Paper Info
Title
The non-contradiction principle related to natural negations of fuzzy implication functions.
Abstract
The translation of the classical Non-Contradiction (NC) principle, as well as its dual law: the Excluded-Middle (EM) principle, to the framework of fuzzy logic leads to a well-known functional equation involving appropriate aggregation and negation functions. When the involved negation is the natural negation of a fuzzy implication function, the NC principle becomes specially important because then it is a necessary condition for the fulfillment of the Modus Ponens inequality, as well as for the residuation property for residuated implications. In this paper, the functional equation corresponding to the NC principle is deeply studied in the case when both, the aggregation function and the fuzzy negation, are as general as possible. Moreover, the results are applied to the case when the fuzzy negation is the natural negation of a fuzzy implication function, extending this study to the most usual classes of fuzzy implication functions.
Year
DOI
Venue
2019
10.1016/j.fss.2018.03.012
Fuzzy Sets and Systems
Keywords
Field
DocType
Non-contradiction,Fuzzy negation,Natural negation,Fuzzy implication function,Aggregation function,Disjunctor,Conjunctor
Discrete mathematics,Modus ponens,Fuzzy implication,Algebra,Negation,Fuzzy logic,Fuzzy negation,Functional equation,Mathematics,Contradiction
Journal
Volume
ISSN
Citations 
359
0165-0114
0
PageRank 
References 
Authors
0.34
18
4
Name
Order
Citations
PageRank
Ana Pradera115916.09
Sebastià Massanet243834.95
Daniel Ruiz-Aguilera334525.56
Joan Torrens4125992.67