We are now living in an era of multimedia data. The past decades have witnessed an unprecedented upsurge in “big data” in China. Mobile multimedia devices are becoming mainstream, promoting the conversion of big data technologies into practices. The deployment of big data provides people with great opportunities to deal with what were formerly great challenges.

Against this background, research is ongoing to explore further possibilities in mobile multimedia developing. Mobile Multimedia Big Data Embedded Systems are transforming science, engineering, healthcare, medicine, finance, business, and ultimately our society itself. This special issue focuses on the state-of-the-art initiatives and the great promise in this field.

We thank all of the authors who submitted papers for this special section. We are also highly appreciative of the reviewers who provided valuable review feedback on the submissions. The editor hopes that this special issue will attract researchers’ interest and contribute to further developments in this field.

On September 6, 2017, we lost a great researcher, Prof. Lotfi A. Zadeh, the one who introduced one of the most important mathematical concepts that gets a good rapport with reality. “Fuzzy Sets” was the paper he published in 1965. Many researchers and practitioners of mathematics, science, engineering, medicine, and economics found it fascinating. In Japan, consumer electronics incorporating ambiguity in human thought and behavior became popular. As these products became big topics, the term “fuzzy” also became popular in the 1990s.

This set of papers offers a sample of the expanding development of fuzzy logic and soft computing. One review paper is written by Prof. Takeshi Yamakawa, an internationally famous fuzzy researcher of fuzzy hardware systems. Four of these papers were selected through a peer review process. One, “Design of Fuzzy Logic Controller and its Distinctive Features” by Prof. Takeshi Yamakawa, describes the design of a fuzzy logic controller and its application to controlling mouse-platform stabilization. The distinctive features of fuzzy logic control are also discussed.

The first original paper, “MMMs-Induced Possibilistic Fuzzy Co-Clustering and its Characteristics” by Ubukata et al., describes an NPCCMM scheme by considering variable cluster volumes and the fuzziness degree of item memberships to investigate the specific aspects of fuzzy rather than probabilistic nature in co-clustering tasks. The second original paper, “Inner Evaluation of Writing in a Foreign Language Based on Expert Judgment for Correction” by Entani et al., proposes a method of numerically deriving each writer’s writing preference from an expert’s initial evaluation. Third, “A 3-Dimensional Fuzzy Linguistic Evaluation Model” by Suprasongsin et al., describes a new model for determining criteria weights in group decision-making problems, a model based on the concept of probabilistic linguistic terms. The fourth original paper, “Natural Language Generation Using Monte Carlo Tree Search” by Kumagai et al., proposes a method for generating simulation-based natural language. The method accounts for both building a correct syntactic structure and reflecting the given situational information as input in the sentences generated.

We appreciate Prof. Takeshi Yamakawa for the excellent review of fuzzy controllers. We also thank all of the authors who submitted original articles and all of the reviewers who offered their valuable comments and suggestions.

Various applications of data analysis and their effects have been reported recently. With the remarkable progress in classification methods, one example being support vector machines, clustering as the main method of unsupervised classification has also been studied extensively. Consequently, fuzzy methods of clustering is becoming a standard technique. However, unsolved theoretical and methodological problems in fuzzy clustering remain and have to be studied more deeply. This issue collects five papers concerned with fuzzy clustering and related fields, and in all of them the main interest is methodology. Kondo and Kanzawa consider fuzzy clustering with a new objective function using q-divergence, which is a generalization of the well-known Kullback-Leibler divergence. Among different data types, they focus on categorical data. They also show the relations of different methods of fuzzy c-means. Thus, this study tends to further generalize methods of fuzzy clustering, trying to find the methodological boundaries of the capabilities of fuzzy clustering models. Kitajima, Endo, and Hamasuna propose a method of controlling cluster sizes so that the resulting clusters have an even size, which is different from the optimizing of cluster sizes dealt with in other studies. This technique enhances application fields of clustering in which cluster sizes are more important than cluster shapes. Hamasuna et al. study the validity measures of clusters for network data. Cluster validity measures are generally proposed for points in Euclidean spaces, but the authors consider the application of validity measures to network data. Several validity measures are modified and adapted to network data, and their effectiveness is examined using simple network examples. Ubukata et al. propose a new method of c-means related to rough sets, a method based on a different idea from well-known rough c-means by Lingras. Finally, Kusunoki, Wakou, and Tatsumi study the maximum margin model for the nearest prototype classifier that leads to the optimization of the difference of convex functions. All papers include methodologically important ideas that have to be further investigated and applied to real-world problems.