Geodesic
Principal Intuitionistic Fuzzy Ideals and Filters on a Lattice
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 75-88.

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In this paper, we generalize the notion of principal ideal (resp. filter) on a lattice to the setting of intuitionistic fuzzy sets and investigate their various characterizations and properties. More specifically, we show that any principal intuitionistic fuzzy ideal (resp. filter) coincides with an intuitionistic fuzzy down-set (resp. up-set) generated by an intuitionistic fuzzy singleton. Afterwards, for a given intuitionistic fuzzy set, we introduce two intuitionistic fuzzy sets: its intuitionistic fuzzy down-set and up-set, and we investigate their interesting properties.
Keywords: lattice, intuitionistic fuzzy set, principal intuitionistic fuzzy ideal, principal intuitionistic fuzzy filter 
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Boudaoud, Sarra; Zedam, Lemnaouar; Milles, Soheyb. Principal Intuitionistic Fuzzy Ideals and Filters on a Lattice. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 1, pp. 75-88. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_1_a6/

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