The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions
| dc.contributor.author | Pereira Dimuro, Graçaliz | |
| dc.contributor.author | Bedregal, Benjamin | |
| dc.contributor.author | Fernández Fernández, Francisco Javier | |
| dc.contributor.author | Sesma Sara, Mikel | |
| dc.contributor.author | Pintor Borobia, Jesús María | |
| dc.contributor.author | Bustince Sola, Humberto | |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Ingeniaritza | eu |
| dc.contributor.department | Institute of Smart Cities - ISC | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.contributor.department | Ingeniería | es_ES |
| dc.date.accessioned | 2020-01-15T11:54:53Z | |
| dc.date.available | 2021-02-01T00:00:11Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | Overlap and grouping functions are special kinds of non necessarily associative aggregation operators proposed for many applications, mainly when the associativity property is not strongly required. The classes of overlap and grouping functions are richer than the classes of t-norms and t-conorms, respectively, concerning some properties like idempotency, homogeneity, and, mainly, the self-closedness feature with respect to the convex sum and the aggregation by generalized composition of overlap/grouping functions. In previous works, we introduced some classes of fuzzy implications derived by overlap and/or grouping functions, namely, the residual implications R-0-implications, the strong implications (G, N)-implications and the Quantum Logic implications QL-implications, for overlap functions O, grouping functions G and fuzzy negations N. Such implications do not necessarily satisfy certain properties, but only weaker versions of these properties, e.g., the exchange principle. However, in general, such properties are not demanded for many applications. In this paper, we analyze the so-called law of O-Conditionality, O(x, 1(x, y)) <= y, for any fuzzy implication I and overlap function O, and, in particular, for Ro-implications, (G, N)-implications, QL-implications and D-implications derived from tuples (O, G, N), the latter also introduced in this paper. We also study the conditional antecedent boundary condition for such fuzzy implications, since we prove that this property, associated to the left ordering property, is important for the analysis of the O-Conditionality. We show that the use of overlap functions to implement de generalized Modus Ponens, as the scheme enabled by the law of O-Conditionality, provides more generality than the laws of T-conditionality and U-conditionality, for t-norms T and uninorms U, respectively. | en |
| dc.description.sponsorship | This work was partially supported by the Spanish Ministry of Science and Technology under the project TIN2016-77356-P (AEI/FEDER, UE), and by the Brazilian funding agency CNPQ under Processes 305882/2016-3, 481283/2013-7, 306970/2013-9, 232827/2014-1 and 307681/2012-2. | en |
| dc.embargo.lift | 2021-02-01 | |
| dc.embargo.terms | 2021-02-01 | |
| dc.format.extent | 25 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1016/j.ijar.2018.11.006 | |
| dc.identifier.issn | 0888-613X | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/36075 | |
| dc.language.iso | eng | en |
| dc.publisher | Elsevier | en |
| dc.relation.ispartof | International Journal of Approximate Reasoning, 105 (2019) 27-48 | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/ES/1PE/TIN2016-77356-P/ | |
| dc.relation.publisherversion | https://doi.org/10.1016/j.ijar.2018.11.006 | |
| dc.rights | © 2018 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0. | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | Overlap functions | en |
| dc.subject | Grouping functions | en |
| dc.subject | Fuzzy implications | en |
| dc.subject | O-conditionality | en |
| dc.subject | Conditional antecedent boundary condition | en |
| dc.title | The law of O-conditionality for fuzzy implications constructed from overlap and grouping functions | en |
| dc.type | info:eu-repo/semantics/article | |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | |
| dspace.entity.type | Publication | |
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