In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the conv...

This paper studies structural aspects of lattice path matroids, a class of transversal matroids that is closed under taking minors and duals. Among the basic topics treated are direct sums, duals, minors, circuits, and connected flats. One of the main results is a characterization of lattice path matroids in terms of fundamental flats, which are special connected flats from which one can recove...

For a minor-closed class M of matroids, we let h(k) denote the maximum number of elements of a simple rank-k matroid in M. We prove that, if M does not contain all simple rank-2 matroids, then h(k) grows either linearly, quadratically, or exponentially.

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper an intuitionistic fuzzy generalized pre-closed sets and an intuitionistic fuzzy generalized pre-open sets are introduced. Some of its properties are studied. Also we have provided some applications of intuitionistic fuzzy generalized pre-closed sets namely intuitionistic fuzzy pT1/2 space and intuitioni...

In this paper, first a new algorithm for pole assignment of closed-loop multi-variable controllable systems in a prescribed region of the z-plane is presented. Then, robust state feedback controllers are designed by implementing a neural fuzzy system for the placement of closed-loop poles of a controllable system in a prescribed region in the left-hand side of z-plane. A new method based on the...

the main aim of the present study was to examine the effect of field-independent and field-dependent cognitive styles on learning an aiming task in closed and open environments based on fuzzy and classic logics. 60 male students with an age range of 16-17 were assigned to four groups (each group 15 subjects): field-independent with classic approach, field-dependent with classic approach, field-...

This paper studies Lebesgue integral of a fuzzy closed set-valued stochastic process with respect to the time t. Firstly, a progressively measurable fuzzy closed set-valued stochastic process is discussed and an almost everywhere problem in the former Aumann type Lebesgue integral of the level-set process is pointed out. Secondly, a new definition of the Lebesgue integral by decomposable closur...

As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (c...