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Article ; Online: Computing and Clustering in the Environment of Order-2 Information Granules.

Pedrycz, Witold

IEEE transactions on cybernetics

2023 Volume 53, Issue 9, Page(s) 5414–5423

Abstract: A visible trend in representing knowledge through information granules manifests in the developments of information granules of higher type and higher order, in particular, type-2 fuzzy sets and order-2 fuzzy sets. All these constructs are aimed at the ... ...

Abstract	A visible trend in representing knowledge through information granules manifests in the developments of information granules of higher type and higher order, in particular, type-2 fuzzy sets and order-2 fuzzy sets. All these constructs are aimed at the formalization and processing data at a certain level of abstraction. Along the same line, in the recent years, we have seen intensive developments in fuzzy clustering, which are not surprising in light of a growing impact of clustering on fundamentals of fuzzy sets (as supporting ways to elicit membership functions) as well as algorithms (in which clustering and clusters form an integral functional component of various fuzzy models). In this study, we investigate order-2 information granules (fuzzy sets) by analyzing their formal description and properties to cope with structural and hierarchically organized concepts emerging from data. The design of order-2 information granules on a basis of available experimental evidence is discussed and a way of expressing similarity (resemblance) of two order-2 information granules by engaging semantically oriented distance is discussed. In the sequel, the study reported here delivers highly original contributions in the realm of order-2 clustering algorithms. Formally, the clustering problem under discussion is posed as follows: given is a finite collection of reference information granules. Determine a structure in data defined over the space of such granules. Conceptually, this makes a radical shift in comparison with data defined in the p -dimensional space of real numbers Rp. In this situation, expressing distance between two data deserves prudent treatment so that such distance properly captures the semantics and consequently, the closeness between any two information granules to be determined in cluster formation. Following the proposal of the semantically guided distance (and its ensuing design process), we develop an order-2 variant of the fuzzy C-means (FCM), discuss its detailed algorithmic steps, and deliver interpretation of the obtained clustering results. Several relevant applied scenarios of order-2 FCM are identified for spatially and temporally distributed data, which deliver interesting motivating arguments and underline the practical relevance of this category of clustering. Experimental studies are provided to further elicit the performance of the clustering method and discuss essential ways of interpreting results.
Language	English
Publishing date	2023-08-17
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2022.3163350
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Negation of the Quantum Mass Function for Multisource Quantum Information Fusion With its Application to Pattern Classification.

Xiao, Fuyuan / Pedrycz, Witold

IEEE transactions on pattern analysis and machine intelligence

2023 Volume 45, Issue 2, Page(s) 2054–2070

Abstract: In artificial intelligence systems, a question on how to express the uncertainty in knowledge remains an open issue. The negation scheme provides a new perspective to solve this issue. In this paper, we study quantum decisions from the negation ... ...

Abstract	In artificial intelligence systems, a question on how to express the uncertainty in knowledge remains an open issue. The negation scheme provides a new perspective to solve this issue. In this paper, we study quantum decisions from the negation perspective. Specifically, complex evidence theory (CET) is considered to be effective to express and handle uncertain information in a complex plane. Therefore, we first express CET in the quantum framework of Hilbert space. On this basis, a generalized negation method is proposed for quantum basic belief assignment (QBBA), called QBBA negation. In addition, a QBBA entropy is revisited to study the QBBA negation process to reveal the variation tendency of negation iteration. Meanwhile, the properties of the QBBA negation function are analyzed and discussed along with special cases. Then, several multisource quantum information fusion (MSQIF) algorithms are designed to support decision making. Finally, these MSQIF algorithms are applied in pattern classification to demonstrate their effectiveness. This is the first work to design MSQIF algorithms to support quantum decision making from a new perspective of "negation", which provides promising solutions to knowledge representation, uncertainty measure, and fusion of quantum information.
Language	English
Publishing date	2023-01-06
Publishing country	United States
Document type	Journal Article
ISSN	1939-3539
ISSN (online)	1939-3539
DOI	10.1109/TPAMI.2022.3167045
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Oscillation-Bound Estimation of Perturbations Under Bandler-Kohout Subproduct.

Tang, Yiming / Pedrycz, Witold

IEEE transactions on cybernetics

2022 Volume 52, Issue 7, Page(s) 6269–6282

Abstract: The Bandler-Kohout subproduct (BKS) method is one of the two widely acknowledged fuzzy relational inference (FRI) schemes. The previous works related to its stability and robustness mainly concentrated on how the output values were changed with ... ...

