this paper continues the study of the connection between hyper- groups and fuzzy sets, investigating the length of the sequence of join spaces associated with a hypergroup. the classes of complete hypergroups and of 1-hypergroups are considered and analyzed in this context. finally, we give a method to construct a nite hypergroup with the strong fuzzy grade equal to a given natural number

in this paper we determine the sequences of join spaces and atanassov's intuitionistic fuzzy sets associated with all i.p.s. hypergroups of order less than or equal to 6, focusing on the calculation of their lengths.

In two previous papers we introduced the notion of an Affine Klingenberg space A and presented a geometric description of its free subspaces. Presently, we consider the operations of join, intersection and parallelism on the free subspaces of A. As in the case of ordinary affine spaces, we obtain the Parallel Postulate. The situation with join and intersection is not that straightforward. In pa...

Let 2 be a finite set of join dependencies (JDs), multivalued dependencies (MVDs) and functional dependencies (IDS). To test whether .% implies an MVD X -+ Y or an PD X -+ A, the procedure in [ 31 first generates the dependency basis DEP( X) of X with respect to 2. Then, X + Y if and only if Y is the union of some elements in DEP( X) , and X -+ A if and only if A E DEP( X), and there is an PD V...

Bandelt, H.-J. and H.M. Mulder, Pseudo-median graphs are join spaces, Discrete Mathematics 109 (1992) 13-26. Median graphs are known to share a number of geometrica! properties with Euclidean space, as is testified by the fact that median graphs ale (c!osed) join spaces-the segments of the associated join space being the geodesic intervals of the graph. As is shown in this paper the median join...

We propose a new multi-way spatial join algorithm called M-way R-tree join which synchronously traverses M R-trees. The Mway R-tree join can be considered as a generalization of the 2-way R-tree join. Although a generalization of the 2-way R-tree join has recently been studied, it did not properly take into account the optimization techniques of the original algorithm. Here, we extend these opt...

Join is an operation that is frequently used and the most expensive in processing database queries. In this paper we propose a new efficient join algorithm(called the MLGFJoin) for relations indexed by the tnul~ilevrl grirlfile(MLGF), a multidimensional dynamic hashed file organization. The MLGF-Join uses the domain space partition maintained in the directory of the MLGF. The MLGF-Join can proc...