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"justifiable"
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The people vs. Alex Cross
Alex Cross has never been on the wrong side of the law--until he's charged with gunning down followers of his nemesis Gary Soneji in cold blood. Now Cross is being turned into the poster child for trigger-happy cops who think they're above the law. It was self-defense; will a jury see it that way? As Cross fights for his professional life and his freedom, his former partner John Sampson brings him a gruesome, titillating video tied to the mysterious disappearances of several young girls. Despite his suspension from the department, Cross can't say no to Sampson. The illicit investigation leads them to the darkest corners of the Internet, where murder is just another form of entertainment. As the prosecution presents its case, and the nation watches, even those closest to Cross begin to doubt his innocence. If he can't convince his own family that he didn't pull the trigger with intent to kill, how can he hope to persuade a jury? But even with everything on the line, Cross will do whatever it takes to stop a dangerous criminal, even if he can't save himself. -- Adapted from dust jacket.
Book
DVRP with limited supply and variable neighborhood region in refined oil distribution
Limited supply can be an emergent issue in refined oil distribution, which may increase operating cost and decrease gasoline station satisfaction with shortage. Hence, how to devise an optimal distribution scheme is the central problem for oil distribution companies. The main problem with limited supply involves: (I) depicting the dynamic efforts on vehicle routing driven by the demand and priority of gasoline stations, and (II) incorporating the efforts into variable distribution region division associated with oil depots. In this paper, we propose a multi-objective optimization model for dynamic vehicle routing problem with limited supply in oil distribution with variable neighborhood region. First, a preliminary multi-stage model for dynamic vehicle routing problem is designed, which takes operating cost, gasoline station satisfaction and priority into consider in the setting of limited supply. Based on the preliminary model, a variable neighborhood region division model is presented for oil depot supply and tanker delivery, in light of Fuzzy C-means algorithm and justifiable granularity principle. Finally, the experimental results show that the dynamic vehicle programming model with variable neighborhood performs better than other comparable scenarios at cost savings and satisfaction improvement.
Journal Article
Electric-load forecasting using interval models based on granularity and justifiable principles
Traditional load-forecasting methods rely heavily on extensive historical data to predict future values, thus limiting their applicability in long-term forecasts where historical data may be unavailable or irrelevant. While several forecasting techniques, such as regression models and machine learning/deep learning approaches, have been tested, the inherent uncertainty in long-horizon predictions remains a major challenge. To address this gap, an interval-based modeling framework grounded in granular computing is proposed. Specifically, justifiable granules are constructed to define interpretable lower and upper bounds around the central tendency of load values, optimized through a justification criterion that balances coverage and specificity. This approach enables the quantification of uncertainty without assuming specific distributional forms. These granules are generated for multiple temporal resolutions (daily, weekly, and monthly) using historical load data from 2020 to 2022 and evaluated against unseen data from 2023. A detailed overlap analysis is performed to assess the alignment between combined and year-specific intervals, providing insights into generalizability and robustness. Visualizations further demonstrate the interpretability of the proposed intervals, offering a practical solution for long-term load modeling under uncertainty.
Journal Article
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.
Journal Article
Forming Learners Through Citizenship Education to Recognise and Counter Lawlessness in their Surroundings
Due to various conditions, countries such as Venezuela, Nigeria, and South Africa suffer from lawlessness (disregard of norms and rules of society) today, threatening their social fabric. It is contended on the basis of the situation in South Africa that citizenship education is arguably a suitable vehicle (in combination with, for instance, religion education, moral education, and forgiveness education) for offering tolerance, forgiveness, hospitality, and reconciliation education in schools, all of these as means for counteracting lawless (deviant, errant) behaviour. Thus far, reflection on citizenship education has, however, been characterised by conceptual uncertainty, controversy, and a wide range of applications in practice. The paper reports on theoretical interpretive-constructivist research. This research is aimed at the question of how citizenship education could be employed to form (equip, educate) young people so that they can be able to display morally justifiable behaviour and recognise and counteract lawlessness wherever they encounter it in their lifeworld.
Journal Article
A novel multifactor type-2 fuzzy time series model based on improved fuzzy C-means algorithm and justifiable granularity for stock index forecasting
Fuzzy time series (FTS) models are widely used in prediction tasks due to their ability to handle uncertain and nonlinear problems effectively. However, type-1 fuzzy sets have limitations in dealing with data noise and linguistic ambiguity, particularly in multifactor situations. This study proposes a multifactor stock index forecasting model based on type-2 fuzzy sets and a variable size interval partitioning technique. Firstly, information granules are constructed with enhanced effectiveness and interpretability. This is achieved using the fuzzy C-means (FCM) clustering algorithm and the principle of justifiable granularity to partition the universe of discourse. The FCM algorithm in this model attains optimal clustering results by employing an interval type-2 fuzzy approach to adjust the fuzzy parameter m in FCM. Secondly, to more accurately capture the non-determinacy in the time series, three observations of the stock index are modeled as type-2 fuzzy sets, which results in a group of refined first-order fuzzy relationships. To evaluate the performance of this model, experiments were conducted using six benchmark datasets from the Taiwan Stock Exchange Index (TAIEX). The corresponding root mean square error (RMSE) was calculated as the evaluation criterion. Compared with nine representative time series forecasting approaches, the experimental results demonstrate that our model not only guarantees effectiveness and robustness but also achieves enhanced prediction performance.
