Abstract
After defining the complementary relation R of a binary relation R on a set X, this paper constructs the binary relation C (‘is a complementary property of’) on the set P of nine well known elementary properties that R might possess. It deduces some theorems about C; especially that symmetry is the only one of these possible properties of R on X that is possessed by C on P. The set P may be enlarged to contain other elementary properties of R on X without changing the truth of these theorems, when the symbols of sets are properly modified. Finally, the paper discusses the desirability of a general theory of elementary properties of binary relations for the further development of statistical decision theory.
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Burros, R.H. Complementary properties of binary relations. Theor Decis 6, 177–183 (1975). https://doi.org/10.1007/BF00169105
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DOI: https://doi.org/10.1007/BF00169105