This paper shows that the k-means quantization of a signal can be interpreted both as a crisp indicator function and as a fuzzy membership assignment describing fuzzy clusters and fuzzy boundaries. Combined crisp and fuzzy indicator functions are defined here as natural generalizations of the ordinary crisp and fuzzy indicator functions, respectively. An application to iris segmentation is pres...

Cysteine-rich secretory protein-1 (CRISP-1) is a glycoprotein secreted by the epididymal epithelium. It is a member of a large family of proteins characterized by two conserved domains and a set of 16 conserved cysteine residues. In mammals, CRISP-1 inhibits sperm-egg fusion and can suppress sperm capacitation. The molecular mechanism of action of the mammalian CRISP proteins remains unknown, b...

BACKGROUND Whole grain rye products have been shown to increase satiety and elicit lower postprandial insulin response without a corresponding change in glucose response compared with soft refined wheat bread. The underlying mechanisms for these effects have not been fully determined The primary aim of the study was to investigate if whole grain rye crisp bread compared to refined wheat crisp b...

Conceptual neighborhood graphs capture the similarity among qualitative relations. This paper derives the graphs for the thirty-three topological relations between two crisp, undirected lines and for the seventy-seven topological relations between two lines with uncertain boundaries. The analysis of the graphs shows that the normalized node degrees increases, from the crisp to the broad-boundar...

Grass carp (Ctenopharyngodon idellus) is one of the most important freshwater fish that is native to China, and crisp grass carp is a kind of high value-added fishes which have higher muscle firmness. To investigate biological functions and possible signal transduction pathways that address muscle firmness increase of crisp grass carp, microarray analysis of 14,900 transcripts was performed. Co...

Fuzzy logic and fuzzy set theory enable us to use experts’ uncertain (“fuzzy”) knowledge in decision making. The corresponding methods usually generalize known methods of decision making which are based on the crisp (non-fuzzy) knowledge about the environment. These crisp methods enable us to come up with a crisp decision: e.g., whether we should build a plant or not. When we generalize these m...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...