在有界雙容錯大小（Bounded bitolerance order）中，我們利用不同的限制條件可以得到一些不同的有界雙容錯大小族群。
在論文中，整個有界雙容錯大小階層，我們界定了其中某部份族群的差別，並找出一些不同大小來區別其它的族群。

An ordered set P = (V,≺) is a bounded bitolerance order if it has a representation as follows. Each v ∈ V is assigned a real interval Iv = [L(v),R(v)] and two additional tolerant points p(v), q(v) ∈ Iv satisfying p(v) L(v) and q(v) R(v) so that x ≺ y ⇐⇒ R(x) < p(y) and q(x) < L(y). The collection where I ={ Iv | v ∈ V }, p = {p(v) | v ∈ V } and q = {q(v) | v ∈ V } is called a bounded bitolerance representation of P.
There are some classes of bounded bitolerance orders with different restriction.
We find some orders of difference between each of different classes.

Chapter 1 Introduction……………..……………………………...1
1.1 Ordered Sets…………………..……………………………. 1
1.1.1 Interval Orders……………..………………………………..2
1.2 Bounded Bitolerance Orders….………………………….….2
1.2.1 Three Types of Restrictions………………………….......….4
1.3 Trapezoid orders………………………………..……...…….6
Chapter 2……………………………………………………………..12
2.1 unit tolerance order and unit tot. bnd bitolerance order……..12
2.2 unit interval , unit tot.bnd.tolerance , uint pt-core bitolerance oredr…………………………………………………………15
Chapter 3………………………………………………………………18
3.1 N1 , N2 , N3 order……………………………………………19
3.2 A1 , A2 , A3 , H order…………………………………………..22
Chapter 4 Conclusion and Future Work………………………….30
Appendix……………………………………………………………….31
Referencd……………………………………………………………...35

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