In this communication, we introduce an original algorithm for computing both dominant and absorbent kernels in a bipolar ordinal valued digraph. The approach relies on theoretical results recently obtained by Bisdorff, Pirlot and Roubens [8] which give a constructive – fixpoint equation based – proof of the bijection between bipolar ordinal valued kernels of such a valued digraph and the crisp ...

An ilttempt is made here to delnonslrale tile way of implemenllng the concept of fuzzy geometry in image proeessing/"Ilalysls prohlems. Some new measures "re also provided in lhis eontexL Four ,Jigorilhllls ,Ire described for objeet/baekgroulld classification and skeleton extraction in both fuzzy and nonfuZ7.y (crisp) forms. Their effectiveness is demollsl r;'lc<! Oil various lypes of images. T...

Our reasoning is clearly fuzzy, so why is crisp logic so often adequate? We explain this phenomenon by showing that in the presence of noise, an arbitrary continuous (e.g., fuzzy) system can be well described by its discrete analog. However, as the description gets more accurate, the continuous description becomes necessary. 1 Formulation of the Problem Fuzzy logic is needed. Our reasoning is c...

Two recently developed methods for extraction of crisp logical rules from neural networks trained with backpropagation algorithm are compared. Both methods impose constraints on the structure of the network by adding regularization terms to the error function. Networks with minimal number of connections are created, leading to a small number of crisp logical rules. The two methods are compared ...