Information Granules Research Articles

Medical Diagnosis Based on Multi-Attribute Group Decision-Making Using Extension Fuzzy Sets, Aggregation Operators and Basic Uncertainty Information Granule

Medical Diagnosis Based on Multi-Attribute Group Decision-Making Using Extension Fuzzy Sets, Aggregation Operators and Basic Uncertainty Information Granule

Causalities-multiplicity oriented joint interval-trend fuzzy information granulation for interval-valued time series multi-step forecasting

Interval-valued time series (ITSs) multi-step forecasting research is still in its infancy. Two cruces here lie in counterintuitive or conservative nature of semantic descriptors for ITSs, and disregard for multiplicity of causalities resulting from uncertainty in causalities between data or between trends within a set of interval-valued data. In this paper, we put forth a type of joint interval-trend fuzzy information granules, which takes non-loss of within-interval information as the main design criterion. A modified fuzzy information granulation method carries originality in portraying intuitive and accurate interval-trends, directly linked with inherent relational constraints such as lower bound data should not be greater than upper bound data. Furthermore, we formulate a legible format of multi-factor fuzzy IF-THEN rules, which exhibits interesting interpretations to causalities between interval-trends at a higher level of multiplicity. The forecasting process is fuzzy rules-based, resulting in wise results by calculating rule firing weights. Thus, we develop a well construct of accuracy and interpretability for multi-step forecasting of ITSs, manifested in: (a) reducing cumulative errors by operating at the granular level, and (b) perceiving interval-trends in an intelligible manner and emphasizing multiple causalities via transparent fuzzy logic inference. Experimental results convincingly confirm the validity of the model.

Privacy-Preserving Modeling of Trajectory Data: Secure Sharing Solutions for Trajectory Data Based on Granular Computing

Trajectory data are embedded within driving paths, GPS positioning systems, and mobile signaling information. A vast amount of trajectory data play a crucial role in the development of smart cities. However, these trajectory data contain a significant amount of sensitive user information, which poses a substantial threat to personal privacy. In this work, we have constructed an internal secure information granule model based on differential privacy to ensure the secure sharing and analysis of trajectory data. This model deeply integrates granular computing with differential privacy, addressing the issue of privacy leakage during the sharing of trajectory data. We introduce the Laplace mechanism during the granulation of information granules to ensure data security, and the flexibility at the granularity level provides a solid foundation for subsequent data analysis. Meanwhile, this work demonstrates the practical applications of the solution for the secure sharing of trajectory data. It integrates trajectory data with economic data using the Takagi–Sugeno fuzzy rule model to fit and predict regional economies, thereby verifying the feasibility of the granular computing model based on differential privacy and ensuring the privacy and security of users’ trajectory information. The experimental results show that the information granule model based on differential privacy can more effectively enable data analysis.

Incremental learning and granular computing from evolving data streams: An application to speech-based bipolar disorder diagnosis

We apply an evolving granular-computing modeling approach, called evolving Optimal Granular System (eOGS), to bipolar mood disorder (BD) diagnosis based on speech data streams. The eOGS online learning algorithm reveals information granules in the flow and design the structure and parameters of a granular rule-based model with a certain degree of interpretability based on acoustic attributes obtained from phone calls made over 7 months to the Psychiatry department of a hospital. A multi-objective programming problem that trades-off information specificity, model compactness, and numerical and granular error indices is presented. Spectral and prosodic attributes are ranked and selected based on a hybrid Pearson-Spearman correlation coefficient. Low attribute-class correlation, ranging from 0.03 to 0.07, is observed, as well as high class overlap, which is typical in the psychiatric field. eOGS models for BD recognition overcome alternative computational-intelligence models, namely, Dynamic Evolving Neural-Fuzzy Inference System (DENFIS) and Fuzzy-set-Based evolving Modeling (FBeM-Gauss), by a small margin in both best and average cases; followed by eXtended Takagi-Sugeno (xTS) and evolving Takagi Sugeno (eTS) types of models. The proposed eOGS model using only 8 of the original acoustic attributes, and about 15 ‘If-Then’ inference rules, has exhibited the best root mean square error, 0.1361, and 91.8% accuracy in sharp BD class estimates. Granules associated to linguistic labels and a granular input-output map offer human understandability with relation to the inherent process of generating class estimates. Linguistically readable eOGS rules may assist physicians in explaining symptoms and making a diagnosis.

