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In this paper, we give a new characterization of M-fuzzifying span mappings defined by M-fuzzifying rank functions. Then we research the relations between M-fuzzifying span mappings and other M-fuzzifying mappings on M-fuzzifying matroid, and characterize the M-fuzzifying coindependent, nonspan and hyperplane mappings. Based on these characterizations, we put forward one class of special fuzzifying matroids. [ABSTRACT FROM AUTHOR]

In this paper, we give a new characterization of M-fuzzifying span mappings defined by M-fuzzifying rank functions. Then we research the relations between M-fuzzifying span mappings and other M-fuzzifying mappings on M-fuzzifying matroid, and characterize the M-fuzzifying coindependent, nonspan and hyperplane mappings. Based on these characterizations, we put forward one class of special fuzzifying matroids. [ABSTRACT FROM AUTHOR]

In this paper, the concept of strong inclusion orders between L-subsets is introduced. As a tool, it is applied to the following aspects. Firstly, the notion of algebraic L-closure operators is proposed and the resulting category is shown to be isomorphic to the category of L-convex spaces (also called algebraic L-closure spaces). Secondly, restricted L-hull operators, as generalizations of restricted hull operators, are introduced and the resulting category is also proved to be isomorphic to the category of L-convex spaces. Finally, by using the properties of strong inclusion orders, it is shown that the category of convex spaces can be embedded in the category of stratified L-convex spaces as a reflective subcategory and the concrete form of the coreflective functor from the category of L-convex spaces to the category of stratified L-convex spaces is presented. [ABSTRACT FROM AUTHOR]

In this paper, the concept of M-fuzzifying geodesic interval operators is introduced in M-fuzzifying metric spaces. It is a generalization of geodesic interval operators in metric spaces. And an M-fuzzifying geometric characterization of M-fuzzifying geodesic interval operators is obtained. Based on M-fuzzifying geodesic interval operators, M-fuzzifying geodesic convexities can be induced. [ABSTRACT FROM AUTHOR]

The concepts of I-greedoids, fuzzifying greedoids, and (I,I)-fuzzy greedoids are introduced and feasibility preserving mappings between greedoids are defined. Then I-feasibility preserving mappings, fuzzifying feasibility preserving mappings, and (I,I)-fuzzy feasibility preserving mappings are given as generalizations of feasibility preserving mappings. We study the relations among greedoids, I-greedoids, fuzzifying greedoids, and (I,I)-fuzzy greedoids from a categorical point of view. [ABSTRACT FROM AUTHOR]