A review of the relationships between implication, negation and aggregation functions from the point of view of material implication

Pradera, A., Beliakov, G., Bustince, H. and De Baets, B. 2016, A review of the relationships between implication, negation and aggregation functions from the point of view of material implication, Information sciences, vol. 329, Special issue on discovery science, pp. 357-380, doi: 10.1016/j.ins.2015.09.033.

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Title A review of the relationships between implication, negation and aggregation functions from the point of view of material implication
Author(s) Pradera, A.
Beliakov, G.ORCID iD for Beliakov, G. orcid.org/0000-0002-9841-5292
Bustince, H.
De Baets, B.
Journal name Information sciences
Volume number 329
Season Special issue on discovery science
Start page 357
End page 380
Total pages 24
Publisher Elsevier
Place of publication Amsterdam, The Netherlands
Publication date 2016-02-01
ISSN 0020-0255
Keyword(s) Science & Technology
Technology
Computer Science, Information Systems
Computer Science
Material implication
Implication function
Negation function
Aggregation function
Disjunctor
Implication and aggregation functions properties
PSEUDO-T-NORMS
IMPLICATION OPERATORS
RESIDUAL IMPLICATIONS
FUZZY IMPLICATIONS
COMPLETE LATTICE
R-IMPLICATIONS
UNINORMS
DISTRIBUTIVITY
CONSTRUCTION
OVERLAP
Summary Implication 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).
Language eng
DOI 10.1016/j.ins.2015.09.033
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
01 Mathematical Sciences
08 Information And Computing Sciences
09 Engineering
080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, Elsevier
Persistent URL http://hdl.handle.net/10536/DRO/DU:30081994

Document type: Journal Article
Collection: School of Information Technology
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