Best Approximation of Ruspini Partitions in Goedel Logic

摘要

A Ruspini partition is a finite family of fuzzy sets {f_1,…, f_n}, f_i : [0,1]→ [0,1], such that ∑_i=1~n f_i(x) = 1 for all x ∈ [0,1], We analyze such partitions in the language of Godel logic. Our main result identifies the precise degree to which the Ruspini condition is expressible in this language, and yields inter alia a constructive procedure to axiomatize a given Ruspini partition by a theory in Goedel logic.