The following scheme summarizes the different families introduced
in this chapter and the connections between them. Family of
interval orders f Row-homogeneous Column-homogeneous Family of
family of interval semi orders family of interval orders orders
Homogeneous family of i nterva 1 orders Homogeneous family of semi
orders Family of weak orders 85 5.13. EXAMPLES We let to the reader
the verification of the following assertions. Example 1 is a family
of interval orders which is neither row-homogeneous nor
column-homogeneous. Example 2 is a column-homogeneous family of
interval orders which is not row-homogeneous but where each
interval order is a semiorder. Example 3 is an homogeneous family
of interval orders which are not semiorders. Example 4 is an
homogeneous family of semi orders . . 8 ~ __ --,b ~---i>---_ C a
.2 d c Example Example 2 .8 .6 c .5 a 0 a d Example 3 Example 4
5.14. REFERENCES DOIGNON. J.-P ** Generalizations of interval
orders. in E. Degreef and J. Van Buggenhaut (eds). T~ndS in
MathematiaaZ PsyahoZogy. Elsevier Science Publishers B.V.
(North-Holland), Amsterdam, 1984. FISHBURN. P.C., Intransitive
indifference with unequal indifference intervals. J. Math. Psyaho.~
7 (1970) 144-149. FISHBURN. P.C., Binary choice probabilities: on
the varieties of stochastic transitivity. J. Math. Psyaho.~ 10
(1973) 327-352.
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