CATEGORICAL RELATIONS AMONG MATROIDS, FUZZY MATROIDS AND FUZZIFYING MATROIDS

Abstract

The aim of this paper is to study the categorical relations between<br />matroids, Goetschel-Voxman's fuzzy matroids and Shi's fuzzifying matroids.<br />It is shown that the category of fuzzifying matroids is isomorphic to that of<br />closed fuzzy matroids and the latter is concretely coreflective in the category<br />of fuzzy matroids. The category of matroids can be embedded in that of<br />fuzzifying matroids as a simultaneously concretely reflective and coreflective<br />subcategory.