Ruspini partition is a finite family of fuzzy sets {f 1, ..., f n }, f i : [0,1] →[0,1], such that 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.
Best Approximation of Ruspini Partitions in Gödel Logic / P. Codara, O.M. D'Antona, V. Marra - In: Symbolic and quantitative approaches to reasoning with uncertainty / [a cura di] K. Mellouli. - Berlin : Springer, 2007. - ISBN 978-3-540-75255-4. - pp. 161-172 [10.1007/978-3-540-75256-1_17]
Best Approximation of Ruspini Partitions in Gödel Logic
P. CodaraPrimo
;O.M. D'AntonaSecondo
;V. MarraUltimo
2007
Abstract
Ruspini partition is a finite family of fuzzy sets {f 1, ..., f n }, f i : [0,1] →[0,1], such that 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.
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