The authors have been coping with new computational methodologies such as rough sets, information incompleteness, data mining, granular computing, etc., and developed some software tools on association rules as well as new mathematical frameworks. They simply term this research Rough sets Non-deterministic Information Analysis (RNIA). They followed several novel types of research, especially Pawlak's rough sets, Lipski's incomplete information databases, Orłowska's non-deterministic information systems, Agrawal's Apriori algorithm. These are outstanding researches related to information incompleteness, data mining, and rule generation. They have been trying to combine such novel researches, and they have been trying to realise more intelligent rule generator handling data sets with information incompleteness. This study surveys the authors’ research highlights on rule generators, and considers a combination of them.

This study follows the previous study entitled ‘Rough set-based rule generation and Apriori-based rule generation from table data sets: A survey and a combination’, and this is the second study on ‘Rough set-based rule generation and Apriori-based rule generation from table data sets’. The theoretical aspects are described in the previous study, and here the aspects of application, an SQL-based environment for rule generation and decision support, are described. At first, the implementation of rule generator defined in the previous study is explained, then the application of the obtained rules to decision support is considered. Especially, the following two issues are focused on, (i) Rule generator from table data sets with uncertainty in SQL, (ii) The manipulation in decision support below: (ii-a) In the case that an obtained rule matches the condition, (ii-b) In the case that any obtained rule does not match the condition. The authors connect such cases with decision support and realised an effective decision support environment in SQL.

It is a basic task to measure the similarity between two uncertain concepts in many real-life artificial intelligence applications, such as image retrieval, collaborative filtering, public opinion guidance, and so on. As an important cognitive computing model, cloud model has been used in many fields of artificial intelligence. It can realise the bidirectional cognitive transformation between qualitative concept and quantitative data based on the theory of probability and fuzzy set. The similarity measure of two uncertain concepts is a fundamental issue in cloud model theory. Popular similarity measure methods of cloud model are surveyed in this study. Their limitations are analysed in detail. Some related future research topics are proposed.

Fuzzy decision implication is an extension of decision implication in the fuzzy setting, serving to uncover the dependencies of fuzzy attributes. This study presents the interpretation of fuzzy decision implication in the fuzzy decision context. Specially, they will show that from fuzzy decision contexts one can obtain a closed fuzzy set of fuzzy decision implications, and the semantical characteristic of the obtained fuzzy set can be interpreted by fuzzy decision context and can be represented by some operators of fuzzy decision context. Conversely, starting from a fuzzy set of fuzzy decision implications, they can form a fuzzy decision context, from which the given fuzzy set can be derived. The result actually implies that they have constructed a correspondence between closed fuzzy sets of fuzzy decision implications and fuzzy decision contexts, and thus shows the equivalence of two interpretations of fuzzy decision implications.

Information tables having continuous domains are handled by neighborhood rough sets. Two approximations in complete information tables are extended to handle incomplete information. Consequently, four approximations are obtained: certain and possible lower ones and certain and possible upper ones without computational complexity. These extended approximations create the same results as the ones from possible world semantics by using possible indiscernibility relations. Therefore, the extension is justified. In complete information tables two types of single rules that an object supports are obtained: consistent and inconsistent ones. The single rule has low applicability. To increase applicability, a series of single rules are brought into one combined rule with an interval value. In incomplete information tables four kinds of single rules are obtained. From them, four kinds of combined rules are obtained: certain and consistent, possible and consistent, certain and inconsistent, and possible inconsistent ones. A combined rule has higher applicability than the single rules from which it is assembled.

Attribute reduction of formal decision context mainly uses the relationship between two concept lattices generated by the condition and decision attributes to remove redundant condition attributes. By using decision attributes to observe the covering of objects, this study defines two types of consistent sets and reducts in a consistent formal decision context based on neighbourhood systems. Four types of reductions in inconsistent formal decision contexts are also studied. The methods to calculate all types of reductions are formulated by discernibility matrix. Finally, an approach to obtain the decision rules in consistent formal decision context is proposed.

Classical radial basis function network (RBFN) is widely used to process the non-linear separable data sets with the introduction of activation functions. However, the setting of parameters for activation functions is random and the distribution of patterns is not taken into account. To process this issue, some scholars introduce the kernel clustering into the RBFN so that the clustering results are related to the parameters about activation functions. On the base of the original kernel clustering, this study further discusses the influence of kernel clustering on an RBFN when the setting of kernel clustering is changing. The changing involves different kernel-clustering ways [bubble sort (BS) and escape nearest outlier (ENO)], multiple kernel-clustering criteria (static and dynamic) etc. Experimental results validate that with the consideration of distribution of patterns and the changes of setting of kernel clustering, the performance of an RBFN is improved and is more feasible for corresponding data sets. Moreover, though BS always costs more time than ENO, it still brings more feasible clustering results. Furthermore, dynamic criterion always cost much more time than static one, but kernel number derived from dynamic criterion is fewer than the one from static.