The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank functions for a given closure operator, which determine bounds on the entropy of that operator. This yields new axioms for matroids based on their closure operators...

The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank functions for a given closure operator, which determine bounds on the entropy of that operator. This yields new axioms for matroids based on their closure operators...

Let M be a matroid. When M is 2-connected, Cunningham and Edmonds gave a tree decomposition of M that displays all of its 2-separations. This result was extended by Oxley, Semple, and Whittle, who showed that, when M is 3-connected, there is a corresponding tree decomposition that displays all non-trivial 3-separations of M up to a certain natural equivalence. This equivalence is based on the n...

By fuzzifying the number of occurrences of an element of a multiset, we obtain a new fuzzy structure; similarly, by fuzzifying the number of occurrences of an element of a hybrid set, we obtain another new fuzzy structure. The aim of the present work is twofold: to provide a concise definition of these new fuzzy structures and their properties and to apply them in natural computing. More specif...

D. Molodtsov (1999) introduced the concept of a soft set as a new approach for modeling uncertainties. The aim of this work is to define special kinds of soft sets, namely soft, L-fuzzifying soft, L-soft, and L-fuzzy soft neighborhood sets and to use them in order to give an alternative characterization of categories related to topology: crisp topological, L-topological, L-fuzzifying topologica...