Journal Article
A novel multi-level framework for anomaly detection in time series data
Anomaly detection is a challenging problem in science and engineering that appeals to numerous scholars. It is of great relevance to detect anomalies and analyze their potential implications. In this study, a multi-level anomaly detection framework with information granules of higher type and higher order is developed based on the principle of justifiable granularity and Fuzzy C-Means (FCM) clustering algorithm, including two different types of approaches, namely abstract level approach (ALA) and detailed level approach (DLA). The ALA approach is implemented at a comparatively abstract level (viz., level-1), in which two distinct types of information granules of order-1 (viz., information granules of type-1 and type-2) are employed for anomaly detection. The DLA approach is formulated and derived from the ALA approach at a more detailed level (viz., level-2), which generates more detailed information granules, namely information granules of order-2, through successive splitting information granules and the FCM clustering algorithm to refine the problem at various levels. Furthermore, a similarity measurement algorithm is designed for anomaly detection utilizing information granules of higher type and higher order. Comprehensive performance indexes are produced to quantify the performance of the proposed framework compared with the methods of two single-level approaches and two multi-level approaches. Synthetic data and several real-world data coming from various areas are engaged to demonstrate and support the superiority of the proposed approaches over other classical methods in terms of detection accuracy and data anomaly resolution.
Journal Article
Advancing Federated Learning with Granular Computing
Over the recent years, we have been witnessing spectacular achievements of Artificial Intelligence (AI) and Machine Learning (ML), in particular. We have seen highly visible accomplishments encountered in natural language processing and computer vision impacting numerous areas of human endeavours. Being driven inherently by the technologically advanced learning and architectural developments, ML constructs are highly impactful coming with far reaching consequences; just to mention autonomous vehicles, health care imaging, decision-making processes in critical areas, among others. The quality of ML architectures and credibility of generated results are inherently implied by the nature, quality, and amount of available data. The credibility of ML models and confidence quantified their results are also of paramount concern to any critical application. In this study, we advocate that the credibility (confidence) of results produced by ML constructs is inherently expressed in the form of information granules. Several development scenarios are carefully revisited including those involving constructs in statistics (confidence and prediction intervals), probability (Gaussian process models), and granular parameters (fuzzy sets and interval techniques). We augment the commonly encountered and challenging category of applications of ML referred to as federated learning where the aspect of quality of the model and its results calls for a thorough assessment.
Journal Article
An Enhanced Fuzzy Time Series Forecasting Model Integrating Fuzzy C-Means Clustering, the Principle of Justifiable Granularity, and Particle Swarm Optimization
In this paper, we propose a novel fuzzy time series forecasting model that integrates fuzzy C-means (FCM) clustering, the principle of justifiable granularity (PJG), and particle swarm optimization (PSO), with a focus on leveraging symmetry in subinterval partitioning to enhance model interpretability and forecasting accuracy. First, the FCM method is employed to partition the universe of discourse, generating an initial division of subintervals. To ensure symmetric information representation, triangular fuzzy information granules are constructed for these subintervals in accordance with the principle of justifiable granularity. Then, an objective function is formulated for the entire universe of discourse, and the PSO algorithm is utilized to optimize the subinterval division, resulting in the final optimal partition. This process ensures that the subintervals achieve a balance between coverage and specificity, thereby introducing a form of symmetry in the partitioning of the universe of discourse. Leveraging the optimized symmetric partition, the framework of the fuzzy time series model is implemented for forecasting. Finally, the proposed approach is carried out on the Taiwan Weighted Stock Index (TAIEX) datasets and the Shanghai Composite Index (SHCI) datasets. The forecasting results demonstrate that the proposed approach achieves higher prediction accuracy and semantic accuracy compared with other methods.
Journal Article
DBSCAN-based granular descriptors for rule-based modeling
Rule
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based modeling is a useful approach in modeling both complex nonlinear and non-numeric systems, e.g. having linguistic information. However, modeling complex systems in big data era brings new challenges for conventional rule-based modeling, such as high computation overhead and low representation ability of rule. To address these problems, this paper proposed an advanced rule-based modeling method-based DBSCAN-inspired granular descriptors. First, to understand the essential characteristics of data and enhance rules’ representation ability, data structures are obtained by DBSCAN clustering algorithm, which has high flexibility at coping with diverse geometry. Second, numerous granular descriptors are constructed in the refined representation of data structures and used for fuzzy rule formation. This granular computing process could effectively reduce computation overhead of big data analysis. Finally, the proposed rule-based model consists of fuzzy rules and interval outputs, which are resulted from structural granular descriptors and justifiable granulating respectively. Experimental studies concerning synthetic data and publicly available data illustrated that the proposed method can achieve prior performance on both modeling and time consuming than conventional rule-based modeling via FCM. Therefore, it is verified the developed approach is feasible and useful to be applied in modeling real complex engineering systems.
Journal Article