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Abstract: Hesitant fuzzy cognitive information provides an effective and convenient form for expressing human subjective cognition about the research object, i.e., hesitant fuzzy sets (HFSs). Studies on decision making with HFSs have become an important branch in decision theory, in which operational laws of hesitant fuzzy elements (HFEs) play a core role in the solution. However, current HFE computational laws have the disadvantages of subjectivity and dimensional problems. Therefore, how to define an objective HFE operational rule without dimensional problems is an open issue. This paper introduces an idempotent HFE computing rule to overcome current disadvantages. The weighted mean of HFEs under the developed computing rule is further discussed. In addition, a novel comparison law between HFEs is proposed. The property of idempotence is introduced to provide an intuitive integrated result of HFEs. To decrease the integrated HFEs dimensions, the sliding window model is utilized. Fundamental mathematical properties of the developed operations are discussed. Furthermore, the normal weighted means of HFEs are extended by using the developed idempotent computing rules. Finally, a novel comparison law for comparing HFEs is designed, which is further used to provide a multiattribute decision procedure. Additive idempotent is developed as a special and intuitive property for the HFE additive operation. Normal weighted means of HFEs, including arithmetic and geometric means, are correspondingly derived. Numerical examples have shown that the proposed HFE operational laws are valid, which can effectively decrease the dimensions of integrated results. The developed idempotent computing rules provide a novel HFE algebra structure, which includes the additive operation, multiplicative operation, scalar multiplication and power operation. By using the sliding window model, the developed idempotent computing rules can effectively reduce the integrated HFEs dimensions. The strength of the developed computational model is that integrating two identical pieces of cognitive information produces the same result. In addition, the modified HFE comparison law can overcome the drawback of current comparison laws, and a much more reasonable comparison result can be obtained. PubDate: 2021-10-12
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Abstract: neurolib is a computational framework for whole-brain modeling written in Python. It provides a set of neural mass models that represent the average activity of a brain region on a mesoscopic scale. In a whole-brain network model, brain regions are connected with each other based on biologically informed structural connectivity, i.e., the connectome of the brain. neurolib can load structural and functional datasets, set up a whole-brain model, manage its parameters, simulate it, and organize its outputs for later analysis. The activity of each brain region can be converted into a simulated BOLD signal in order to calibrate the model against empirical data from functional magnetic resonance imaging (fMRI). Extensive model analysis is made possible using a parameter exploration module, which allows one to characterize a model’s behavior as a function of changing parameters. An optimization module is provided for fitting models to multimodal empirical data using evolutionary algorithms. neurolib is designed to be extendable and allows for easy implementation of custom neural mass models, offering a versatile platform for computational neuroscientists for prototyping models, managing large numerical experiments, studying the structure–function relationship of brain networks, and for performing in-silico optimization of whole-brain models. PubDate: 2021-10-12
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Abstract: In order to obtain high satisfaction from experts, the consensus reaching process (CRP) is an essential requirement for dealing with multi-criteria group decision making (MCGDM) problems. Single-valued neutrosophic number (SVNN) is an effective tool to describe the uncertainty of the expert cognition. Thus, we develop a consensus reaching model for single-valued neutrosophic MCGDM in this paper. First, each expert makes his/her judgment on each alternative with respect to multiple criteria by SVNNs, and the group solution is obtained by the generalized Shapley single-valued neutrosophic Choquet integral (GS-SVNCI) operator to consider the correlations among elements comprehensively. Second, the projection-based consensus measure is proposed to reflect the agreement between the individual and collective opinions. Then, a threshold value is used to determine the CRP whether to be executed based on the expert’s consensus level. If yes, the feedback mechanism provides the experts with personalized adjustment advices based on their psychic utility to group pressure. Finally, we illustrate the feasibility of the proposed consensus model by an example and analyze the superiority by comparing with some existing MCGDM methods and different CRP models. The developed consensus model can consider interrelationships between experts, which is more effective and reasonable to obtain the collective resolution. Further, the consensus measure based on the projection can comprehensively reflect the closeness between the individual and collective opinions. In addition, the personalized adjustment advices considering the experts’ psychic utility to group pressure improve their acceptance of these advices. PubDate: 2021-10-11
