Principle Of Justifiable Granularity Research Articles

Weighted Fuzzy Clustering for Time Series With Trend-Based Information Granulation.

The highly dimensional characteristic of time series brings many challenges on direct mining time series, such as high cost in time and space. Granular computing provides a potential strategy for representing and dealing with time series at a higher level of abstraction. In this study, we propose an information granulation-based weighted fuzzy C -means (wFCM) method to realize time-series clustering, which could avoid high dimensionality processing and provide a concise and visible granular prototype for each cluster. In this method, each time series is first transformed into a series of information granules with trend following the principle of justifiable granularity. The formed granular time series can well capture the main features lying in the original time series and help realize dimensionality reduction. Then, the wFCM method is developed to complete time-series clustering in the granular space. Here, the dynamic time warping (DTW) is extended to capture the similarity for trend-based granular time series. Furthermore, the weighted DTW barycenter averaging is introduced to derive prototypes presented in a granular format, capturing the level, the fluctuation, and the changing trend, which are meaningful and understandable clustering results. The experiments conducted on real-world datasets coming from the UCR time-series database and Chinese stocks are presented to illustrate the effectiveness and practicality of the designed time-series clustering model.

Local Boundary Fuzzified Rough K-Means-Based Information Granulation Algorithm Under the Principle of Justifiable Granularity.

Information granularity and information granules are fundamental concepts that permeate the entire area of granular computing. With this regard, the principle of justifiable granularity was proposed by Pedrycz, and subsequently a general two-phase framework of designing information granules based on Fuzzy C-means clustering was successfully developed. This design process leads to information granules that are likely to intersect each other in substantially overlapping clusters, which inevitably leads to some ambiguity and misperception as well as loss of semantic clarity of information granules. This limitation is largely due to imprecise description of boundary-overlapping data in the existing algorithms. To address this issue, the rough k -means clustering is introduced in an innovative way into Pedrycz's two-phase information granulation framework, together with the proposed local boundary fuzzy metric. To further strengthen the characteristics of support and inhibition of boundary-overlapping data, an augmented parametric version of the principle is refined. On this basis, a local boundary fuzzified rough k -means-based information granulation algorithm is developed. In this manner, the generated granules are unique and representative whilst ensuring clearer boundaries. The validity and performance of this algorithm are demonstrated through the results of comparative experiments.

Build interval-valued time series forecasting model with interval cognitive map trained by principle of justifiable granularity

Build interval-valued time series forecasting model with interval cognitive map trained by principle of justifiable granularity

Three-way evidence theory-based density peak clustering with the principle of justifiable granularity

Clustering by fast search and find of density peaks (DPC) is an effective clustering approach that can find all the cluster centers at once with just one parameter and without iterative processing. However, the cutoff distance, a key parameter of density measurement in the DPC approach, affects the quality of the final clustering results. Its selection relies on experimental experience and lacks of a semantic explanation. Furthermore, the allocation strategy of the traditional DPC approach may cause several points to be assigned incorrectly, leading to subsequent points being assigned incorrectly and ultimately forming continuous allocation errors. To overcome the deficiencies, this paper proposes a novel three-way evidence theory-based density peak clustering with the principle of justifiable granularity (3 W-PEDP). First, the computation of the cutoff distance is converted into the search for nearest neighbors. From the perspective of granular computing, 3 W-PEDP transforms the neighbor selection issue into the construction of justifiable granularity. And the optimal neighbors can be achieved with the construction of coverage and specificity criteria. Second, inspired by three-way clustering, we adopt a two-stage method for sample allocation. On the one hand, for core point allocation, a two-layer nearest neighbor is constructed based on the achieved optimal neighbors. On the other hand, we designed a new evidence mass function to guide us in assigning the remaining points. In this novel evidence mass function, not only the labels of the assigned samples are considered, but also the information of the neighborhoods around the unassigned samples is fused. Finally, we assess the effectiveness of 3 W-PEDP on numerous public synthetic datasets and UCI real-world datasets. Then, detail comparing results with several popular clustering methods are presented. In addition, experimental studies verify the effectiveness of constructing justifiable granularity in selecting the optimal neighbors. The experimental results demonstrate 3 W-PEDP has good adaptability and robustness, which can achieve better clustering performance. Our source code is available at https://github.com/Luyangabc/3W-PEDP.

