Open AccessConstruction of some algebras of logics by using intuitionistic fuzzy filters on hoops
Author(s) -
M. Aaly Kologani,
Rajab Ali Borzooei,
Hee Sik Kim,
Young Bae Jun,
Sun Shin Ahn
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021693
Subject(s) - mathematics , semilattice , quotient , relation (database) , algebra over a field , pure mathematics , distributive property , congruence relation , fuzzy logic , algebraic structure , discrete mathematics , computer science , artificial intelligence , data mining , semigroup
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.