Similarities for crisp and fuzzy probabilistic expert systems. (English) Zbl 1145.68543

Bello, Rafael (ed.) et al., Granular computing: At the junction of rough sets and fuzzy sets. Several papers based on the presentations at the 1st international symposium of fuzzy and rough sets (ISFUROS 2006), Santa Clara, Cuba, December 5–8, 2006. Berlin: Springer (ISBN 978-3-540-76972-9/hbk). Studies in Fuzziness and Soft Computing 224, 23-42 (2008).
Summary: As stressed in [F. Bacchus, “Lp, a logic for representing and reasoning with statistical knowledge”, Comput. Intell. 6, 209–231 (1990)] and [J. Y. Halpern, Artif. Intell. 46, No. 3, 311–350 (1990; Zbl 0723.03007)], an interesting question on philosophy of probability is to assign probabilistic valuations to individual phenomena. In [(*) G. Gerla, Int. J. Intell. Syst. 9, No. 4, 403–409 (1994; Zbl 0942.68720)] such a question was discussed and a solution was proposed. In this chapter we start from the ideas in (*) to sketch a method to design expert systems, probabilistic in nature. Indeed, we assume that the probability that an individual satisfies a property is the percentage of similar individuals satisfying such a property. In turn, we call two individuals sharing the same observable properties “similar”. Such an approach is extended to the case of vague properties. We adopt a formalism arising from formal concept analysis.
For the entire collection see [Zbl 1132.68003].


68T35 Theory of languages and software systems (knowledge-based systems, expert systems, etc.) for artificial intelligence
68T30 Knowledge representation
68T37 Reasoning under uncertainty in the context of artificial intelligence