An interval forecast model for infectious diseases using fuzzy information granulation and spatial-temporal graph neural network

To enhance infection diseases interval prediction, an improved model is proposed by integrating neighborhood fuzzy information granulation (NNIG) and spatial-temporal graph neural network (STGNN). Additionally, the NNIG model can efficiently extract the most representative features from the time series data and identifies the support upper and lower bounds. NNIG model transfers time series data from numerical level to granular level, and processes data feed it into STGNN for interval prediction. Finally, experiments are conducted for evaluation based on the COVID-19 data. The results demonstrate that the NNIG outperforms baseline models. Further, it proves beneficial in offering a valuable approach for policy-making.

Prediction of building cooling load: an innovative design for GA-SVM and IG-SVM system for the estimation of hourly precision and computational fluctuation range

ABSTRACT Anticipating the loads that buildings will bear is a crucial strategy in the pursuit of energy efficiency and the reduction of emissions. In this paper, we introduce an interactive and comprehensive joint prediction model, specifically crafted to elevate the precision of forecasts related to building loads. The resultant Genetic Algorithm-Support Vector Machine (GA-SVM) prediction model is put into action to provide hourly predictions of cooling loads for buildings. In scenarios where the prediction of building cooling load (BCL) fluctuations becomes imperative, especially in the face of extreme weather conditions, the information granulation (IG) method is employed. The findings of this validation process unveil significant improvements. The coefficient of variation of root mean square error (CV-RMSE) and mean absolute percentage error (MAPE) for the GA-SVM model are reduced by 58.85% and 68.04%, respectively, when compared to the conventional SVM model. Furthermore, in a comparative analysis against three widely utilized prediction models, the SVM model demonstrates a reduction in CV-RMSE and MAPE ranging from 2.04% to 68.04%. The application of the joint prediction model showcases impressive results, with R 2 values ranging from 97.27% to 99.68%, MAPE ranging from 2.59% to 2.84%, and CV-RMSE ranging from only 0.0249 to 0.0319.

Long-Term Multivariate Time-Series Forecasting Model Based on Gaussian Fuzzy Information Granules

Long-Term Multivariate Time-Series Forecasting Model Based on Gaussian Fuzzy Information Granules

A fusion model for multiple partial-order quotient spaces based on three-way decision

With a quotient space, a complex problem can be transformed into an appropriate granularity for processing. However, within a quotient space, there are no partial order relations between information granules. In practical decision-making, it may be necessary to deal with quotient spaces that have partial order relations between information granules. In this paper, first, the concept of a partial-order quotient space is proposed and some of its properties are studied. Second, a fusion model for multiple partial-order quotient spaces based on three-way decision is proposed, and some related theorems are proved. Finally, a case study of teacher evaluation, an experiment on real data, and several simulation experiments are presented to demonstrate the practicality of the proposed model in this paper.

Counterfactuals in fuzzy relational models

Given the pressing need for explainability in Machine Learning systems, the studies on counterfactual explanations have gained significant interest. This research delves into this timely problem cast in a unique context of relational systems described by fuzzy relational equations. We develop a comprehensive solution to the counterfactual problems encountered in this setting, which is a novel contribution to the field. An underlying optimization problem is formulated, and its gradient-based solution is constructed. We demonstrate that the non-uniqueness of the derived solution is conveniently formalized and quantified by admitting a result coming in the form of information granules of a higher type, namely type-2 or interval-valued fuzzy set. The construction of the solution in this format is realized by invoking the principle of justifiable granularity, another innovative aspect of our research. We also discuss ways of designing fuzzy relations and elaborate on methods of carrying out counterfactual explanations in rule-based models. Illustrative examples are included to present the performance of the method and interpret the obtained results.