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Abstract: A generalized predictive control method based on neuro-fuzzy network (NFN-GPC) is presented for a 1000-MW ultra-supercritical (USC) power plant to improve control performance. First, to decrease the nonlinearity, local linear models are elaborately constructed for approximating the studied system by virtue of neuro-fuzzy network (NFN). Second, a compensation mechanism is delicately developed to further increase the accuracy of local models. Through gauss function and B-spline function, the memberships of local models which represent the weights of local regions are determined. Finally, based on the obtained models, a multi-variable generalized predictive controller is designed to realize the optimal control over the whole operating region combined with the membership of the current neuro-fuzzy network. This scheme closely connects engineering with artificial intelligence; compared with traditional generalized predictive control, the merit of proposed NFN-GPC is that it can capture the details over the whole operating range which can get more accurate and faster control effects. The simulation results show that the proposed neuro-fuzzy generalized predictive control method can achieve the satisfactory performance even in the case of strong coupling and nonlinearity. In conclusion, the proposed method is an effective long-term approach to control the USC power plant. PubDate: 2021-10-08
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Abstract: The performance of biometric modalities based on things done by the subject, like signature and text-based recognition, may be affected by the subject’s state. Fatigue is one of the conditions that can significantly affect the outcome of handwriting tasks. Recent research has already shown that physical fatigue produces measurable differences in some features extracted from common writing and drawing tasks. It is important to establish to which extent physical fatigue contributes to the intra-person variability observed in these biometric modalities and also to know whether the performance of recognition methods is affected by fatigue. In this paper, we assess the impact of fatigue on intra-user variability and on the performance of signature-based and text-based writer recognition approaches encompassing both identification and verification. Several signature and text recognition methods are considered and applied to samples gathered after different levels of induced fatigue, measured by metabolic and mechanical assessment and also by subjective perception. The recognition methods are dynamic time warping and multi-section vector quantization, for signatures, and allographic text-dependent recognition for text in capital letters. For each fatigue level, the identification and verification performance of these methods is measured. Signature shows no statistically significant intra-user impact, but text does. On the other hand, performance of signature-based recognition approaches is negatively impacted by fatigue, whereas the impact is not noticeable in text-based recognition, provided long enough sequences are considered. PubDate: 2021-10-03
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Abstract: Noninvasive brain–computer interface (BCI)-based electroencephalograms (EEGs) have made great progress in cognitive activities detection. However, the decoding of premovements from EEG signals remains a challenge for noninvasive BCI. This work aims to decode human intention (movement or rest) before movement onset from EEG signals. We propose to decode premovement patterns from movement-related cortical potential activities with task-related component analysis and canonical correlation patterns (TRCA+CCPs). Specifically, we first optimize the MRCP data with the spatial filter TRCA. CCPs are then extracted from the optimized signals. The extracted CCPs are classified with the linear discriminated analysis classifier. We applied the classification in a sliding window, which changes from readiness potential (RP section) to movement-monitoring potential (MMP section). The classification result on event-related desynchronization (ERD) indicates that the motor cortex becomes active as the limbs move. When applying classification between elbow flexion and rest, the proposed TRCA+CCP method achieves an accuracy of 0.9001±0.0997 in the RP section. The previous methods, discriminative canonical pattern matching + common spatial pattern (DCPM+CSP) and the optimized DCPM+CSP method, exhibit accuracy values of 0.7827± 0.1276 and 0.8141±0.1295 for the RP section, respectively. Compared with these methods, the proposed TRCA+CCP method achieves higher average accuracy in the RP section. The proposed TRCA+CCP method can decode the patterns in the RP section efficiently, which indicates that the premovement patterns in EEG signals can be decoded before execution of the movement. The system is expected to assist movement detection in ERD analysis. PubDate: 2021-10-02
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Abstract: Advantageous property of behavioural signals (e.g. handwriting), in contrast to morphological ones (e.g. iris, fingerprint, hand geometry), is the possibility to ask a user to perform many different tasks. This article summarises recent findings and applications of different handwriting/drawing tasks in the field of security and health. More specifically, it is focused on on-line handwriting and hand-based interaction, i.e. signals that utilise a digitizing device (specific devoted or general-purpose tablet/smartphone) during the realization of the tasks. Such devices permit the acquisition of on-surface dynamics as well as in-air movements in time, thus providing complex and richer information when compared to the conventional “pen and paper” method. Although the scientific literature reports a wide range of tasks and applications, in this paper, we summarize only those providing competitive results (e.g. in terms of discrimination power) and having a significant impact in the field. PubDate: 2021-10-01
