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.


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


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