Variable-Basis Fuzzy Filters

Abstract

U. H{ö}hle and A. {Š}ostak have developed in \cite{HS} the category of complete quasi-monoidal lattices; S. E. Rodabaugh in \cite{RO} proposed its opposite category and with a subcategory $\mathbf{C}$ of the latter, he define grounds of the form $\mathbf{SET}\times \mathbf{C}$. In this paper, for each ground category of the form $\mathbf{SET}\times \mathbf{C}$, we study categorical frameworks for variable-basis fuzzy filters, particularly the category $\mathbf{C}-\mathbf{FFIL}$ of variable-basis fuzzy filters, as a natural generalization of the category of fixed-basis fuzzy filters which was introduced in \cite{LO}. In addition, we get some relations between the category of variable-basis fuzzy filters and the category of variable-basis fuzzy topological spaces.