A rough set, first described by Polish computer scientist Zdzis?aw Pawlak, is a formal approximation of a crisp set, and it is now known as a new mathematical tool to process vague concepts.They are used for machine learning, knowledge discovery, feature selection, etc., and are applied to artificial intelligence, medical informatics, civil engineering, Kansei engineering, decision science, business administration, and so on. Especially, research on data mining using rough sets is widely spreading, and the obtained association rules are applied to the characterisation of data and decision support.

Rough set research started with the use of equivalence classes defined in the table data, but has recently expanded to granularity calculation, which is a broader concept. Rough sets and granular computing provide a framework to adjust the granularity of information according to purpose. The combination of rough sets and fuzzy sets also needs to be considered. Both sets compensate for the weak points of frameworks mutually, thereby defining more robust frameworks. On the other hand, the progress of artificial intelligence technology seen in deep learning in recent years is remarkable.

In this Special Issue entitled “Rough Sets and Data Mining from IET CAAI Transactions on Intelligence Technology” the latest research trends of rough sets, partly fuzzy sets and clustering,granularity calculation and data mining are summarised, and fundamental and applied research towards strengthening their association with artificial intelligence are introduced. Following comprehensive peer review seven papers were accepted.

The first paper in this Special Issue,“Fuzzy decision implications:Interpretation within fuzzy decision context”,by Jing Zhang,Yanhui Zhai, and Deyu Li, considers fuzzy decision implications A ?B under fuzzy decision tables. The authors define the interpretation of fuzzy decision implication in fuzzy decision context, and show that ‘a(chǎn) closed fuzzy set of fuzzy decision implications can be obtained from fuzzy decision contexts’ and its converse. A correspondence between closed fuzzy sets of fuzzy decision implications and fuzzy decision contexts is shown. Since a rule is often defined as an implication satisfying proper constraint, it is important to clarify the characteristics of such implications and decision tables.

The second paper in this Special Issue, “Rough set-based rule generation and Apriori-based rule generation from table data sets:A survey and a combination”, by Hiroshi Sakai and Michinori Nakata, surveys rough set-based rule generation and Apriori-based rule generation. The authors combine multiple methodologies,including: Pawlak’s rough sets, Lipski’s incomplete information databases, Or?owska’s nondeterministic information systems (NIS)and Agrawal’s Apriori algorithm. They then propose the framework termed Rough sets Non-deterministic Information Analysis (RNIA). In this paper, the details of the investigated NIS-Apriori algorithm, which is an adjusted Apriori algorithm to NIS, are described. The NIS-Apriori algorithm realised rule generation from NIS.

The third paper in this Special Issue, “Rough set-based rule generation and Apriori-based rule generation from table data sets II: SQL-based environment for rule generation and decision support”, by Hiroshi Sakai and Zhiwen Jian, is twinned with the second paper, and focuses on the application of the obtained rules to decision support. In order to realise the convenient decision support system, sub-programs in SQL are implemented. An example is presented to show the sequence of rule generation and decision support.

The fourth paper in this Special Issue, “Survey on cloud model based similarity measure of uncertain concepts”, by Shuai Li,Guoyin Wang, and Jie Yang, gives similarity measure methods of a cloud model, which are applied to image retrieval, collaborative filtering, public opinion guidance, as well as, many fields of artificial intelligence. In this paper, especially Gaussian Cloud Model (GCM) is picked up, and related algorithms are described.The authors also consider the problems of current similarity measures from four aspects: discriminability, efficiency, stability and interpretability. Throughout this paper, cloud model and its application are surveyed. Finally, the authors give future perspectives on similarity measure of cloud model based on axiomatization.

The fifth paper in this Special Issue, “Rule induction based on rough sets from information tables having continuous domains”,by Michinori Nakata, Hiroshi Sakai, and Keitarou Hara, discusses rough sets and rule induced from tables with continuous values.The authors start from neighbourhood rough sets handling complete information, and extend it to the case of handling incomplete information. They propose four types of rules: certain consistent, certain inconsistent, possible consistent and possible inconsistent combined rules, and present the methods to induce the four types of rules. The validity of each method is ensured by using possible world semantics in logic. These combined rules express more applicable regulation from tables with incomplete information and continuous domains.

The sixth paper in this Special Issue, “Neighborhood systems based attribute reduction in formal decision contexts”, by Xiaohe Zhang, Jusheng Mi, Meishe Liang, and Meizheng Li, presents attribute reduction and rule acquisition in formal decision contexts.In formal decision context, it is necessary to remark the relationship between concept lattices and redundant condition attributes. The authors consider consistent formal decision contexts at first and extend it to inconsistent formal decision contexts.Weak neighbourhood granular decision rules and strong neighbourhood granular decision rules are proposed, and they are obtained by using the discernibility matrix methods. Theoretical results supporting the validity of the authors’ framework are given.

The seventh paper in this Special Issue, “Influence of kernel clustering on a radial basis function network”, by Changming Zhu and Duoqian Miao, investigates classical radial basis function network (RBFN) and the influence of kernel clustering. In order to strengthen RBFN, the authors propose kernel clustering algorithm and dynamic kernel clustering. Using experiments the authors examine the capabilities of kernel clustering algorithms and state that ‘the performance of RBFN with a new kernel clustering method becomes better than the original algorithm’. Finally, the authors describe the necessity of kernel clustering for achieving a better performance for classification.

In closing, the Guest Editors would like to acknowledge the efforts of all of the authors for their generous and insightful contributions. We also thank the reviewers for their decisive,on-time reviews. We are grateful to Professors Cesare Alippi and Hong Liu, Chief Editors-in-Chief of CAAI Transactions on Intelligence Technology for inviting us to serve as Guest Editors of this Journal and to Ms Liu He of the Editorial Office Staff for her ongoing assistance in the publication of this Special Issue.