The research in the field of the so called Fuzzy Mathematics can be conditionally devided into two mainstreams: the first one emphasizes on the study of different fuzzy structures (topological, algebraic, analytical, etc) on an ordinary set X, while for the second one the starting point are L-valued sets, that is a set equipped with some L-valued equality E : X × X → L (L being a lattice usuall...

We define a class of L-convex-concave subsets of RP , where L is a projective line in RP . These are sets whose sections by any plane containing L are convex and concavely depend on this plane. We prove a version of Arnold’s conjecture for these sets, namely we prove that each such set contains a line.

We define a class of L-convex-concave subsets of RP 3 , where L is a projective line in RP 3. These are sets whose sections by any plane containing L are convex and concavely depend on this plane. We prove a version of Arnold hypothesis for these sets, namely we prove that each such set contains a line.

Previous work on counting maximal independent sets for paths and certain 2-dimensional grids is extended in two directions: 3-dimensional grid graphs are included and, for some/any l ∈ N, maximal distance-l independent (or simply: maximal l-independent) sets are counted for some grids. The transfer matrix method has been adapted and successfully applied.

We continue to develop a construction of an L-fuzzy valued measure by extending a measure defined on a σalgebra of crisp sets to an L-fuzzy valued measure defined on a TM-tribe in the case when operations with L-sets and L-fuzzy numbers are defined by using the minimum triangular norm TM . We introduce an L-fuzzy valued integral over an L-set with respect to an L-fuzzy valued measure, consider ...

R. Shore proved that every recursively enumerable (r.e.) set can be split into two (disjoint) nowhere simple sets. Splitting theorems play an important role in recursion theory since they provide information about the lattice E of all r.e. sets. Nowhere simple sets were further studied by D. Miller and J. Remmel, and we generalize some of their results. We characterize r.e. sets which can be sp...