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A review of the relationships between implication, negation and aggregation functions from the point of view of material implication
journal contribution
posted on 2016-02-01, 00:00 authored by A Pradera, Gleb BeliakovGleb Beliakov, H Bustince, B De BaetsImplication and aggregation functions play important complementary roles in the field of fuzzy logic. Both have been intensively investigated since the early 1980s, revealing a tight relationship between them. However, the main results regarding this relationship, published by Fodor and Demirli DeBaets in the 1990s, have been poorly disseminated and are nowadays somewhat obsolete due to the subsequent advances in the field. The present paper deals with the translation of the classical logical equivalence p → q = ¬pvq, often called material implication, to the fuzzy framework, which establishes a one-to-one correspondence between implication functions and disjunctors (the class of aggregation functions that extend the Boolean disjunction to the unit interval). The construction of implication functions from disjunctors via negation functions, and vice versa, is reviewed, stressing the properties of disjunctors (respectively, implication functions) that ensure certain properties of implication functions (disjunctors).
History
Journal
Information sciencesVolume
329Season
Special issue on discovery sciencePagination
357 - 380Publisher
ElsevierLocation
Amsterdam, The NetherlandsPublisher DOI
ISSN
0020-0255Language
engPublication classification
C Journal article; C1 Refereed article in a scholarly journalCopyright notice
2015, ElsevierUsage metrics
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No categories selectedKeywords
Science & TechnologyTechnologyComputer Science, Information SystemsComputer ScienceMaterial implicationImplication functionNegation functionAggregation functionDisjunctorImplication and aggregation functions propertiesPSEUDO-T-NORMSIMPLICATION OPERATORSRESIDUAL IMPLICATIONSFUZZY IMPLICATIONSCOMPLETE LATTICER-IMPLICATIONSUNINORMSDISTRIBUTIVITYCONSTRUCTIONOVERLAP
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