Granular fuzzy rule-based model construction under the collaboration of multiple organizations

In the real world, phenomena are often observed and recorded by multiple organizations which results in multiple sources of data. When dealing with such data, the centralized modeling approach aims to achieve collaborative modeling by fusing multiple sources of data into a single data set, which may pose challenges to data privacy. Unlike centralized modeling, the distributed modeling approach can effectively solve the privacy issue. However, modeling approaches based on this idea still suffer from either low prediction accuracy or high communication costs. In this study, we propose a collaborative modeling strategy for multi-source data based on fuzzy rule-based models (FRBMs) to balance the needs of both model prediction accuracy and efficiency. First, we adopt the concept and algorithm of collaborative fuzzy clustering (CFC) to improve prediction accuracy and reduce communication costs by improving the CFC algorithm. Then, we construct a granular FRBM for multi-source data based on the principle of justifiable granularity (PJG) by integrating local models into a more robust and perfect global model. Finally, we improve the performance evaluation index of the existing granular FRBM and propose two model optimization schemes to further improve the performance of the model. We conduct experiments on both synthetic and publicly available data sets to demonstrate the effectiveness of the proposed method.

A Granular Computing-Driven Best–Worst Method for Supporting Group Decision Making

In group decision making (GDM), there are seldom ideal scenarios that all the preference information given by all individuals reach a highly level of agreement. Conflicts are present in the information fusion process and decision makers (DMs) have to negotiate and reconcile differences. To address this issue, it becomes inevitable to consider intelligent GDM method. In this article, we propose the granular neural network (GNN) to realize the aggregation process from the perspective of granular computing and machine learning. Our study is involved in an extension of best–worst method to the GDM scenario. The procedure is outlined as follows: first, information granules are allocated around the prototype of individuals’ preferences, complying with the principle of justifiable granularity. Thereby, the granular inputs are brought into a well-trained GNN. An adaptive particle swarm optimization algorithm is applied to optimize allocation of information granules. We calculate the threshold of consistency index for this granular model. Finally, a case study about hotel selection on Booking.com is presented to illustrate the performance of the proposed model. In addition, we use the stochastic analysis method to randomize the weights of group members with the objective to assess the robustness of the model. The feasibility and validity of the model are demonstrated by completing comparative analysis. The originality of this article is to establish a real data-driven granular GDM model both considering the optimization of group consistency and consensus.

Granular Data Compression and Representation

We develop a comprehensive and original methodology of data compression realized in the setting of Granular Computing. It is advocated that a compression process is inherently associated with the emergence of information granules forming compressed data. This entails that compression goes hand-in-hand with the elevated level of abstraction of the generated results. The performance of the method is evaluated with the aid of the indexes of coverage and specificity commonly encountered when processing and describing information granules. A two-phase design environment is systematically established along with the detailed algorithmic layer exploring mechanisms of fuzzy clustering and the principle of justifiable granularity and its generalizations. Reconstruction error and granular reconstruction error criteria are introduced and analyzed. Experimental studies carried out on publicly available data are reported and illustrate the process of granular compression and analyze the performance of the obtained results.

An Enhanced Interval‐Based Approach for Anomaly Detection in Time Series

Since anomalies are usually caused by changes in shape and amplitude in time series data, and most of the interval‐based methods utilized appear in the literature from a global perspective to detect anomalies. Nevertheless, the anomalies are also usually caused by local changes in shape and amplitude. Following these limitations, an enhanced interval‐based approach based on the interval information granules with the principle of justifiable granularity, viz., the EIA method, is formulated in this study for anomaly detection. First, the interval information granules are produced separately from the global and local perspectives in an abstracted manner on the basis of this principle. An interval‐based similarity measurement algorithm is then designed based on the abstraction results to calculate the anomaly scores from the various interval information granules for anomaly detection. Compared with classical methods, the proposed approach exhibits better performance in terms of data anomaly resolution and detection accuracy, which have been verified and supported in much of real‐world data. © 2023 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

A Design of Granular Classifier Based on Granular Data Descriptors.

Designing effective and efficient classifiers is a challenging task given the facts that data may exhibit different geometric structures and complex intrarelationships may exist within data. As a fundamental component of granular computing, information granules play a key role in human cognition. Therefore, it is of great interest to develop classifiers based on information granules such that highly interpretable human-centric models with higher accuracy can be constructed. In this study, we elaborate on a novel design methodology of granular classifiers in which information granules play a fundamental role. First, information granules are formed on the basis of labeled patterns following the principle of justifiable granularity. The diversity of samples embraced by each information granule is quantified and controlled in terms of the entropy criterion. This design implies that the information granules constructed in this way form sound homogeneous descriptors characterizing the structure and the diversity of available experimental data. Next, granular classifiers are built in the presence of formed information granules. The classification result for any input instance is determined by summing the contents of the related information granules weighted by membership degrees. The experiments concerning both synthetic data and publicly available datasets demonstrate that the proposed models exhibit better prediction abilities than some commonly encountered classifiers (namely, linear regression, support vector machine, Naïve Bayes, decision tree, and neural networks) and come with enhanced interpretability.

