− Spatial data mining knows a more and more important interest. Fundamental processes of spatial data mining are in particular clustering and structural patterns detection. These processes are influenced strongly by the concept of proximity or neighborhood. This paper introduces some structures to the construction of a spatial data mining integrating fuzzy structural primitives and propose to o...

The problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations and their applications. Several variations of the acclaimed Szpilrajn’s theorem have been provided, inclusive of the case when some order conditions between elements are imposed on the extension. We extend the analysis of that topic by Alcantud to the fuzzy case....

Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous archimedean t-norm are given. The first one aggregates the transitive closure R of R with a (maximal) T -transitive relation B contained in R. The second one modifies the values of R or B to better fit them with the ones of R.

We introduce the subcategory VRelR(H) of VRel(H) consisting of H-fuzzy reflexive relational space on sets and we study structures of VRelR(H) in a viewpoint of the topological universe introduced by L.D.Nel. We show that VRelPO(H) of VRelR(H). We show that VRelPR(H) [resp. VRelP (H) and VRelE(H)] is a topological universe over Set. Mathematics Subject Classification: 04A72, 18B10, 18D15

The robotic rehabilitation devices can undertake the difficult physical therapy tasks and provide improved treatment procedures for post stroke patients. During passive working mode, the speed of the exercise needs to be controlled continuously by the robot to avoid excessive injurious torques. We designed a fuzzy controller for a hand rehabilitation robot to adjust the exercise speed by consid...

Let R ∈ Cm×m and S ∈ Cn×n be nontrivial unitary involutions, i.e., R = R = R−1 = ±Im and S = S = S−1 = ±In. A ∈ Cm×n is said to be a generalized reflexive (anti-reflexive) matrix if RAS = A (RAS = −A). Let ρ be the set of m × n generalized reflexive (anti-reflexive) matrices. Given X ∈ Cn×p, Z ∈ Cm×p, Y ∈ Cm×q and W ∈ Cn×q, we characterize the matrices A in ρ that minimize ‖AX−Z‖2+‖Y HA−WH‖2, a...

Fuzzy operators are an essential tool in many fields and the operation of composition is often needed. In general, composition is not a commutative operation. However, it is very useful to have operators for which the order of composition does not affect the result. In this paper, we analyze when permutability appears. That is, when the order of application of the operators does not change the ...

This paper provides computational algorithms for a Korean reflexive caki, for which both sentence-bound and long-distance readings are possible. Its analyses are based on Chierichia's theory in Categorial Grammar, and a CCG-like system is introduced for the implementation. In this system, we can get both readings of caki with the same resolution mechanisms, while the difference is where the ref...