Clustering method for production of Z-number based if-then rules

Application of clustering algorithms to extract or summarize data from large data sets is a straightforward and effective approach. Sometimes data sets are not only large in size but also include imprecise and partially reliable pieces of information of probabilistic and possibilistic (fuzzy) nature. Information of this kind is referred to as bimodal information. There is a need to summarize such data into a compact set of human tractable “If-Then” rules, being a result of synergy of imprecision of both types. In this paper, we first present an approach to clustering with the purpose of extraction of probabilistic and fuzzy information (bimodal) categories suitable for formation of human-tractable rules. The suggested clustering algorithm utilizes the FCM objective function and an evolutionary algorithm to produce fuzzy sets of fuzzy clusters. To form Z-clusters and use them as components for the rules we exploit the relationship existing between Type-2 Fuzzy and Z-number concepts. A benchmark problem and a real-world application are considered to demonstrate the usefulness of the proposed approach.