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Abstract: Emotion detection classifiers traditionally predict discrete emotions. However, emotion expressions are often subjective, thus requiring a method to handle compound and ambiguous labels. We explore the feasibility of using crowdsourcing to acquire reliable soft-target labels and evaluate an emotion detection classifier trained with these labels. We hypothesize that training with labels that are representative of the diversity of human interpretation of an image will result in predictions that are similarly representative on a disjoint test set. We also hypothesize that crowdsourcing can generate distributions which mirror those generated in a lab setting. We center our study on the Child Affective Facial Expression (CAFE) dataset, a gold standard collection of images depicting pediatric facial expressions along with 100 human labels per image. To test the feasibility of crowdsourcing to generate these labels, we used Microworkers to acquire labels for 207 CAFE images. We evaluate both unfiltered workers and workers selected through a short crowd filtration process. We then train two versions of a ResNet-152 neural network on soft-target CAFE labels using the original 100 annotations provided with the dataset: (1) a classifier trained with traditional one-hot encoded labels and (2) a classifier trained with vector labels representing the distribution of CAFE annotator responses. We compare the resulting softmax output distributions of the two classifiers with a 2-sample independent t-test of L1 distances between the classifier’s output probability distribution and the distribution of human labels. While agreement with CAFE is weak for unfiltered crowd workers, the filtered crowd agree with the CAFE labels 100% of the time for happy, neutral, sad, and “fear + surprise” and 88.8% for “anger + disgust.” While the F1-score for a one-hot encoded classifier is much higher (94.33% vs. 78.68%) with respect to the ground truth CAFE labels, the output probability vector of the crowd-trained classifier more closely resembles the distribution of human labels (t = 3.2827, p = 0.0014). For many applications of affective computing, reporting an emotion probability distribution that accounts for the subjectivity of human interpretation can be more useful than an absolute label. Crowdsourcing, including a sufficient filtering mechanism for selecting reliable crowd workers, is a feasible solution for acquiring soft-target labels. PubDate: 2021-09-27
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Abstract: Multi-attribute group decision-making (MAGDM) is one of the most active research fields in modern social cognition and decision science theory. An obvious challenge in MAGDM problems is that it is not easy to appropriately describe decision-makers’ (DMs’) cognitive information, which is because the cognition of DMs is usually diverse and contains a lot of uncertainties and fuzziness. The recently proposed q-rung dual hesitant fuzzy set (q-RDHFS), encompassing diverse cognition and providing wide information space, has been proved to be effective to depict DMs’ cognitive information in the MAGDM process. However, existing operations and aggregation operators of q-RDHFSs still have limitations, which result in the weakness of existing q-RDHFS-based MAGDM methods. Therefore, this paper aims at introducing new operational rules and aggregation operators to deal with q-rung dual hesitant fuzzy information. To this end, we first propose a wide range of generalized operations for q-rung dual hesitant fuzzy elements (q-RDHFEs) based on Archimedean t-norm and t-conorm. Second, we put forward some new aggregation operators by generalizing the recently invented extended power average (EPA) operator into q-RDHFSs. Existing literature has revealed the powerfulness and flexibility of the EPA operator over the classical power average operator. Finally, a new MAGDM approach based on the proposed operators is developed. Our proposed method can effectively handle MAGDM problems with q-rung dual hesitant fuzzy cognitive information. Some numerical examples are conducted to demonstrate the validity of the new MAGDM method. Further, we conduct parameter analysis and comparative analysis to prove the flexibility and superiority of our proposed MAGDM method, respectively. In a word, this paper contributes to a new q-rung dual hesitant fuzzy MAGDM method, which absorbs the advantages of EPA operator and Archimedean operations. This method can be applied to describe complex cognitive information and solving realistic MAGDM problems effectively. PubDate: 2021-09-25
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Abstract: Background State-of-the-art lane detection methods have achieved prominent performance in complex scenarios, but many limits have also existed. For example, only a fixed number of lanes can be detected, and the cost of detection time is unaffordable in many cases. Methods Inspired by human vision, attention mechanism makes network learning more concerned features. In this paper, we propose a real-time lane detection method by using attention mechanism. The network proposed consists of three modules: an encoder module that extracts the feature of lanes; the instance feature maps of lanes are predicted by two decoder modules, namely binary decoder and embeddable decoder. In the encoder, we use the biologically inspired attention to extract features, which contain many details of the target area. The correlation between the features obtained from the convolutions and that extracted by the attention is established to learn the contextual information. In the decoder, the contextual information is fused with the features from up-sampling, to compensate for the lost detailed information. Binary decoder classifies all the pixels into lane or background. Embeddable decoder obtains the distinguishable lanes. And then, the outputs of the binary decoder serve as one of the inputs to the embeddable decoder to guiding the generation of exact pixel points on the lanes. Results Comparative experiments on two benchmarks (TuSimple and Caltech lanes datasets) show that the proposed method is independent of lane number and lane pattern. It can handle an indefinite number of lanes and run at 10ms in the TuSimple dataset. Conclusions Experiments verify that our method outperforms a lot of state-of-the-art methods while maintaining a real-time performance. PubDate: 2021-09-24