Integrating granular computing with density estimation for anomaly detection in high-dimensional heterogeneous data

Detecting anomalies in complex data is crucial for knowledge discovery and data mining across a wide range of applications. While density-based methods are effective for handling varying data densities and diverse distributions, they often struggle with accurately estimating densities in heterogeneous, uncertain data and capturing interdependencies among features in high-dimensional spaces. This paper proposes a fuzzy granule density-based anomaly detection algorithm (GDAD) for heterogeneous data. Specifically, GDAD first partitions high-dimensional attributes into subspaces based on their interdependencies and employs fuzzy information granules to represent data. The core of the method is the definition of fuzzy granule density, which leverages local neighborhood information alongside global density patterns and effectively characterizes anomalies in data. Each object is then assigned a fuzzy granule density-based anomaly factor, reflecting its likelihood of being anomalous. Through extensive experimentation on various real-world datasets, GDAD has demonstrated superior performance, matching or surpassing existing state-of-the-art methods. GDAD's integration of granular computing with density estimation provides a practical framework for anomaly detection in high-dimensional heterogeneous data.

Information fusion in order-2 fuzzy environments: A matrix transformation perspective

Order-2 information granules, as a representation of multi-layer structured information, have recently rekindled discussions. It is usually generated by abstracting order-1 information granules. When the dependence relationship and corresponding membership function of the order-1 information granules (reference information granules) are known, Pedrycz et al. used a method based on gradient optimization to complete the aggregation of the order-2 information granules. In this paper, we discuss a more specific scenario: not only the dependencies between reference information granules are captured, but also the order-1 information granules can be expressed as specific fuzzy information distributions. For this, we propose a fusion scheme of order-2 fuzzy sets based on matrix transformation called CQRP. To our knowledge, it is the first method that completely integrates the structural information of the order-2 environment into the fusion of order-2 fuzzy sets. In the process, we also creatively proposed the attraction and exclusion of structural information, deepening the understanding of structural information. Through sufficient comparison and analysis, we prove that it makes fuller use of information in the order-2 environment and is more reasonable and effective in tasks such as classification and identification.

Granular computing-based time series anomaly pattern detection with semantic interpretation

Time series analysis may suffer from the “curse of dimensionality” due to its high-dimensionality characteristics. In terms of this issue, information granulation offers an effective vehicle to process time series at a higher level of abstraction. To take this advantage, this study conducts an interpretable time series anomaly pattern detection under the framework of granular computing, where each time series is granulated into a series of semantics according to its patterns and the anomaly ones are identified based on the obtained semantics. First, the time series is partitioned into a predefined number of segments and trend-based information granules are formed for the data points in each time interval. Guided by the principle of justifiable granularity, the granular results maintaining the main features of the original time series realize informative feature extraction and meaningful dimensionality reduction. Then, to realize semantic anomaly pattern detection, the Axiomatic Fuzzy Set (AFS) theory is generalized to construct and compute with semantic time series, and an AFS-based anomaly score is proposed to discover anomaly patterns. In the experiments, the proposed method is conducted on both UCR data sets and real-world time series, where the detected anomaly patterns are equipped with well-defined semantics.

An interval uncertainty modeling method based on information granulation and improved multidimensional parallelepiped

Interval uncertainty modeling is essential for non-probabilistic reliability analysis of uncertain structures in the context of small samples, which confronts the difficulties of obtaining marginal intervals and characterizing variables correlation. A novel method for interval uncertainty modeling based on information granulation and improved multidimensional parallelepiped is proposed in this paper. Firstly, the method for constructing marginal intervals of uncertain variables is presented by integrating the up-sampling method based on kernel density estimation and information granulation theory (KDE-IG). Secondly, a relatively simple correlation coefficient expression based on the correlation angle is defined, and an improved multidimensional parallelepiped modeling method is proposed by optimizing the correlation coefficient within the marginal intervals. Additionally, two evaluation indexes are proposed to evaluate the robustness and accuracy of the constructed model. Finally, the applicability and effectiveness of the proposed method are demonstrated through two examples.

