Best Approximation of Ruspini Partitions in Gödel Logic
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چکیده
A Ruspini partition is a finite family of fuzzy sets {f1, . . . , fn}, fi : [0, 1] → [0, 1], such that ∑ n i=1 fi(x) = 1 for all x ∈ [0, 1]. We analyze such partitions in the language of Gödel 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 Gödel logic.
منابع مشابه
An Analysis of Ruspini Partitions in Gödel Logic
By a Ruspini partition we mean a finite family of fuzzy sets {f1, . . . , fn}, fi : [0, 1] → [0, 1], such that ∑n i=1 fi(x) = 1 for all x ∈ [0, 1], where [0, 1] denotes the real unit interval. We analyze such partitions in the language of Gödel logic. Our first main result identifies the precise degree to which the Ruspini condition is expressible in this language, and yields inter alia a const...
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تاریخ انتشار 2007