Abstract
A Ruspini partition is a finite family of fuzzy sets {f 1, ..., f n }, f i : [0, 1] →[0, 1], such that \(\sum^n_{i=1} f_i(x) = 1\) 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.
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Codara, P., D’Antona, O.M., Marra, V. (2007). Best Approximation of Ruspini Partitions in Gödel Logic. In: Mellouli, K. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2007. Lecture Notes in Computer Science(), vol 4724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75256-1_17
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DOI: https://doi.org/10.1007/978-3-540-75256-1_17
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