1. The Relation Between Elevation of Equivalence Relation, Elevation of Distance, Hypertopology, Quotient Topology and Topological Entropy.

2. The equivalence relation is the basic Concept of the rough set theory.

3. The equivalence relation could be applied to the performance evaluation of ALOHA-type system.

4. In allusion to the equivalence relation and priority relation of the condition attributes, the method of data mining of rough set is analysized to treat with the attributes with priority.

5. By means of analyzing the equivalence relation of reversible gate logic network to permutation group, the reversible gate network cascade was converted into the cycle of symmetric group.

6. Fuzzy cluster based on equivalence relation is one of the methods of cluster analysis.

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7. It is important that the equivalence relation (face, edges) of packing boxes is studied.

8. The equivalence relation is established by the constraint implied by passing an instance of C in the method call from B to A.

9. Recall that an equivalence relation in a set is a reflexive, symmetric and transitive relation.

10. Bisimulation is often chosen as the equivalence relation in equivalence checking.

11. It also makes use of the equivalence relation between keywords. this can reflect the relation between keywords, so it can search the Synonyms.

12. Also, the reduction on the scheme is achieved by defining an equivalence relation to adversary structure. Analysis shows that reduced scheme still preserves the properties of original one.

13. Unfortunately, all the transitive signature schemes available are undirected ones and can only be used in the case of equivalence relation.

14. This irreflexivity can be used to set up an equivalence relation—that is, for Key s a and b , if comp(a, b) is false and comp(b, a) is false , then a and b must be equivalent.

15. Moreover, the modified rough entropy and the fuzzy entropy based on equivalence relation is extended to the generalized modified rough entropy and the generalized fuzzy entropy.

16. The course of cluster analysis is a course for compartmentalizing. And equivalence relation is the base of compartmentalizing. The paper does construct equivalence relation by comparability.

17. In this paper, the notion of key feature is defined based on the consistency of a decision system, then the equivalence relation between the set of all key features and the feature core is discovered.

18. Based on the method of similarity measure, it proves that the equivalence relation of rough set can be transformed into fuzzy equivalence matrix comp.

19. Based on the method of similarity measure, it proves that the equivalence relation of rough set can be transformed into fuzzy equivalence matrix completely.