‎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.

We investigate notions of randomness in the space C[2] of nonempty closed subsets of {0, 1}. A probability measure is given and a version of the Martin-Löf Test for randomness is defined. Π 2 random closed sets exist but there are no random Π 1 closed sets. It is shown that a random closed set is perfect, has measure 0, and has no computable elements. A closed subset of 2 may be defined as the ...

one of the models that can be used to study the relationship between boolean random sets and explanatory variables is growth regression model which is defined by generalization of boolean model and permitting its grains distribution to be dependent on the values of explanatory variables. this model can be used in the study of behavior of boolean random sets when their coverage regions variation...

It is known that the box dimension of any Martin-Löf random closed set of {0, 1}N is log2( 43 ). Barmpalias et al. [Journal of Logic and Computation, Vol. 17, No. 6 (2007)] gave one method of producing such random closed sets and then computed the box dimension, and posed several questions regarding other methods of construction. We outline a method using random recursive constructions for comp...

The members of Martin-Löf random closed sets under a distribution studied by Barmpalias et al. are exactly the infinite paths through Martin-Löf random Galton-Watson trees with survival parameter 2 3 . To be such a member, a sufficient condition is to have effective Hausdorff dimension strictly greater than γ = log2 3 2 , and a necessary condition is to have effective Hausdorff dimension greate...

The translative intersection formula of integral geometry yields an expression for the mean Euler characteristic a stationary random closed set intersected with fixed observation window. We formulate this result in setting sets positive reach and using flag measures which yield curvature as marginals. As application, we consider excursion fields $C^{1,1}$ realizations, particular, Gaussian fiel...