Generalized Possibility and Necessity Measures on Fields of Sets
نویسندگان
چکیده
We give a generalization of possibility and necessity measures: their domains are extended towards fields of sets, and their codomains towards arbitrary complete lattices. In this way, these measures can be associated with (Q,≤)-fuzzy sets, where (Q,≤) is at least a poset. An important inconsistency problem, intricately linked with this association, is solved. It is argued that order lies at the basis of a mathematical description of vagueness and linguistic uncertainty. The results obtained here allow us to mathematically represent and manipulate linguistic uncertainty in the presence of incomparability.
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