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Abstract: We address the problem of recognizing emotion cause in conversations, define two novel sub-tasks of this problem, and provide a corresponding dialogue-level dataset, along with strong transformer-based baselines. The dataset is available at https://github.com/declare-lab/RECCON. Recognizing the cause behind emotions in text is a fundamental yet under-explored area of research in NLP. Advances in this area hold the potential to improve interpretability and performance in affect-based models. Identifying emotion causes at the utterance level in conversations is particularly challenging due to the intermingling dynamics among the interlocutors. We introduce the task of Recognizing Emotion Cause in CONversations with an accompanying dataset named RECCON, containing over 1,000 dialogues and 10,000 utterance cause/effect pairs. Furthermore, we define different cause types based on the source of the causes, and establish strong Transformer-based baselines to address two different sub-tasks on this dataset. Our transformer-based baselines, which leverage contextual pre-trained embeddings, such as RoBERTa, outperform the state-of-the-art emotion cause extraction approaches on our dataset. We introduce a new task highly relevant for (explainable) emotion-aware artificial intelligence: recognizing emotion cause in conversations, provide a new highly challenging publicly available dialogue-level dataset for this task, and give strong baseline results on this dataset. PubDate: 2021-09-13
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Abstract: Chimp optimization algorithm (ChOA) is a newly proposed meta-heuristic algorithm inspired by chimps’ individual intelligence and sexual motivation in their group hunting. The preferable performance of ChOA has been approved among other well-known meta-heuristic algorithms. However, its continuous nature makes it unsuitable for solving binary problems. Therefore, this paper proposes a novel binary version of ChOA and attempts to prove that the transfer function is the most important part of binary algorithms. Therefore, four S-shaped and V-shaped transfer functions, as well as a novel binary approach, have been utilized to investigate the efficiency of binary ChOAs (BChOA) in terms of convergence speed and local minima avoidance. In this regard, forty-three unimodal, multimodal, and composite optimization functions and ten IEEE CEC06-2019 benchmark functions were utilized to evaluate the efficiency of BChOAs. Furthermore, to validate the performance of BChOAs, four newly proposed binary optimization algorithms were compared with eighteen novel state-of-the-art algorithms. The results indicate that both the novel binary approach and V-shaped transfer functions improve the efficiency of BChOAs in a statistically significant way. PubDate: 2021-09-13
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Abstract: Bayesian confirmation provides a practical approach to reasoning about the truth of hypotheses based on the observation of evidence. It has been applied in many topics closely related to cognitive computing, such as decision makings and problem solving, especially those involving learning and reasoning based on the descriptions of objects. This paper investigates the application of Bayesian confirmation into classification which is a basis in many cognitive computing topics. Bayesian confirmation measures are adopted to evaluate the degree to which a description of objects (i.e., a piece of evidence) confirms the belongingness of the objects to a given class (i.e., a hypothesis). Accordingly, a description space is divided into three regions of confirmatory, disconfirmatory, and neutral descriptions, formulating a three-way Bayesian confirmation model. Based on a sequence of description spaces induced by either attributes or attribute–value pairs, the neutral regions can be further refined, which leads to a sequential model. Furthermore, with a discussion on constructing meaningful trisections of attributes or attribute–value pairs according to their utility, we present a three-level three-way Bayesian confirmation framework where each level focuses on one set in a trisection. Due to their different utility levels, the three sets in a trisection are used in different appropriate ways in constructing the three levels. Bayesian confirmation provides a meaningful perspective of evaluating descriptions in the context of classifications. This work may bring new insights into research on related topics such as decision makings, three-level analysis, rough set theory, and concept analysis. PubDate: 2021-09-13
