The linguistic time-series forecasting model (LTS-FM), which has been recently proposed, uses linguistic words of linguistic variable domains generated by hedge algebras (HAs) to describe historical numeric time-series data. Then, the LTS-FM was established by utilizing real numeric semantics of words induced by the fuzziness parameter values (FPVs) of HAs. In the existing LTS-FMs, just the FPVs of HAs are optimized, while the used word set is still chosen by human experts. This paper proposes a co-optimization method of selecting the optimal used word set that best describes numeric time-series data in parallel with choosing the best FPVs of HAs to improve the accuracy of LTS-FMs by utilizing particle swarm optimization (PSO). In this co-optimization method, the outer loop optimizes the FPVs of HAs, while the inner loop optimizes the used word set. The experimental results on three datasets, i.e., the “enrollments of the University of Alabama” (EUA), the “killed in car road accidents in Belgium” (CAB), and the “spot gold in Turkey” (SGT), showed that our proposed forecasting model outperformed the existing forecasting models in terms of forecast accuracy.

The linguistic summarization of data is one of the study trends in data mining because it has many useful practical applications. A linguistic summarization of data aims to extract an optimal set of linguistic summaries from numeric data. The blended learning format is now popular in higher education at both undergraduate and graduate levels. A lot of techniques in machine learning, such as classification, regression, clustering, and forecasting, have been applied to evaluate learning activities or predict the learning outcomes of students. However, few studies have been examined to transform the data of blended learning courses into the knowledge represented as linguistic summaries. This paper proposes a method of linguistic summarization of blended learning data collected from a learning management system to extract compact sets of interpretable linguistic summaries for understanding the common rules of blended learning courses by utilizing enlarged hedge algebras. Those extracted linguistic summaries in the form of sentences in natural language are easy to understand for humans. Furthermore, a method of detecting the exceptional cases or outliers of the learning courses based on linguistic summaries expressing common rules in different scenarios is also proposed. The experimental results on two real-world datasets of two learning courses of Discrete Mathematics and Introduction to Computer Science show that the proposed methods have promising practical applications. They can help students and lecturers find the best way to enhance their learning methods and teaching style.

During last years, lots of the fuzzy rule based classifier (FRBC) design methods have been proposed to improve the classification accuracy and the interpretability of the proposed classification models. Most of them are based on the fuzzy set theory approach in such a way that the fuzzy classification rules are generated from the grid partitions combined with the pre-designed fuzzy partitions using fuzzy sets. Some mechanisms are studied to automatically generate fuzzy partitions from data such as discretization, granular computing, etc. Even those, linguistic terms are intuitively assigned to fuzzy sets because there is no formalisms to link inherent semantics of linguistic terms to fuzzy sets. In view of that trend, genetic design methods of linguistic terms along with their (triangular and trapezoidal) fuzzy sets based semantics for FRBCs, using hedge algebras as the mathematical formalism, have been proposed. Those hedge algebras-based design methods utilize semantically quantifying mapping values of linguistic terms to generate their fuzzy sets based semantics so as to make use of fuzzy sets based-classification reasoning methods proposed in design methods based on fuzzy set theoretic approach for data classification. If there exists a classification reasoning method which bases merely on semantic parameters of hedge algebras, fuzzy sets-based semantics of the linguistic terms in fuzzy classification rule bases can be replaced by semantics - based hedge algebras. This paper presents a FRBC design method based on hedge algebras approach by introducing a hedge algebra- based classification reasoning method with multi-granularity fuzzy partitioning for data classification so that the semantic of linguistic terms in rule bases can be hedge algebras-based semantics. Experimental results over 17 real world datasets are compared to existing methods based on hedge algebras and the state-of-the-art fuzzy sets theoretic-based approaches, showing that the proposed FRBC in this paper is an effective classifier and produces good results.

Forecasting methods based on fuzzy time series have been examined intensively during last years. Three main factors which affect the accuracy of those forecasting methods are length of intervals, the way of establishing fuzzy logical relationship groups, and defuzzification techniques. Many researches focus on optimizing length of intervals in order to improve forecasting accuracies by utilizing various optimization techniques. In the line of that research trend, in this paper, a hybrid particle swarm optimization combined with simulated annealing (PSO-SA) algorithm is proposed to optimize length of intervals to improve forecasting accuracies. The experimental results in comparison with the existing forecasting models show that the proposed forecasting model is an effective forecasting model.

Trong vài thập kỷ gần đây, nhiều nghiên cứu về mô hình dự báo dựa trên chuỗi thời gian mờ đã được đề xuất. Có nhiều nhân tố ảnh hưởng đến kết quả dự báo đã được nhiều tác giả tập trung nghiên cứu như kỹ thuật chia khoảng tập nền, các luật dự báo và kỹ thuật giải mờ. Tuy nhiên, các kết quả nghiên cứu vẫn còn nhiều hạn chế và chưa làm hài lòng người sử dụng. Trong bài báo này, chúng tôi đề xuất một phương pháp nâng cao hiệu quả của mô hình dự báo chuỗi thời gian mờ trên cơ sở kết hợp tối ưu các khoảng chia tập nền bằng thuật toán tối ưu bầy đàn và kỹ thuật giải mờ mới hiệu quả. Mô hình dự báo được đề xuất được ứng dụng để dự báo số sinh viên nhập học của Trường Đại học Alabama từ năm 1971 đến năm 1992. Kết quả thực nghiệm cho thấy, mô hình dự báo được đề xuất hiệu quả hơn các mô hình dự báo hiện có đối với cả chuỗi thời gian mờ bậc nhất và chuỗi thời gian mờ bậc cao.