The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

2 Stabilisers of Parabolic Centralisers 6 2.1 Stabiliser Subgroups . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Generators for the Stabiliser of L . . . . . . . . . . . . . . . . 7 2.3 Ordering L and the stabiliser of L-maximal elements . . . . . 9 2.4 Ordering X and closures of elements . . . . . . . . . . . . . . 10 2.5 A matrix representation of St(L) . . . . . . . . . . . . . . . . 1...

In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develo...

We use information theory to study recovering sets RL and strongly cancellative sets CL on different lattices. These sets are special classes of recovering pairs and cancellative sets previously discussed in the papers of Simonyi, Frankl, and Füredi. We mainly focus on the lattices Bn and D k l . Specifically, we find upper bounds and constructions for the sets RBn , CBn , and CDk l .

The paper deals with special types of $L$-ordered sets, $L$-fuzzy complete lattices, and fuzzy directed complete posets.First, a theorem for constructing monotone maps is proved, a characterization for monotone maps on an $L$-fuzzy complete lattice is obtained, and it's proved that if $f$ is a monotone map on an $L$-fuzzy complete lattice $(P;e)$, then the least fixpoint of $f$ is meet of a spe...

We derive new bounds on the periodic (cyclic) total squared correlation (PTSC) of binary antipodal signature sets for any number of signatures K and any signature length L. Optimal designs that achieve the new bounds are then developed for several (K,L) cases. As an example, it is seen that complete (K = L + 2) Gold sets are PTSC optimal, but not, necessarily, Gold subsets of K < L + 2 signatur...

Background: The use of conventional stains including Giemsa, Wright and Leishman have become an essential tool for differential diagnosis of cells in peripheral blood. Aims: The aim of the study was to develop a new combination of Leishman-Giemsa (L&G;) stain for avian blood smears and to compare its efficacy with conventional staining methods. Methods:<...

in this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.