Synergizing Two Types of Fuzzy Information Granules for Accurate and Interpretable Multistep Forecasting of Time Series

Synergizing Two Types of Fuzzy Information Granules for Accurate and Interpretable Multistep Forecasting of Time Series

Polynomial fuzzy information granule based [formula omitted]-triple I fuzzy reasoning algorithm and its short-term forecasting of time series

Short-term forecasting of time series is an important research topic, which involves data characteristic capture and intelligent reasoning. For this topic, the Gaussian polynomial fuzzy information granule with interpretability is granulated on data, enabling the extraction of data trend characteristic, besides, the associate characteristic within the data is captured through building fuzzy association rule. Building upon the data characteristics captured in fuzzy information granule and fuzzy association rule, an intelligent reasoning algorithm called the fuzzy information granule based α-Triple I algorithm is proposed, where the membership degree of data to granule is considered in reasoning, and next the accurate level of deviation from data to granule can be inferenced. Based on the excavated data characteristics and a rational inference, a short-term forecasting model is established. Its superiority in terms of accuracy and reliability when compared to 7 other models in real time series has been tested. Notably, the prediction of the novel model is accurate because the function of FAR is identified from FAR’s truth degree, which means the validity degree of prediction. The application of the proposed model for short-term forecasting holds a potential impact across various fields.

Oriented to a multi-learning mode: Establishing trend-fuzzy-granule-based LSTM neural networks for time series forecasting

In the construction of information granule based neural networks for time series multi-step forecasting, the existing works tend to focus on consecutive-learning mode while rarely explore multi-learning mode. In fact, only under the multi-learning mode can diversified associations among data collected over time granules be well learned. Also, the existing works exhibit limited time interpretability. Here the problem centers around how to endow information granule based neural networks with a multi-learning mode to learn diversified associations simultaneously, and well-articulated trend semantics. To solve these problems, the first originality of this paper stems from a scale equalization method for multilinear-trend fuzzy information granules to track complex trend changes of data in a more accurate and explainable manner from both global and local views. Furthermore, an adaptive rather than empirical or traversal method, which is trend-driven in nature, is tailored for mining diversified associations. The resulting model can give forecasts in the form of granules as well as numerical values, being interpretable and accurate in the sense that: (a) its inputs and output are granules which come with well-defined trend semantics under a customary time concept, and (b) a clump of data is considered in a concise granule whilst roles of diversified associations are ware of during forecasting, making the model less prone to cumulative errors. Appealing experimental results corroborate the effectiveness of the proposed model.

Two-way concept-cognitive learning method: a perspective from progressive learning of fuzzy skills

ABSTRACT Concept-cognitive learning and two-way concept-cognitive learning have been widely used to learn concepts from given cues, and fruitful results have been obtained. However, there are still some limitations: (i) The existing two-way concept-cognitive learning methods based on competences focused on dichotomous skills, but they did not consider the proficiency of skills in the concept-cognitive learning process and ignored the dynamic learning of skills. (ii) The existing necessary and sufficient information granules based on competences cannot be learned directly from any information granule. (iii) Most of the other existing two-way concept-cognitive learning models in fuzzy formal context have been studied through an antitone Galois connection, but they cannot directly deal with an isotone Galois connection between items and fuzzy skills. To overcome these issues, we propose a novel two-way concept-cognitive learning model based on fuzzy skills to learn fuzzy skill-based cognitive concepts (i.e. necessary and sufficient fuzzy skill-based information granules) from a perspective of skill proficiency. And we optimize the two-way concept-cognitive learning model to learn directly fuzzy skill-based cognitive concepts from any information granule and save time for learning concepts. Furthermore, a progressive learning mechanism is explored to deal with dynamic data. The experimental results of 12 UCI data sets show that the proposed concept-cognitive learning models in this paper are feasible and effective.

