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Upper and lower possibilities induced by a multivalued mapping. (English) Zbl 0562.94023
Fuzzy information, knowledge representation and decision analysis, Proc. IFAC Symp., Marseille 1983, IFAC Proc. Ser. 6, 147-152 (1984).
Summary: [For the entire collection see Zbl 0549.00029.]
In a seminal paper [Ann. Math. Stat. 38, 325-339 (1967; Zbl 0168.175)], A. P. Dempster introduced the concepts of upper and lower probabilities by considering a probability space together with a multivalued mapping. In this paper, we study the analogous situation when a possibility space is given and the same multivalued mapping. Then, we get upper and lower possibilities. While an upper possibility is still a possibility, a lower possibility is no longer a possibility usually. These concepts are applied to an approximate reasoning problem which turns out to be a ”possibilistic” version of a classical problem dealt with in decision theory.

94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory)