In this paper, we propose an Interactive Fuzzy Interval Reasoning (FIR) method by combining fuzzy logic with interval computing to better serve Web users in terms of effectiveness and flexibility. Web users may use convenient interval inputs for online shopping. In order to serve different customers based on their preferences, different personalized fuzzy partitions to meet different needs are ...

Many indices have been proposed in literature for the comparison of two crisp data partitions, as resulting from two different classifications attempts, two different clustering solutions or the comparison of a predicted vs. a true labelling. Crisp partitions however cannot model ambiguity, vagueness or uncertainty in class definition and thus are not suitable to model all cases where informati...

The concept of Lucky k-polynomials and in particular Lucky χ-polynomials was recently introduced. This paper introduces Stirling number of the fourth kind and Lucky partitions of a finite set in order to determine either the Lucky k- or Lucky χ-polynomial of a graph. The integer partitions influence Stirling partitions of the second kind.

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Cluster validation is an important issue in fuzzy clustering research and many validity measures, most of which are motivated by intuitive justification considering geometrical features, have been developed. This paper proposes a new validation approach, which evaluates the validity degree of cluster partitions from the view point of the optimality of objective functions in FCM-type clustering....

Cluster validation is an important issue in fuzzy clustering research and many validity measures, most of which are motivated by intuitive justification considering geometrical features, have been developed. This paper proposes a new validation approach, which evaluates the validity degree of cluster partitions from the view point of the optimality of objective functions in FCM-type clustering....

Cluster validation is an important issue in fuzzy clustering research and many validity measures, most of which are motivated by intuitive justification considering geometrical features, have been developed. This paper proposes a new validation approach, which evaluates the validity degree of cluster partitions from the view point of the optimality of objective functions in FCM-type clustering....

Cluster validation is an important issue in fuzzy clustering research and many validity measures, most of which are motivated by intuitive justification considering geometrical features, have been developed. This paper proposes a new validation approach, which evaluates the validity degree of cluster partitions from the view point of the optimality of objective functions in FCM-type clustering....