Title :
Relationships among sets, relations, lattices, and Boolean algebra
Author :
Lee, Edward T. ; Yang, Chih-Ling
Author_Institution :
Dept. of Electr. & Comput. Eng., Florida Int. Univ., Miami, FL, USA
Abstract :
Conventionally, Boolean algebra is introduced by means of the postulate-oriented approach. In the present work, the set-theory-oriented approach is developed. It is shown that the relationships among sets, relations, lattices, and Boolean algebra form a distributed but not complemented lattice. Illustrative examples are shown with Hasse diagrams. The results may have applications to chromosome classification, image sciences, fuzzy languages, fuzzy neural networks, and a theory of usuality
Keywords :
Boolean algebra; fuzzy logic; set theory; Boolean algebra; Hasse diagrams; chromosome classification; fuzzy languages; fuzzy neural networks; image sciences; postulate-oriented approach; set-theory-oriented; usuality; Biological cells; Boolean algebra; Educational institutions; Fuzzy logic; Fuzzy neural networks; Lattices; Set theory; Upper bound;
Conference_Titel :
Southeastcon '91., IEEE Proceedings of
Conference_Location :
Williamsburg, VA
Print_ISBN :
0-7803-0033-5
DOI :
10.1109/SECON.1991.147926