Optimal scale combination selection in generalized multi-scale hybrid decision systems

When processing multi-scale hybrid data, the existing methods are insufficient to directly select the optimal scale for different types of data. To deal with this issue, the concept of generalized multi-scale hybrid decision systems (GMHDSs) consisting of numerical, nominal and set-valued values is first introduced. Then, under a scale combination, the information granules of different types of attributes in a GMHDS are constructed and they further fused as the granules of the system. Based on these granules of a given scale combination, positive region and conditional entropy are specified in a GMHDS. To select appropriate single scale systems to keep the positive region and the conditional entropy unchanged for final decision, concepts of positive region optimal scale combinations (POSCs) and conditional entropy optimal scale combinations (CEOSCs) in GMHDSs are defined, respectively. Furthermore, algorithms for calculating a POSC and a CEOSC in a GMHDS are also formulated. Finally, a comparative study of our methods with these based on original data under KNN and NB classifiers is conducted on twelve UCI datasets for the assessment of their classification performance. The experimental results indicate that the proposed methods are of better classification performance than the original data based methods in most cases.

Point and interval forecasting approach for short-term urban subway passenger flow based on residual term decomposition and fuzzy information granulation

Accurate forecasting information of short-term subway passenger flow is an important scientific reference for daily operations and urban management. The rapid time-varying nature of subway passenger flow caused by various factors that affect travel behavior poses a huge challenge to accurate forecasting. The complexity and uncertainty of data mainly focus on residual terms that deeply reflect the fluctuations. Reasonably mining the residual terms has become the key to achieving accurate forecasting. Therefore, this paper proposes a sophisticated decomposition strategy to extract and analyze the useful information hidden in the residual terms. Firstly, the potential trend, seasonal and residual terms from the original data are extracted by seasonal-trend decomposition procedure based on loess. Secondly, the residual term is decomposed into a series of subcomponents with different frequency features by symplectic geometric mode decomposition. Thirdly, these subcomponents are classified into three clusters based on fuzzy C-means clustering (FCM), and then the corresponding forecasting models are matched to the three obtained clusters and trend and seasonal terms. Finally, based on a decomposition-ensemble framework and information granulation for high-frequency components, we have established point and interval forecasting approach, respectively. Three experiments on real data sets in Beijing, Guangzhou and Shenzhen are conducted to verify the performance of the proposed approach, and the experimental results show that our approach is superior to all benchmark models and contributes to improving operational management and service quality.

Особенности оценки вредоносной активности в инфраструктуре Умного города на основе гранулирования информации и гранулярных моделей вычислений

The object of the research is a new methodological approach to information granulation and fuzzy granular calculations, as a mathematical and methodological tool for improving the reliability of assessing the level of information security of the Smart City infrastructure. The proposed approach is one of the options for the practical application of elements of the theory of fuzzy sets in the tasks of search, identification and current assessment of signs of time-bearing activity. A detailed analysis of the features of this approach has been carried out, determining the expediency and conditions of its application for assessing malicious activity in the infrastructure of a Smart City. The theoretical aspects of the application of information granulation and fuzzy granular computing to the assessment of malicious activity combining various signs for various categories of potential threats to the infrastructure and subjects of a Smart City - the categories “cyberattack”, “malicious virus threat” or “data leakage (loss)” are studied and described. The analysis of the features of the proposed approach is carried out, which allows taking into account the opinions of experts and eliminating the vagueness associated with noise, disorder and lack of formalization of surveillance data collected and pre-processed in the interests of assessing threats and consequences of negative manifestations of malicious activity. A sequence of calculations and analytical expressions for calculating the estimated values of signs of harmful activity for various categories of potential threats to the infrastructure and subjects of a Smart City has been developed and described in detail. The approach assumes the practical possibility of evaluating signs of malicious activity using information granules formed on the basis of a minimum numerical distance between the values of membership functions characterizing vaguely specified data on the presence or absence of observed signs (attributes) of malicious activity, as well as granular summation and determination of the trace function of the granular sum. At the same time, the proposed approach makes it possible to obtain estimates of signs of malicious activity that are adequate to the tasks of monitoring the Smart City security policy and, ultimately, provides increased reliability of proactive threat control and analysis of the possible consequences of a negative manifestation of suspicious activity.