Title :
On lattice-isomorphism between fuzzy equivalence relations and fuzzy partitions
Author :
Schmechel, Norbert
Author_Institution :
Dept. of Comput. Sci. 1, Dortmund Univ., Germany
Abstract :
We present our results concerning the fact that fuzzy equivalence relations and fuzzy partitions together with appropriate partial orderings form lattices and that these lattices are isomorphic. In our investigation we apply the results of H. Thiele, N. Schmechel (1995) concerning the definitions of fuzzy equivalence relations, fuzzy partitions and the existence of a bijection between them. We show that this bijection is a lattice isomorphism
Keywords :
equivalence classes; fuzzy set theory; lattice theory; pattern recognition; bijection; cluster analysis; fuzzy equivalence relations; fuzzy partitions; lattice isomorphism; lattice-isomorphism; partial orderings; Computer science; Fuzzy set theory; Fuzzy sets; Lattices;
Conference_Titel :
Multiple-Valued Logic, 1995. Proceedings., 25th International Symposium on
Conference_Location :
Bloomington, IN
Print_ISBN :
0-8186-7118-1
DOI :
10.1109/ISMVL.1995.513523