Abstract	The Bandler-Kohout subproduct (BKS) method is one of the two widely acknowledged fuzzy relational inference (FRI) schemes. The previous works related to its stability and robustness mainly concentrated on how the output values were changed with perturbation parameters of input values. However, the works on estimating oscillation bounds of output values with regard to varying limits of input, are lacking. In this study, we investigate the oscillation-bound estimation of perturbations for BKS. First, the BKS output variation scopes are acquired for interval perturbation, where the R -implication, ( S, N )-implication, QL-implication, and t -norm implication are adopted. Second, in allusion to the more sophisticated problem of the fuzzy reasoning chain with BKS, the oscillation bounds of BKS output resulting from input interval perturbation are offered. Third, we construct the upper and lower bounds of BKS output deviation originated in the simple perturbation of the input fuzzy set, in which the situations of one rule and multiple rules are both dissected. Finally, the stable properties of all these BKS strategies are confirmed. It is emphasized that interval perturbation and simple perturbation are more general ways to give expression describing the robustness issue, and the obtained oscillation bounds also deliver more detailed characterization of the output deviation along with the input perturbation. This study further validates the sound properties of the BKS method.
Language	English
Publishing date	2022-07-04
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2020.3025793
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Weighted Fuzzy Clustering for Time Series With Trend-Based Information Granulation.

Guo, Hongyue / Wan, Mengjun / Wang, Lidong / Liu, Xiaodong / Pedrycz, Witold

IEEE transactions on cybernetics

2024 Volume 54, Issue 2, Page(s) 903–914

Abstract: 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 ... ...

Abstract	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.
Language	English
Publishing date	2024-01-17
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2022.3190705
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Incremental Fuzzy Clustering-Based Neural Networks Driven With the Aid of Dynamic Input Space Partition and Quasi-Fuzzy Local Models.

Zhang, Congcong / Oh, Sung-Kwun / Fu, Zunwei / Pedrycz, Witold

IEEE transactions on cybernetics

2024 Volume 54, Issue 5, Page(s) 2978–2991

Abstract: Fuzzy clustering-based neural networks (FCNNs) based on information granulation techniques have been shown to be effective Takagi-Sugeno (TS)-type fuzzy models. However, the existing FCNNs could not cope well with sequential learning tasks. In this study, ...

Abstract	Fuzzy clustering-based neural networks (FCNNs) based on information granulation techniques have been shown to be effective Takagi-Sugeno (TS)-type fuzzy models. However, the existing FCNNs could not cope well with sequential learning tasks. In this study, we introduce incremental FCNNs (IFCNNs), which could dynamically update themselves whenever new learning data (e.g., single datum or block data) are incorporated into the dataset. Specifically, we employ dynamic (incremental) fuzzy C-means (FCMs) clustering algorithms to reveal a structure in data and divide the entire input space into several subregions. In the aforementioned partition, the dynamic FCM adaptively adjusts the position of its prototypes by using sequential data. Due to the time-sharing arrival of training data, compared with batch learning models, incremental learning methods may lose classification (prediction) accuracy. In order to tackle this challenge, we utilize quasi-fuzzy local models (QFLMs) based on modified Schmidt neural networks to replace the popular linear functions in TS-type fuzzy models to refine and enhance the ability to represent the behavior of fuzzy subspaces. Meanwhile, the recursive least square error (LSE) estimation is utilized to update the weights of QFLMs from one-by-one or block-by-block (fixed or varying block size) learning data. In addition, the L
Language	English
Publishing date	2024-04-16
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2022.3228303
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: A Design of Granular Classifier Based on Granular Data Descriptors.

Zhu, Xiubin / Wang, Dan / Pedrycz, Witold / Li, Zhiwu

IEEE transactions on cybernetics

2023 Volume 53, Issue 3, Page(s) 1790–1801

Abstract: 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 ... ...

Abstract	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.
Language	English
Publishing date	2023-02-15
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2021.3132636
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: From Numeric to Granular Models: A Quest for Error and Performance Analysis.

Zhu, Xiubin / Pedrycz, Witold / Qu, Ting / Li, Zhiwu

IEEE transactions on cybernetics

2023 Volume 54, Issue 1, Page(s) 150–161

Abstract: In this study, we establish a new design methodology of granular models realized by augmenting the existing numeric models through analyzing and modeling their associated prediction error. Several novel approaches to the construction of granular ... ...

Abstract	In this study, we establish a new design methodology of granular models realized by augmenting the existing numeric models through analyzing and modeling their associated prediction error. Several novel approaches to the construction of granular architectures through augmenting existing numeric models by incorporating modeling errors are proposed in order to improve and quantify the numeric models' prediction abilities. The resulting construct arises as a granular model that produces granular outcomes generated as a result of the aggregation of the outputs produced by the numeric model (or its granular counterpart) and the corresponding error terms. Three different architectural developments are formulated and analyzed. In comparison with the numeric models, which strive to achieve the highest accuracy, granular models are developed in a way such that they produce comprehensive prediction outcomes realized as information granules. In virtue of the granular nature of results, the coverage and specificity of the constructed information granules express the quality of the results of prediction in a more descriptive and comprehensive manner. The performance of the granular constructs is evaluated using the criteria of coverage and specificity, which are pertinent to granular outputs produced by the granular models.
Language	English
Publishing date	2023-12-20
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2022.3175479
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Consensus Reaching Based on Social Influence Evolution in Group Decision Making.

