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Factoring fuzzy transitivity. (English) Zbl 1017.91012

For precise (“nonfuzzy”) weak preference relation its transitivity is equivalent to the transitivity of both its components: asymmetric (strict preference) and symmetric (indifference). The authors examine four different ways in which fuzzy weak preference may be split (factorize) into fuzzy strict preference and fuzzy indeference [cf. e.g., J. C. Bezdek and J. D. Harris, same journal 1, 111-127 (1978; Zbl 0442.68093)], study eight alternative concepts of fuzzy transitivity [cf., e.g., B. Dutta, Math. Soc. Sci. 13, 215-229 (1987; Zbl 0628.90002)] and discuss each of the resulting thirty two “transitivity-factorization” pairs from the point of view of links between the fuzzy transitivity of a fuzzy weak preference relation and that of its two fuzzy factors. Connections with the theory of consumer behavior and with the social choice theory are mentioned.

MSC:

91B02 Fundamental topics (basic mathematics, methodology; applicable to economics in general)
91B08 Individual preferences
91B42 Consumer behavior, demand theory
91B14 Social choice
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References:

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