In this work, we consider matroid theory. After presenting three different (but equivalent) definitions of matroids, we mention some of the most important theorems of such theory. In particular, we note that every matroid has a dual matroid and that a matroid is regular if and only if it is binary and includes no Fano matroid or its dual. We show a connection between this last theorem and octon...

Techniques for using the Monte Carlo method to evaluate fuzzy Riemann integrals and improper fuzzy Riemann integrals are proposed in this paper. Owing to the α-level set of the (improper) fuzzy Riemann integral being the closed interval whose end points are the classical (improper) Riemann integrals, it is possible to invoke the Monte Carlo method to approximate the end points of the α-level cl...

This paper considers the truncation of matroids and geometric lattices. It is shown that the truncated matroid of a representable matroid is again representable. Truncation formulas are given for the coboundary and Möbius polynomial of a geometric lattice and the spectrum polynomial of a matroid, generalizing the truncation formula of the rank generating polynomial of a matroid by Britz. Mathem...

A link between matroid theory and p-branes is discussed. The Schild type action for p-branes and matroid bundle notion provide the two central structures for such a link. We use such a connection to bring the duality concept in matroid theory to p-branes physics. Our analysis may be of particular interest in M-theory and in matroid bundle theory.

A fuzzy ideal on a set X is a non empty collection of subsets of X with heredity property which is also closed under arbitrary union and finite intersections. In this paper, we introduce a weak form of fuzzy ideals namely fuzzy pre-ideals and a way to obtain new fuzzy topologies is presented in this paper. Furthermore some interesting results for fuzzy ideals are generalized to fuzzy pre-ideal.