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...

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...

We present a wide class of reflexive, precompact, non-compact, Abelian topological groupsG determined by three requirements. They must have the Baire property, satisfy the open refinement condition, and contain no infinite compact subsets. This combination of properties guarantees that all compact subsets of the dual group G are finite. We also show that many (non-reflexive) precompact Abelian ...

Equivalence relations are important in many branches of knowledge and especially in Classification theories and Cluster Analysis since they generate a partition on the universe of discourse and permit to classify their elements and make clusters. In many cases the relation we start with is not an equivalence relation but only a reflexive and symmetric one. A very important family of fuzzy relat...

in the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(p,q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}a_{l}xb_{l}+overset{v} ‎{underset{s=1}{sum}}c_{s}widetilde{x}d_{s}=f$‎. ‎by this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎when the‎ ‎matrix equation is consistent over...

In the present paper‎, ‎we propose an iterative algorithm for‎ ‎solving the generalized $(P,Q)$-reflexive solution of the quaternion matrix‎ ‎equation $overset{u}{underset{l=1}{sum}}A_{l}XB_{l}+overset{v} ‎{underset{s=1}{sum}}C_{s}widetilde{X}D_{s}=F$‎. ‎By this iterative algorithm‎, ‎the solvability of the problem can be determined automatically‎. ‎When the‎ ‎matrix equation is consistent over...

Fuzzy sets are naturally ordered by the subsethood relation A ⊆ B. If we only know which set which fuzzy set is a subset of which – and have no access to the actual values of the corresponding membership functions – can we detect which fuzzy sets are crisp? In this paper, we show that this is indeed possible. We also show that if we start with interval-valued fuzzy sets, then we can similarly d...