The aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy Cflats, fuzzy alternative-sets and fuzzy i-flats. Moreover, we characterize some peculiar fuzzy matroids via these notions. Finally, we provide a decomposition of fuzzy strong maps.

The aim of this work is to show that (oriented) matroid methods can be applied to many discrete geometries, namely those based on modules over integral (ordered) domains. The trick is to emulate the structure of a vector space within the module, thereby allowing matroid methods to be used as if the module were a vector space. Only those submodules which are “closed under existing divisors,” and...

We prove that for every proper minor-closed class M of Fp-representable matroids, there exists a O(1)-competitive algorithm for the matroid secretary problem on M. This result relies on the extremely powerful matroid minor structure theory being developed by Geelen, Gerards and Whittle. We also note that for asymptotically almost all matroids, the matroid secretary algorithm that selects a rand...

in this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.we also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

in this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. by using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. moreover, we investigate the ...

The class of simplicial complexes representing triangulations and subdivisions of Lawrence polytopes is closed under Alexander duality. This gives a new geometric model for oriented matroid duality.

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets. Alongwith the study of fundamental results of such closed sets, we define and characterize fuzzy weakly compact space and fuzzy weakly closed space.

Matroid theory is a generalization of the idea of linear independence. A matroid M consists of a finite set E (called the ground set) and a collection S of subsets of E satsifying the following conditions: (1) ∅ ∈ S; (2) if I ∈ S, then every subset of I is in S; (3) if I1 and I2 are in S and |I1| < |I2|, then there is an element e of I2 − I1 such that I1 ∪ e is in S. The elements of S are calle...

This sequel to Afzali Borujeni et. al. (2015) considers minors and duals of infinite gammoids. We prove that the class of gammoids defined by digraphs not containing a certain type of substructure, called an outgoing comb, is minor-closed. Also, we prove that finite-rank minors of gammoids are gammoids. Furthermore, the topological gammoids of Carmesin (2014) are proved to coincide, as matroids...

Graphic matroids form one of the most significant classes in matroid theory. When introducing matroids, Whitney concentrated on relations to graphs. The definition of some basic operations like deletion, contraction and direct sum were straightforward generalizations of the respective concepts in graph theory. Most matroid classes, for example those of binary, regular or graphic matroids, are c...