Abstract
In this chapter we define partial interval order and partial semiorder structures. In order to ensure terminology coherence we require the following properties:
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(i)
partial structures must coincide with corresponding total structures when R = ø;
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(ii)
partial structures must coincide with a quasi order (partial preorder) structure when property I c I is satisfied and with a partial order structure when I = {(a,a), ∀ a ∈ A},
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(iii)
partial structures must be compatible with a numerical representation.
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References
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Roubens, M. and Vincke, P., A definition of partial interval orders, in E. Degreef and J. Van Buggenhout (Eds), Trends in Mathematical Psychology, Elsevier Science Publishers B.V. (North-Holland), Amsterdam, 1984, 309–315.
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Roubens, M., Vincke, P. (1985). Two New Preference Structures. In: Preference Modelling. Lecture Notes in Economics and Mathematical Systems, vol 250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46550-5_4
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DOI: https://doi.org/10.1007/978-3-642-46550-5_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15685-7
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