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Abstract: Different artists have their unique painting styles, which can be hardly recognized by ordinary people without professional knowledge. How to intelligently analyze such artistic styles via underlying features remains to be a challenging research problem. In this paper, we propose a novel multi-task feature fusion architecture (MTFFNet), for cognitive classification of traditional Chinese paintings. Specifically, by taking the full advantage of the pre-trained DenseNet as backbone, MTFFNet benefits from the fusion of two different types of feature information: semantic and brush stroke features. These features are learned from the RGB images and auxiliary gray-level co-occurrence matrix (GLCM) in an end-to-end manner, to enhance the discriminative power of the features for the first time. Through abundant experiments, our results demonstrate that our proposed model MTFFNet achieves significantly better classification performance than many state-of-the-art approaches. In this paper, an end-to-end multi-task feature fusion method for Chinese painting classification is proposed. We come up with a new model named MTFFNet, composed of two branches, in which one branch is top-level RGB feature learning and the other branch is low-level brush stroke feature learning. The semantic feature learning branch takes the original image of traditional Chinese painting as input, extracting the color and semantic information of the image, while the brush feature learning branch takes the GLCM feature map as input, extracting the texture and edge information of the image. Multi-kernel learning SVM (supporting vector machine) is selected as the final classifier. Evaluated by experiments, this method improves the accuracy of Chinese painting classification and enhances the generalization ability. By adopting the end-to-end multi-task feature fusion method, MTFFNet could extract more semantic features and texture information in the image. When compared with state-of-the-art classification method for Chinese painting, the proposed method achieves much higher accuracy on our proposed datasets, without lowering speed or efficiency. The proposed method provides an effective solution for cognitive classification of Chinese ink painting, where the accuracy and efficiency of the approach have been fully validated. PubDate: 2021-09-10
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Abstract: Background Emotion recognition is an interesting and challenging problem and has attracted much attention in recent years. To more accurately express emotions, emotion distribution learning (EDL) introduces the emotion description degree to form an emotion distribution at a fine granularity, which is used to describe the fusion of multiple basic emotions at different levels. Challenge Existing EDL research has shown a strong representation ability on emotion recognition, but all studies are based on unimodal information, meaning the results may be one-sided. Method As the first pioneering investigation of multimodal emotion distribution learning, we present a corresponding learning method named MEDL. First, for each modality, we learn an emotion distribution and obtain the corresponding label correlation matrix. Second, we constrain the consistency of label correlation matrices between different modalities to utilize modal complementarity. Finally, the final emotion distribution is achieved based on a simple decision fusion strategy. Results and Conclusions The experimental results demonstrate that our proposal performs better than some state-of-the-art multimodal emotion recognition methods and unimodal emotion distribution learning methods. PubDate: 2021-09-08
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Abstract: Causal asymmetry is an important feature in the description of causality, and it has attracted wide attention in the field of physics and philosophy. It hypothesizes that there is a pervasive and fundamental bias in humans’ understanding of physical causation. However, how to express the causal asymmetry in computer science is still an open, interesting, and important issue. In this paper, we propose a solution to this issue by introducing an incremental concept tree (ICT) representation. The ICT is a structure description method originated from the concept tree and attribute topology methods in the field of concept cognitive learning. It focuses on figuring the cognitive process of human being and has been applied to casual analysis. Firstly, we introduce the concept of “causal asymmetry” into the field of concept-cognitive learning according to the internal unity of attribute topology and causality. Secondly, an Incremental concept tree is designed to represent the incremental evolution of the concepts as time arrows on the basis of attribute topology. Finally, we perform an experimental analysis of the Acute Inflammations data to illustrate the feasibility of the proposed algorithm in visualizing causal asymmetry and compare the ICT to the other structural representations. The experimental results show that the ICT is a promising tool for figuring out the casual asymmetry in the view of concept cognitive learning. PubDate: 2021-09-08
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Abstract: Reversible data hiding in encrypted domain (RDH-ED) technology can embed data into cover media without exposing the original content to third parties. In addition, the recipient can recover the cover media losslessly after extracting the embedded data. Image-based RDH-ED has been widely studied, but RDH-ED based on 3D meshes has obtained few research results due to the complex data structure and irregular geometric structure of 3D meshes. With the widespread application of 3D meshes, the research on 3D meshes has attracted extensive research from researchers in recent years. In this paper, we propose a reversible data hiding for encrypted 3D meshes based on integer mapping and most significant bit (MSB) prediction. The content owner divides all vertices into “embedded” sets and “reference” sets and then maps floating-point coordinates to integers. After calculating the MSB prediction error of the “embedded” sets, the encryption technology is performed. Then, additional data can be embedded through the MSB replacement strategy. According to different permissions, legal recipients can obtain the original meshes, the additional data or both of them by using the proposed separable method. Higher embedding capacity is achieved by adopting MSB embedding strategy, and perfect recovery of the original meshes is achieved by using ring prediction scheme. The experimental results show that the proposed method has greater embedding capacity compared with the state-of-the-art method. PubDate: 2021-09-04
