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oai:riuma.uma.es:10630/317582026-02-03T11:34:02Zcom_10630_2254col_10630_37953

Attribute implications with unknown information based on weak Heyting algebras Cordero-Ortega, Pablo Enciso-García-Oliveros, Manuel Mora, Angel Pérez-Gámez, Francisco Álgebra Simplification logic, a logic for attribute implications, was originally defined for Boolean sets. It was extended to distributive fuzzy sets by using a complete dual Heyting algebra. In this paper, we weaken this restriction in the sense that we prove that it is possible to define a simplification logic on fuzzy sets in which the membership value structure is not necessarily distributive. For this purpose, we replace the structure of the complete dual Heyting algebra by the so-called weak complete dual Heyting algebra. We demonstrate the soundness and completeness of this simplification logic, and provide a characterisation of the operations defining weak complete dual Heyting algebras. 2024-06-26T12:04:01Z 2024-06-26T12:04:01Z 2024-08 journal article Cordero, Pablo, Enciso, Manuel, Mora, Ángel, Pérez-Gámez, Francisco (2024), Attribute implications with unknown information based on weak Heyting algebras, Fuzzy Sets and Systems, Volume 490, 2024, 109026, ISSN 0165-0114 https://hdl.handle.net/10630/31758 10.1016/j.fss.2024.109026 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier