Study of Two Families of Generalized Yager’s Implications for Describing the Structure of Generalized ( h, e )-Implications

Raquel Fernandez-Peralta, Sebastia Massanet and Arnau Mir
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Raquel Fernandez-Peralta: Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain
Sebastia Massanet: Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain
Arnau Mir: Soft Computing, Image Processing and Aggregation (SCOPIA) Research Group, Department of Mathematics and Computer Science, University of the Balearic Islands, 07122 Palma, Spain

Mathematics, 2021, vol. 9, issue 13, 1-27

Abstract: In this study, we analyze the family of generalized ( h , e ) -implications. We determine when this family fulfills some of the main additional properties of fuzzy implication functions and we obtain a representation theorem that describes the structure of a generalized ( h , e ) -implication in terms of two families of fuzzy implication functions. These two families can be interpreted as particular cases of the ( f , g ) and ( g , f ) -implications, which are two families of fuzzy implication functions that generalize the well-known f and g -generated implications proposed by Yager through a generalization of the internal factors x and 1 x , respectively. The behavior and additional properties of these two families are also studied in detail.

Keywords: fuzzy implication function; generalized ( h , e )-implications; generalized Yager’s implications; characterization; horizontal threshold method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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