The Hasse diagram of a semiorder. Two items are comparable when their vertical coordinates differ by at least one unit (the spacing between solid blue lines).
In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are compared by their scores and where scores within a given margin of error are deemed incomparable. Semiorders were introduced and applied in mathematical psychology by Duncan Luce (1956) as a model of human preference. They generalize strict weak orderings, in which items with equal scores may be tied but there is no margin of error. They are a special case of partial orders and of interval orders, and can be characterized among the partial orders by additional axioms, or by two forbidden four-item suborders.
In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores...
other. In mathematics, preferences may be modeled as a weak ordering or a semiorder, two different types of binary relation. One specific variation of weak...
function between two partial orders. Semilattice – Partial order with joins Semiorder – Numerical ordering with a margin of error Szpilrajn extension theorem...
number Narayana polynomials Schröder number Schröder–Hipparchus number Semiorder Tamari lattice Wedderburn–Etherington number Wigner's semicircle law Koshy...
strict partial order. R {\displaystyle R} is irreflexive and satisfies semiorder property 1 (there do not exist two mutually incomparable two-point linear...
fixed threshold before they may be compared leads to the concept of a semiorder, while allowing the threshold to vary on a per-item basis produces an...
Because of this possibility, rankings of this type are better modeled as semiorders than as weak orderings. Suppose throughout that < {\displaystyle \,<\...
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