Zhang, Yangjingjing / Chen, Xia / Pedrycz, Witold / Dong, Yucheng

IEEE transactions on cybernetics

2023 Volume 53, Issue 7, Page(s) 4134–4147

Abstract: A key issue in social network group decision making (SNGDM) is to determine the weights (i.e., social influences) of individuals. Notably, in some SNGDM scenarios, the social influences of individuals may evolve over time. Meanwhile, consensus reaching ... ...

Abstract	A key issue in social network group decision making (SNGDM) is to determine the weights (i.e., social influences) of individuals. Notably, in some SNGDM scenarios, the social influences of individuals may evolve over time. Meanwhile, consensus reaching is another important issue in SNGDM. In this article, we are dedicated to disclosing the natural evolution process of social influence, and further to discussing the consensus reaching issue in SNGDM. First, we establish the social influence evolution model, where the individual's social influence is obtained by combining his/her intrinsic influence and network influence. Afterward, we design the consensus reaching process based on social influence evolution (CRP-SIE) to assist the individuals to reach a consensus. Furthermore, we use a hypothetical application to show the applicability of the proposed CRP-SIE. Finally, simulation analysis is adopted to investigate the effects of social influence evolution on consensus reaching in SNGDM, and comparative analysis is conducted to demonstrate the advantages of our proposal.
MeSH term(s)	Humans ; Female ; Male ; Consensus ; Decision Making ; Computer Simulation
Language	English
Publishing date	2023-06-15
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2021.3139673
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Design of Granular Model: A Method Driven by Hyper-Box Iteration Granulation.

Lu, Wei / Ma, Cong / Pedrycz, Witold / Yang, Jianhua

IEEE transactions on cybernetics

2023 Volume 53, Issue 5, Page(s) 2899–2913

Abstract: Recently, granular models have been highlighted in system modeling and applied to many fields since their outcomes are information granules supporting human-centric comprehension and reasoning. In this study, a design method of granular model driven by ... ...

Abstract	Recently, granular models have been highlighted in system modeling and applied to many fields since their outcomes are information granules supporting human-centric comprehension and reasoning. In this study, a design method of granular model driven by hyper-box iteration granulation is proposed. The method is composed mainly of partition of input space, formation of input hyper-box information granules with confidence levels, and granulation of output data corresponding to input hyper-box information granules. Among them, the formation of input hyper-box information granules is realized through performing the hyper-box iteration granulation algorithm governed by information granularity on input space, and the granulation of out data corresponding to input hyper-box information granules is completed by the improved principle of justifiable granularity to produce triangular fuzzy information granules. Compared with the existing granular models, the resulting one can yield the more accurate numeric and preferable granular outcomes simultaneously. Experiments completed on the synthetic and publicly available datasets demonstrate the superiority of the granular model designed by the proposed method at granular and numeric levels. Also, the impact of parameters involved in the proposed design method on the performance of ensuing granular model is explored.
Language	English
Publishing date	2023-04-21
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2021.3124235
Database	MEDical Literature Analysis and Retrieval System OnLINE

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Article ; Online: Consensus Reaching Process for Traditional Group Decision Making in View of the Optimal Adjustment Mechanism.

Meng, Fan-Yong / Pedrycz, Witold / Tang, Jie

IEEE transactions on cybernetics

2023 Volume 53, Issue 6, Page(s) 3748–3759

Abstract: Consensus reaching process (CRP) is a key topic in the area of group decision making (GDM). When the consensus level is not high enough, it becomes necessary to adjust the original opinions of decision makers (DMs). To offer the adjustment reference for ... ...

Abstract	Consensus reaching process (CRP) is a key topic in the area of group decision making (GDM). When the consensus level is not high enough, it becomes necessary to adjust the original opinions of decision makers (DMs). To offer the adjustment reference for DMs, we build the programming models to determine the minimum modification to be carried out from the individual and global perspectives. Meanwhile, all DMs are divided into two subgroups: DMs with acceptable and unacceptable consensus levels. If some DMs with unacceptable consensus level do not accept the relevant modifications, the Nash bargaining game-based programming model is built for the fairness and efficiency of modifications. When some DMs refuse to make any modifications or tend to modify the opinions in their way, with respect to different group consensus situations, we make the minimum hybrid penalty mechanism by the Nash bargaining game-based programming models. For each case, we determine the corresponding optimal modification mechanism in view of the fixed individual total modification and the maximum consensus level. Furthermore, we study the arrangements of weights of DMs according to their cardinal and ordinal consensus contributions. Based on these results, we present a new algorithm and illustrate its application by a numerical example. Moreover, we carry out the sensitivity and comparison analysis. We summarize the conclusions and future research directions in the end. The main originality of the new method includes: the fairness and efficiency of modifications, and the determination of the hybrid penalty mechanism.
Language	English
Publishing date	2023-05-17
Publishing country	United States
Document type	Journal Article
ISSN	2168-2275
ISSN (online)	2168-2275
DOI	10.1109/TCYB.2022.3170589
Database	MEDical Literature Analysis and Retrieval System OnLINE

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