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Construction of some algebras of logics by using intuitionistic fuzzy filters on hoops

Authors :
Hee Sik Kim
Rajab Ali Borzooei
Mona Aaly Kologani
Sun Shin Ahn
Young Bae Jun
Source :
AIMS Mathematics, Vol 6, Iss 11, Pp 11950-11973 (2021)
Publication Year :
2021
Publisher :
American Institute of Mathematical Sciences (AIMS), 2021.

Abstract

In this paper, we define the notions of intuitionistic fuzzy filters and intuitionistic fuzzy implicative (positive implicative, fantastic) filters on hoops. Then we show that all intuitionistic fuzzy filters make a bounded distributive lattice. Also, by using intuitionistic fuzzy filters we introduce a relation on hoops and show that it is a congruence relation, then we prove that the algebraic structure made by it is a hoop. Finally, we investigate the conditions that quotient structure will be different algebras of logics such as Brouwerian semilattice, Heyting algebra and Wajesberg hoop.

Details

ISSN :
24736988
Volume :
6
Database :
OpenAIRE
Journal :
AIMS Mathematics
Accession number :
edsair.doi.dedup.....c2304953365615a45521050226df9b02