Some properties of minimal open sets and maximal open sets are studied in [1, 2]. In this paper, we define dual concepts of them, namely, maximal closed set and minimal closed set. These four types of subsets appear in finite spaces, for example. More generally, minimal open sets and maximal closed sets appear in locally finite spaces such as the digital line. Minimal closed sets and maximal op...

In this paper a new class of sets called  regular generalized  $delta$-closed set (briefly rg$delta$-closed set)is introduced and its properties are studied. Several examples are provided to illustrate the behaviour of these new class of sets.

‎In this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.

Many real phenomena may be modelled as random closed sets in Rd, of different Hausdorff dimensions. The authors have recently revisited the concept of mean geometric densities of random closed sets Θn with Hausdorff dimension n ≤ d with respect to the standard Lebesgue measure on Rd, in terms of expected values of a suitable class of linear functionals (Delta functions à la Dirac). In many real...

The notion of hit-or-miss dependence is introduced to describe spatial dependence of random closed sets, and its closure properties under various set operations are derived. The hit-or-miss dependence is then applied to Boolean germ-grain models to study local interactions within each grain. The dependence comparison results obtained not only show how local interactions of Boolean germ-grain mo...

Many real phenomena may be modeled as random closed sets in R, of different Hausdorff dimensions. In many real applications such as fiber processes, n-facets of random tessellations of dimension n ≤ d in spaces of dimension d ≥ 1, several problems are related to the estimation of such mean densities. In order to face such problems in the general setting of spatially inhomogeneous processes, we ...