We propose an extension of the Conn-Index to evaluate fuzzy cluster solutions obtained from fuzzy prototype vector quantization, whereas the original Conn-Index was designed for crisp vector quantization models. The fuzzy index explicitly takes the fuzzy assignments resulting from fuzzy vector quantization into account. This avoids the information loss which would occur if the original crisp in...

In this paper ∗–compatible extensions of fuzzy relations are studied, generalizing some results obtained by Duggan in case of crisp relations. From this general result are obtained as particular cases fuzzy versions of some important extension theorems for crisp relations (Szpilrajn, Hansson, Suzumura). Two notions of consistent closure of a fuzzy relation are introduced.

In this paper, we consider a time-optimal control problem with uncertainties. Dynamics of controlled object is expressed by crisp linear system of differential equations with fuzzy initial and final states. We introduce a notion of fuzzy optimal time and reduce its calculation to two crisp optimal control problems. We examine the proposed approach on an example.

Crisp and L-fuzzy ambiguous representations of closed subsets of one space by closed subsets of another space are introduced. It is shown that, for each pair of compact Hausdorff spaces, the set of (crisp or L-fuzzy) ambiguous representations is a lattice and a compact Hausdorff Lawson upper semilattice. The categories of ambiguous and L-ambiguous representations are defined and investigated.

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

Rat protein DE is an androgen-dependent cysteine-rich secretory protein (CRISP) synthesized by proximal epididymal regions. DE, also known as CRISP-1, is localized on the equatorial segment of acrosome-reacted spermatozoa and participates in gamete fusion through binding to egg complementary sites. Immunization of rats with DE inhibits fertility and sperm fusion ability, suggesting that DE repr...

We have developed a new and innovative technique for combining a high-spatial-resolution multispectral image with a lower-spatial-resolution hyperspectral image. The approach, called CRISP, compares the spectral information present in the multispectral image to the spectral content in the hyperspectral image and derives a set of equations to approximately transform the multispectral image into ...

Several approaches generalizing crisp association rules to fuzzy association rules have been proposed. In an our previous paper we introduced a pair of confidence measures for crisp association rules from which one can be obtained the majority known quality measures. In this paper, starting from these results we give an extension to fuzzy association rules.