the characteristics of each industry, this paper constructs a synergistic effect evaluation index system of the main and auxiliary industries from the aspects of management foundation, resource integration, operational efficiency and effectiveness. The variable precision fuzzy rough set (VPFRS) is introduced to screen the index system, eliminate redundant indexes, retain key indexes and improve the efficiency and accuracy of evaluation effectively. Meanwhile, based on the characteristic of dealing with the imprecise problem of the vague set, this paper establishes the evaluation model based on information fusion technology of the variable precision fuzzy rough set and vague set (VPFRS-Vague). In order to verify the validity of the model, five typical companies belonging to power grid enterprises are selected as examples for analysis to prove the validity and applicability of the evaluation method. [ABSTRACT FROM AUTHOR]