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- W1966573642 abstract "Abstract Let P ax , by be the probability of picking the two-dimensional object ax in the set { ax, by }. This paper investigates necessary and/or sufficient conditions for a number of representations for these probabilities: ( f , g , F , K , k , G , u , and v are functions) 1. 1. P ax,by ≤ 1 2 iff f ( a ) + g ( x ) ≤ f ( b ) + g ( y ), 2. 2. P ax , by = F [ f ( a ) + g ( x ), f ( b ) + g ( y )], 3. 3. P ax , by = K { k [ f ( a ) + g ( x )] − k [ f ( b ) + g ( y )]}, 4. 4. P ax , by = K [ u ( a ) v ( x ) − u ( b ) v ( y )], 5. 5. P ax,by = G[(f(a) + g(x)) (f(b) + g(y))] . The results concerning 1, 2, and 3 are essentially trivial consequences of known facts. The results concerning 4 and 5 are new, and amount to representation theorems for these equations. The cases in which k is a convex or concave function in 3 (of which 4 and 5 are special cases) are also analyzed." @default.
- W1966573642 created "2016-06-24" @default.
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- W1966573642 date "1979-04-01" @default.
- W1966573642 modified "2023-09-27" @default.
- W1966573642 title "On a class of probabilistic conjoint measurement models: Some diagnostic properties" @default.
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- W1966573642 doi "https://doi.org/10.1016/0022-2496(79)90013-0" @default.
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