Creation the Overlapping Ordinary Sets by Complementary Approach

• Authors

• . .
• Overlapping Ordinary Sets, Harmonic and non-harmonic sets, Overlap operation, Overlap relation, Overlap function, Overlap system, Overlap diagram.
• The present paper reports definition of overlapping ordinary sets and represent how to nest only one set, comparable sets, and disjoint sets by using basic concepts of the set theory, in especially absolute complement operations.Â Â Â  It found that the most useful entrance to develop a definition of overlapping ordinary sets is reasonable definition of incomparable sets.Â Â  Overlap relation, Overlap operation and Overlap function was studied in a manner featured.Â Â Â  It is shown that the double complement with different types of complement operations (Absolute, Relative), are not necessary equal to the same results.Â  In addition to the paper studied separable overlapping ordinary sets.

Â

Â

• References

1. [1] ZADEH, L.A., "Fuzzy sets". Information and Control 8 (3) 338â€“353, 1965.( references).

[2] JUDITH ROITMAN "INTERODUCTION TO MODERN SET THEORY",AWILEY-INTERSIENCE SERIES OF TEXTS, MONOGRAPHS&TRACTS, ISBN 0-471-63519-7,p.5,1990.( references).

[3] Trotter, William T." Combinatorics Partially Ordered Sets: Dimension Theory", Johns Hopkins Univ,p.3 1992, inpress .

[4] J. Douglas Carroll and James E. Corter, â€œA Graph-Theoretic Method for organizing overlapping clusters into Multiple Trees, or Extended Treesâ€. Journal of classification, 12: 283-313,p.8,1995. ( references).

[5] HALMOS, P. R., "Naive Set Theory" .Van Nostrand, New York, p.17, 1960. ( references)

[6] Devlin, Keith J. Fundamentals of Contemporary Set Theory.p.6. Universitext.Springer. ISBN 0-387-90441-7. Zb l 0407. 04003,1979 .( references).

[7] ROBERT R.STOLI "SET THEORY AND LOGIC", Dover Publication, IncNewYork, ISBN-13:978-0-486-63829-4,p.30,1979 .( references) .

[8] S. Q. XIE, G. G. WANG and Y. LIU.,"Nesting of two dimensional irregular parts: an integrated approach" p.1, International Journal of Computer Integrated Manufacturing.Vol.20, No.8, December, 741-756, 2007.Education and Counseling 53, 309â€“313.