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Abstract: As a popular nondestructive testing (NDT) technique, thermal imaging test demonstrates competitive performance in crack detection, especially for detecting subsurface cracks. In thermal imaging test, the temperature of the crack area is higher than that of the non-crack area during the NDT process. By extracting the features of the thermal image sequences, the temperature curve of each spatial point is employed for crack detection. Nevertheless, the quality of thermal images is influenced by the noises due to the complex thermal environment in NDT. In this paper, a modified generative adversarial network (GAN) is employed to improve the image segmentation performance. To improve the feature extraction ability and alleviate the influence of noises, a penalty term is put forward in the loss function of the conventional GAN. A data preprocessing method is developed where the principle component analysis algorithm is adopted for feature extraction. The data argumentation technique is utilized to guarantee the quantity of the training samples. To validate its effectiveness in thermal imaging NDT, the modified GAN is applied to detect the cracks on the eddy current pulsed thermography NDT dataset. PubDate: 2021-09-04
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Abstract: Three popular application domains of sentiment and emotion analysis are: 1) the automatic rating of movie reviews, 2) extracting opinions and emotions on Twitter, and 3) inferring sentiment and emotion associations of words. The textual elements of these domains differ in their length, i.e., movie reviews are usually longer than tweets and words are obviously shorter than tweets, but they also share the property that they can be plausibly annotated according to the same affective categories (e.g., positive, negative, anger, joy). Moreover, state-of-the-art models for these domains are all based on the approach of training supervised machine learning models on manually annotated examples. This approach suffers from an important bottleneck: Manually annotated examples are expensive and time-consuming to obtain and not always available. In this paper, we propose a method for transferring affective knowledge between words, tweets, and movie reviews using two representation techniques: Word2Vec static embeddings and BERT contextualized embeddings. We build compatible representations for movie reviews, tweets, and words, using these techniques, and train and evaluate supervised models on all combinations of source and target domains. Our experimental results show that affective knowledge can be successfully transferred between our three domains, that contextualized embeddings tend to outperform their static counterparts, and that better transfer learning results are obtained when the source domain has longer textual units than the target domain. PubDate: 2021-09-02
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Abstract: Information measures in neighborhood decision systems underlie information processing and uncertainty measurement, especially regarding neighborhood rough sets. Their constructions on covering structuring and neighborhood counting can acquire theoretical extensions and practical compactness but become difficult and rare when comparing the sample counting approach and its defects. In terms of three-way information measures (i.e., information entropy, conditional entropy, and mutual information), classification-level and class-level complement information measures are established by extending equivalence decision systems to neighborhood decision systems; thus, the construction on nonrepetitive neighborhoods becomes ingenious, and the study of criss-cross structuring and granulation properties becomes valuable. At the classification level, neighborhood-complement information measures are proposed by imitation; they perfectly expand existing complement information measures, and thus, they offer an extended isomorphism regarding systematicity. At the class level, neighborhood-complement information measures are determined by decomposition to generate a hierarchical isomorphism, and they also induce equivalence-complement information measures to yield a degenerate isomorphism. Then, granulation nonmonotonicity and monotonicity of neighborhood-complement information measures are revealed at these two levels, and their uncertainty mechanisms are analyzed deeply by three-level granular structures. Finally, all complement measures are calculated programmatically, and their relationships and nonmonotonicity or monotonicity are effectively verified by virtue of table examples and data experiments. In summary, systematically, there are four criss-cross modes of three-way complement information measures based on two knowledge granulations and two decision levels; the variably extended and degenerated isomorphisms and hierarchically decomposed and integrated isomorphisms are thoroughly uncovered, the granulation nonmonotonicity and monotonicity are deeply mined, and all achievements are found to have good application prospects for feature reduction and rule induction in machine learning. PubDate: 2021-09-02
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