This paper is a survey of fuzzy set theory applied in cluster analysis. These fuzzy clustering algorithms have been widely studied and applied in a variety of substantive areas. They also become the major techniques in cluster analysis. In this paper, we give a survey of fuzzy clustering in three categories. The first category is the fuzzy clustering based on fuzzy relation. The second one is t...

A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.

A general framework for cluster tilting is set up by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal oneorthogonal subcategory) carries an induced abelian structure. These abelian quotients turn out to be module categories of Gorenstein algebras of dimension at most one.

The present study was a cross-sectional study conducted to reveal the prevalence of metabolic syndrome and its components and describe the features of such prevalence among Japanese workers by clustered business category using big data. The data of approximately 120,000 workers were obtained from a national representative insurance organization, and the study analyzed the health checkup and que...

In analogy with the classical theory of filters, for finitely complete or small categories, we provide concepts filter, \(\mathfrak{G}\)-neighborhood (short "Grothendieck-neighborhood") and cover-neighborhood points such to study convergence, cluster point, closure sieves compactness on objects that kind categories. Finally, all these in category \(\mathbf{Loc}\) locales.