By Yigal Mesika; Anthony Brahams; Ori Ashkenazy; Menny Lindenfield
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Extra resources for Animated miracles
Zadeh (1971) introduced the notion of quantitative fuzzy semantics, explaining how linguistic terms could be represented as fuzzy sets on universes of discourse, and how a logical combination of linguistic terms could have a numerical counterpart in terms of fuzzy set-theoretic operations. Interestingly enough, these universes of discourse, as exemplified by Zadeh, were basically numerical scales (for attributes like "age", "size"). His "quantitative fuzzy semantics" provides us with a tool for interfacing numbers and symbols: it respects the continuity of the underlying universes of discourse, and the gradedness of concepts when manipulating the symbols.
On the other hand, fuzzy set connectives are used for expressing compound statements. These two topics are fully reviewed in the volume devoted to Fundamentals of Fuzzy Sets of this Handbook series (see the chapter on fuzzy connectives (Fodor and Yager, 1999) and the one on possibility theory (Dubois, Nguyen and Prade, 1999). 1 A Short Course on Possibility Theory Possibility theory (Dubois and Prade, 1988a) is a theoretical framework for modelling uncertainty, where two dual measures, called possibility and necessity, are used in order to model available information.
2 A REFRESHER ON POSSIBILITY THEORY AND FUZZY CONNECTIVES The necessary background for introducing models of approximate and plausible reasoning based on fuzzy sets and possibility theory is twofold. On the one hand, possibility theory is the framework used for representing pieces of information pervaded with imprecision and uncertainty. On the other hand, fuzzy set connectives are used for expressing compound statements. These two topics are fully reviewed in the volume devoted to Fundamentals of Fuzzy Sets of this Handbook series (see the chapter on fuzzy connectives (Fodor and Yager, 1999) and the one on possibility theory (Dubois, Nguyen and Prade, 1999).