Algebraic Product Is the Only "And-like" Operation for Which Normalized Intersection Is Associative: A Proof - Connaissances, Incertitudes et Données
Communication Dans Un Congrès Année : 2024

Algebraic Product Is the Only "And-like" Operation for Which Normalized Intersection Is Associative: A Proof

Résumé

For normalized fuzzy sets, intersection is, in general, not normalized. So, if we want to limit ourselves to normalized fuzzy sets, we need to normalize the intersection. It is known that for algebraic product, the normalized intersection is associative, and that for many other ``and''-operations (t-norms), normalized intersection is not associative. In this paper, we prove that algebraic product is the only ``and''-operation for which normalized intersection is associative.
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Dates et versions

hal-04436177 , version 1 (03-02-2024)

Identifiants

Citer

Thierry Denœux, Vladik Kreinovich. Algebraic Product Is the Only "And-like" Operation for Which Normalized Intersection Is Associative: A Proof. Fifth International Conference on Artificial Intelligence and Computational Intelligence (AICI 2024), Jan 2024, Hanoi (Vietnam), Vietnam. pp.47-53, ⟨10.1007/978-3-031-63929-6_6⟩. ⟨hal-04436177⟩
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