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In this letter, we give a new, more direct derivation of the con- vergence properties of the fuzzy c-means (FCM) algorithm, using the equivalence between the original and reduced FCM criterion. From the point of view of the reduced criterion, the FCM algorithm is simply a steepest descent algorithm with variable steplength. We prove that steplength adjustment follows from the majorization principle for steplength. By applying the majorization principle we give a straightforward proof of global con- vergence. Further convergence properties follow immediately using known results of optimization theory. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a method for an automatic and complete design of fuzzy systems from data. The main objective is to build fuzzy systems with a user-controllable trade-off between accuracy and interpretability. Whereas criteria for accuracy mostly follow straightforwardly from the application, definition of interpretability and its criteria are subject to controversial discussion. For this reason, a set of interpretability criteria is given which guide the design process. Consequently, interpretability is maintained by structural choices regarding the type of membership functions, rules, and inference mechanism, on the one hand, and by including interpretability criteria in the rule/rule base evaluation, on the other hand. An application in Instrumented Gait Analysis, to characterize a certain group of patients in comparison to healthy subjects, illustrates the proposed algorithm. [Copyright &y& Elsevier]