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Semiorders. Properties, representations, applications. (English) Zbl 0897.06002
Theory and Decision Library. Series B: Mathematical and Statistical Methods. 36. Dordrecht: Kluwer Academic Publishers. x, 187 p. (1997).
Semiorders are a way of representing approximate scales such as preferences, by such a condition as: $$a$$ is preferred to $$b$$ if $$g(a)>g(b)+q$$. They are related to interval orders and have applications in genetics, seriation, taxonomy, archaeology, psychology, and programming, which are described in this readable and informative book. The structure of semiorders is discussed, aggregation of semiorders, with a theorem analogous to Arrow’s as well as methods similar to those of Borda and Condorcet, and generalizations of the theory.

##### MSC:
 06-02 Research exposition (monographs, survey articles) pertaining to ordered structures 90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming 06A06 Partial orders, general 91B08 Individual preferences 91E99 Mathematical psychology 90C99 Mathematical programming 92D10 Genetics and epigenetics