Clustering method for production of Znumber based ifthen rules Abstract   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 xe2x80x9cIfThenxe2x80x9d 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 humantractable rules. The suggested clustering algorithm utilizes the FCM objective function and an evolutionary algorithm to produce fuzzy sets of fuzzy clusters. To form Zclusters and use them as components for the rules we exploit the relationship existing between Type2 Fuzzy and Znumber concepts. A benchmark problem and a realworld application are considered to demonstrate the usefulness of the proposed approach.

An Evolutionary NeuroFuzzy Cmeans Clustering Technique Abstract   One of the standard approaches for data analysis in unsupervised machine learning techniques is cluster analysis or clustering, where the data possessing similar features are grouped into a certain number of clusters. Among several significant ways of performing clustering, Fuzzy Cmeans (FCM) is a methodology, where every data point is hypothesized to be associated with all the clusters through a fuzzy membership function value. FCM is performed by minimizing an objective functional by optimally estimating the decision variables namely, the membership function values and cluster representatives, under a constrained environment. With this approach, a marginal increase in the number of data points leads to an enormous increase in the size of decision variables. This explosion, in turn, prevents the application of evolutionary optimization solvers in FCM, which thereby leads to inefficient data clustering. In this paper, a NeuroFuzzy CMeans Clustering algorithm (NFCM) is presented to resolve the issues mentioned above by adopting a novel Artificial Neural Network (ANN) based clustering approach. In NFCM, a functional map is constructed between the data points and membership function values, which enables a significant reduction in the number of decision variables. Additionally, NFCM implements an intelligent framework to optimally design the ANN structure, as a result of which, the optimal number of clusters is identified. Results of 9 different data sets with dimensions ranging from 2 to 30 are presented along with a comprehensive comparison with the current stateoftheart clustering methods to demonstrate the efficacy of the proposed algorithm.