Abstract
In this chapter we first generalize convex sets by introducing the concept of starshaped sets, which is “one-step” more general than the concept of convex sets. Then we make further steps generalizing the starshaped sets to obtain path-connected sets, Φ-convex sets and some other types of generalized convex sets. The generalized convex sets will serve as a basis for defining generalized concave and convex functions, which will be introduced in the third chapter. We also pay attention to the separability of starshaped sets.
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© 2002 Springer Science+Business Media New York
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Ramík, J., Vlach, M. (2002). Generalized Convex Sets. In: Generalized Concavity in Fuzzy Optimization and Decision Analysis. International Series in Operations Research & Management Science, vol 41. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1485-5_2
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DOI: https://doi.org/10.1007/978-1-4615-1485-5_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5577-9
Online ISBN: 978-1-4615-1485-5
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