Encoding words into interval type-2 fuzzy sets: The retained region approach

The first step of implementing computing with words using a perceptual computer is to establish an encoder to transform words into interval type-2 fuzzy sets. In this paper, a novel approach named the retained region approach is introduced for encoding words into interval type-2 fuzzy sets. In the retained region approach, the data part is redesigned relative to the existing approaches, and a new fuzzy set part is established in accordance with the principle of justifiable granularity. The different means and standard deviations of the embedded type-1 fuzzy sets associated with a word are recognized as the origins of its inter-uncertainty, and the relations between them are taken into account in the construction of interval type-2 fuzzy sets. Importantly, the retained region approach is a versatile approach that does not impose redundant constraints on the selection of embedded type-1 fuzzy sets, and the capacity of the retained region can be flexibly adjusted along the two dimensions of the mean and the standard deviation. Finally, the performance of the retained region approach is illustrated by several simulations and comparisons with existing approaches.

DPC-FSC: An approach of fuzzy semantic cells to density peaks clustering

Density peaks clustering (DPC) algorithm is a succinct and efficient density-based clustering approach to data analysis. It computes the local density and the relative distance for objects to seek cluster centers and form clusters. However, it is difficult to estimate an appropriate local density by a rule of thumb; therefore, the performance of DPC may be poor on real datasets in practice. Thus, this study proposes a novel method for density peaks clustering based on fuzzy semantic cells. Specifically, each object is coarsened into a fuzzy point with the form of the fuzzy semantic cell model. Based on this model, a local density metric is defined and estimated via the principle of justifiable granularity. Our local density estimation can be converted into an optimization problem. In addition, a relative semantic distance is also introduced which concerns the distance between fuzzy semantic cells. The relative semantic distance is more informative for selecting cluster centers in the decision graph. The experimental results show that our method not only exhibits higher performance but also provides a clearer decision graph to select cluster centers.

Information Granulation With Rectangular Information Granules and Its Application in Time-Series Similarity Measurement

Information granules can discover interpretable and meaningful relationships offering a full description for time series. This article presents an information granulation method with rectangular information granules and applies it to time-series similarity measurement. First, the fuzzy <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$c$</tex-math></inline-formula> -means clustering algorithm transforms the time series and its first-order difference time series to data clusters. With the maximum volume of rectangular information granules viewed as the criterion, the optimal rectangular information granules are formed using the data cluster by the principle of justifiable granularity and the gravitational search algorithm. The time-series similarity is measured by calculating the similarity between the upper and lower bounds of the optimal rectangular information granules built from the time series. Finally, an experiment is performed on a public dataset to verify the feasibility of the proposed method. The result shows that the rectangular information granulation method can capture the change characteristics of time series. The similarity measurement method can effectively evaluate the similarity of the time series belonging to different classes.

Granular data modeling and analysis based on optimized subsets of data

The study proposes a way of developing granular models based on optimized subsets of data with different sampling sizes, in which three generally used models, namely Support Vector Machine, K-Nearest Neighbor, and Long Short-Term Memory, are designed and transformed into granular version for achieving a good performance with sufficient functionality. First, a collection of subsets are determined using different sampling methods, which are subsequently applied to play as an essential prerequisite of the proposed models. Then, the principle of justifiable granularity is utilized to the design of interval information granules based on the subsets of data. The design process is associated with a well-defined optimization problem realized by achieving a sound compromise between two conflicting criteria: coverage and specificity. To evaluate the performance of the granular models, two aspects are considered: (i) sampling methods used in determining suitable subsets of data; (ii) different models applied to be transformed into granular models. A series of experimental studies are conducted to verify the feasibility of the proposed granular models.

Trend-Based Granular Representation of Time Series and its Application in Clustering.

Granular computing has been an intense research area over the past two decades, focusing on acquiring, processing, and interpreting information granules. In this study, we focus on the granulation of time series and discover the overall structure of the original time series by clustering the granular time series. During the granulation process, when time series exhibit some trend (up trend, equal trend, or down trend) or consist of a variety of tendencies, the trend is essential to be involved to construct the granular time series. Following the principle of justifiable granularity, we propose to form a series of trend-based information granules to describe the original time series and effectively reduce its dimensionality. Then, the similarity measure between trend-based information granules is provided, and considering the dynamic feature of time-series data, dynamic time warping (DTW) distance is generalized to measure the distance for granular time series. In sum, we show here a novel way of forming trend-based granular time series and the corresponding similarity measure, then based on this, the hierarchical clustering of granular time series is realized. The proposed approach can capture the main essence of time series and help to reduce the computing overhead. Experimental results show that the designed approach can reveal meaningful trend-based information granules, and provide promising clustering results on UCR and real-world datasets.

Hierarchical Decision Granules Optimization through the Principle of Justifiable Granularity

Interpretable Machine Learning (IML) aims to establish more transparent decision processes where the human can understand the reason behind the models’ decisions. In this work a methodology to create intrinsically interpretable models based on fuzzy rules is proposed. There is a selection to identify the rule structure by extracting the most significant elements from a decision tree by the principle of justifiable granularity. There are defined hierarchical decision granules and their quality metrics. The proposal is evaluated with ten publicly available datasets for classification tasks. It is shown that through the principle of justified granularity, rule-based models can be greatly compressed through their fuzzy representation, not only without significantly losing performance but even with compression of 40% it manages to exceed the performance of the initial model.

Design Gaussian information granule based on the principle of justifiable granularity: A multi-dimensional perspective

In this study, based on the principle of justifiable granularity, a method for designing multi-dimensional information granules is proposed. To design information granules, the correlations among the different variables within the data and their confidence levels are considered. The designed information granules reveal the relationships present in the experimental data and help to capture more features of the original data. In addition, a strategy for the exclusion of inhibitory data is considered, making the design of information granules more focused. Several experimental studies are conducted to quantify the effectiveness of the proposed method.

Learning event‐triggered control based on evolving data‐driven fuzzy granular models

AbstractThis article proposes a data‐stream‐driven event‐triggered control strategy using evolving fuzzy models learned by granulation of input–output samples of nonlinear systems with unknown time‐varying dynamics. The evolving fuzzy model is obtained online from a data stream ensuring data coverage based on the principle of justifiable granularity and controlled by an event‐triggering learning mechanism dependent on the model accuracy. This evolving fuzzy model is used to design event‐triggered fuzzy controller to stabilize networked control systems while reducing the used communication resources. The event‐triggered learning mechanism is employed to determine the instants in which the event‐triggered fuzzy controller should be redesigned. Numerical examples illustrate the effectiveness of the proposed learning event‐triggered fuzzy control algorithm.

Robust supervised rough granular description model with the principle of justifiable granularity

In recent years, granular computing has been developed as a unified data description paradigm. As a popular soft computing supervised learning model, rough sets theory-based data description approach has been intensively investigated in data mining research. Feasible information granulation and approximation approaches have been recognized as two key features of data descriptors in rough sets. In this study, we propose a Dempster–Shafer theory-based rough granular description model based on a principle of justifiable granularity. First, we apply evidence information to show the performance of information granules generated from various data density regions, and definitions of lower and upper approximation sets are discussed considering characteristics of data credibility and plausibility, respectively. Furthermore, we propose a robust rough description model to identify some extreme instances, such as outlier and noise instances. Moreover, a set of pseudo labels is provided to enhance the robustness of the proposed model. Finally, to search for an optimum granularity, justifiable granularity is quantified from the perspectives of legitimacy and interpretability, and then optimized by a particle swarm optimization algorithm. Extensive comparative experiments with several representative rough granular description models illustrate that the proposed model achieves almost all the best approximation quality, number difference, and neighborhood credibility values. These experimental results demonstrate that the proposed approach is reasonable, effective, and robust, and is a promising rough granular description model for complex data in real-world applications.

Granular rule-based modeling using the principle of justifiable granularity and boundary erosion clustering

Granular rule-based modeling using the principle of justifiable granularity and boundary erosion clustering

Granular Description of Data Structures: A Two-Phase Design.

The study is concerned with a description of large numeric data with the aid of building a limited collection of representative information granules with the objective of capturing the structure of the original data. The proposed development scheme consists of two steps. First, a clustering algorithm characterized by high flexibility of coping with the diverse geometry of data structure and efficient computational overhead is invoked. At the second step, a clustering algorithm applied to the clusters already formed during the first phase, yielding a collection of numeric prototypes is involved and the numeric prototypes produced there are then generalized into their granular prototypes. The quality of granular prototypes is quantified while their build-up is supported by the mechanisms of granular computing such as the principle of justifiable granularity. In this paper, the clustering algorithms of DBSCAN and fuzzy C -means were used in successive phases of the processed approach. The experimental studies concerning synthetic data and publicly available data are covered and the performance of the developed approach is assessed along with a comparative analysis.